From b096cb5bc97189b9141e58d69ee45a9458679513 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jo=C3=A3o=20Pedro=20Neto?= Date: Wed, 14 Oct 2020 17:44:34 +0100 Subject: [PATCH] Reorganizing index Updated some old links, removed dead ones, and added new links. Also included a resampling test as an alternative to One-way ANOVA --- GraphicalTools/Venn.Rmd | 161 - GraphicalTools/Venn.html | 216 - GraphicalTools/ggvis.Rmd | 237 - GraphicalTools/ggvis.html | 6754 -------------------- GraphicalTools/googleVis.Rmd | 229 - GraphicalTools/googleVis.html | 5017 --------------- bayes.packages/2d4d_hone_2012.csv | 217 - bayes.packages/index.Rmd | 240 - bayes.packages/index.html | 577 -- bayes.packages/part2.Rmd | 278 - bayes.packages/part2.html | 795 --- bayes.packages/roubik_2002_coffe_yield.csv | 29 - bayes.packages/zelig-manual-bayes.pdf | Bin 291461 -> 0 bytes bootstrap/crop.data.csv | 97 + bootstrap/stat_resampling.Rmd | 88 +- bootstrap/stat_resampling.html | 105 +- caret/caret.Rmd | 246 - caret/caret.html | 506 -- caret/train_u6lujuX_CVtuZ9i.csv | 615 -- index.htm | 142 +- manipulate/manipulate.Rmd | 114 - manipulate/manipulate.html | 320 - 22 files changed, 333 insertions(+), 16650 deletions(-) delete mode 100644 GraphicalTools/Venn.Rmd delete mode 100644 GraphicalTools/Venn.html delete mode 100644 GraphicalTools/ggvis.Rmd delete mode 100644 GraphicalTools/ggvis.html delete mode 100644 GraphicalTools/googleVis.Rmd delete mode 100644 GraphicalTools/googleVis.html delete mode 100644 bayes.packages/2d4d_hone_2012.csv delete mode 100644 bayes.packages/index.Rmd delete mode 100644 bayes.packages/index.html delete mode 100644 bayes.packages/part2.Rmd delete mode 100644 bayes.packages/part2.html delete mode 100644 bayes.packages/roubik_2002_coffe_yield.csv delete mode 100644 bayes.packages/zelig-manual-bayes.pdf create mode 100644 bootstrap/crop.data.csv delete mode 100644 caret/caret.Rmd delete mode 100644 caret/caret.html delete mode 100644 caret/train_u6lujuX_CVtuZ9i.csv delete mode 100644 manipulate/manipulate.Rmd delete mode 100644 manipulate/manipulate.html diff --git a/GraphicalTools/Venn.Rmd b/GraphicalTools/Venn.Rmd deleted file mode 100644 index 6061ddd..0000000 --- a/GraphicalTools/Venn.Rmd +++ /dev/null @@ -1,161 +0,0 @@ ---- -title: "Venn Diagrams" -author: "João Neto" -date: October 2014 -output: - html_document: - toc: true - toc_depth: 3 - fig_width: 6 - fig_height: 6 -cache: yes ---- - -Ref: [http://www.rpubs.com/kaz_yos/venn](http://www.rpubs.com/kaz_yos/venn) - -```{r, message=FALSE} -library(VennDiagram) -``` - -```{r} -grid.newpage() # make new page for plot, venn diagrams add to current plot -venn.plot <- draw.single.venn(area = 5, # size of set - category = "\n\nClass XYZ", - cat.cex = 3, - cat.pos = 0, - cat.dist = -0.20, - cat.col = "white", - lwd = 5, # width of the circle's circumference - lty = "blank", # type of circle's circumference - cex = 2, # size of the area label - label.col = "orange", - fill = "red", - alpha = 0.15 # transparecy - ) -``` - -```{r, eval=FALSE} -# Writing to file -png(filename = "Single_Venn_diagram.png"); -grid.draw(venn.plot); -dev.off(); -``` - - -```{r} -grid.newpage() -venn.plot <- draw.pairwise.venn(area1 = 100, - area2 = 70, - cross.area = 30, - category = c("First", "Second")) -grid.newpage() -# switch off scaling -venn.plot <- draw.pairwise.venn(area1 = 100, - area2 = 70, - cross.area = 30, - category = c("First", "Second"), - scaled = FALSE) -``` - -```{r} -grid.newpage() -## A more complicated diagram Demonstrating external area labels -venn.plot <- draw.pairwise.venn(area1 = 100, - area2 = 70, - cross.area = 68, - category = c("First", "Second"), - fill = c("blue", "red"), - lty = "blank", - cex = 2, - cat.cex = 2, - cat.pos = c(285, 105), - cat.dist = 0.09, - cat.just = list(c(-1, -1), c(1, 1)), - ext.pos = 30, - ext.dist = -0.05, - ext.length = 0.85, - ext.line.lwd = 2, - ext.line.lty = "dashed" - ) -``` - -```{r} -grid.newpage() - -## Demonstrating an Euler diagram -venn.plot <- draw.pairwise.venn(area1 = 100, - area2 = 70, - cross.area = 0, - category = c("First", "Second"), - cat.pos = c(0, 180), - euler.d = TRUE, - sep.dist = 0.03, - rotation.degree = 45 - ) -``` - -```{r} -grid.newpage() -venn.plot <- draw.triple.venn(area1 = 4, - area2 = 3, - area3 = 4, - n12 = 2, - n23 = 2, - n13 = 2, - n123 = 1, - category = c('A', 'B', 'C'), - fill = c('red', 'blue', 'green'), - cat.col = c('red', 'blue', 'green'), - cex = c(1/2,2/2,3/2,4/2,5/2,6/2,7/2), - cat.cex = c(1,2,3), - euler = TRUE, - scaled = FALSE - ) -``` - -```{r} -grid.newpage() -venn.plot <- draw.quintuple.venn( - area1 = 301, - area2 = 321, - area3 = 311, - area4 = 321, - area5 = 301, - n12 = 188, - n13 = 191, - n14 = 184, - n15 = 177, - n23 = 194, - n24 = 197, - n25 = 190, - n34 = 190, - n35 = 173, - n45 = 186, - n123 = 112, - n124 = 108, - n125 = 108, - n134 = 111, - n135 = 104, - n145 = 104, - n234 = 111, - n235 = 107, - n245 = 110, - n345 = 100, - n1234 = 61, - n1235 = 60, - n1245 = 59, - n1345 = 58, - n2345 = 57, - n12345 = 31, - category = c("A", "B", "C", "D", "E"), - fill = c("dodgerblue", "goldenrod1", "darkorange1", "seagreen3", "orchid3"), - cat.col = c("dodgerblue", "goldenrod1", "darkorange1", "seagreen3", "orchid3"), - cat.cex = 2, - margin = 0.05, - cex = c(1.5, 1.5, 1.5, 1.5, 1.5, 1, 0.8, 1, 0.8, 1, 0.8, 1, 0.8, 1, 0.8, - 1, 0.55, 1, 0.55, 1, 0.55, 1, 0.55, 1, 0.55, 1, 1, 1, 1, 1, 1.5), - ind = TRUE - ) -``` - -There is also another package: [venneuler](http://cran.r-project.org/web/packages/venneuler/index.html). \ No newline at end of file diff --git a/GraphicalTools/Venn.html b/GraphicalTools/Venn.html deleted file mode 100644 index f1ddf9e..0000000 --- a/GraphicalTools/Venn.html +++ /dev/null @@ -1,216 +0,0 @@ - - - - - - - - - - - - - - -Venn Diagrams - - - - - - - - - - - - - - - - - - - - -
- - - - - -

Ref: http://www.rpubs.com/kaz_yos/venn

-
library(VennDiagram)
-
## Warning: package 'VennDiagram' was built under R version 3.1.1
-
grid.newpage() # make new page for plot, venn diagrams add to current plot
-venn.plot <- draw.single.venn(area      = 5,           # size of set
-                              category  = "\n\nClass XYZ",
-                              cat.cex   = 3,
-                              cat.pos   = 0,
-                              cat.dist  = -0.20,
-                              cat.col   = "white",
-                              lwd       = 5,           # width of the circle's circumference 
-                              lty       = "blank",     # type of circle's circumference
-                              cex       = 2,           # size of the area label
-                              label.col = "orange",
-                              fill      = "red",
-                              alpha     = 0.15         # transparecy
-                             )
-

plot of chunk unnamed-chunk-2

-
# Writing to file
-png(filename = "Single_Venn_diagram.png");
-grid.draw(venn.plot);
-dev.off();
-
grid.newpage()
-venn.plot <- draw.pairwise.venn(area1      = 100,
-                                area2      = 70,
-                                cross.area = 30,
-                                category   = c("First", "Second"))
-

plot of chunk unnamed-chunk-4

-
grid.newpage()
-# switch off scaling
-venn.plot <- draw.pairwise.venn(area1      = 100,
-                                area2      = 70,
-                                cross.area = 30,
-                                category   = c("First", "Second"),
-                                scaled     = FALSE)
-

plot of chunk unnamed-chunk-4

-
grid.newpage()
-## A more complicated diagram Demonstrating external area labels
-venn.plot <- draw.pairwise.venn(area1           = 100,
-                                area2           = 70,
-                                cross.area      = 68,
-                                category        = c("First", "Second"),
-                                fill            = c("blue", "red"),
-                                lty             = "blank",
-                                cex             = 2,
-                                cat.cex         = 2,
-                                cat.pos         = c(285, 105),
-                                cat.dist        = 0.09,
-                                cat.just        = list(c(-1, -1), c(1, 1)),
-                                ext.pos         = 30,
-                                ext.dist        = -0.05,
-                                ext.length      = 0.85,
-                                ext.line.lwd    = 2,
-                                ext.line.lty    = "dashed"
-                               )
-

plot of chunk unnamed-chunk-5

-
grid.newpage()
-
-## Demonstrating an Euler diagram
-venn.plot <- draw.pairwise.venn(area1           = 100,
-                                area2           = 70,
-                                cross.area      = 0,
-                                category        = c("First", "Second"),
-                                cat.pos         = c(0, 180),
-                                euler.d         = TRUE,
-                                sep.dist        = 0.03,
-                                rotation.degree = 45
-                               )
-

plot of chunk unnamed-chunk-6

-
grid.newpage()
-venn.plot <- draw.triple.venn(area1           = 4,
-                              area2           = 3,
-                              area3           = 4,
-                              n12             = 2,
-                              n23             = 2,
-                              n13             = 2,
-                              n123            = 1,
-                              category        = c('A', 'B', 'C'),
-                              fill            = c('red', 'blue', 'green'),
-                              cat.col         = c('red', 'blue', 'green'),
-                              cex             = c(1/2,2/2,3/2,4/2,5/2,6/2,7/2),
-                              cat.cex         = c(1,2,3),
-                              euler           = TRUE,
-                              scaled          = FALSE
-                             )
-

plot of chunk unnamed-chunk-7

-
grid.newpage()
-venn.plot <- draw.quintuple.venn(
-  area1 = 301,
-    area2 = 321,
-    area3 = 311,
-    area4 = 321,
-    area5 = 301,
-    n12 = 188,
-    n13 = 191,
-    n14 = 184,
-    n15 = 177,
-    n23 = 194,
-    n24 = 197,
-    n25 = 190,
-    n34 = 190,
-    n35 = 173,
-    n45 = 186,
-    n123 = 112,
-    n124 = 108,
-    n125 = 108,
-    n134 = 111,
-    n135 = 104,
-    n145 = 104,
-    n234 = 111,
-    n235 = 107,
-    n245 = 110,
-    n345 = 100,
-    n1234 = 61,
-    n1235 = 60,
-    n1245 = 59,
-    n1345 = 58,
-    n2345 = 57,
-    n12345 = 31,
-    category = c("A", "B", "C", "D", "E"),
-    fill = c("dodgerblue", "goldenrod1", "darkorange1", "seagreen3", "orchid3"),
-    cat.col = c("dodgerblue", "goldenrod1", "darkorange1", "seagreen3", "orchid3"),
-    cat.cex = 2,
-    margin = 0.05,
-    cex = c(1.5, 1.5, 1.5, 1.5, 1.5, 1, 0.8, 1, 0.8, 1, 0.8, 1, 0.8, 1, 0.8, 
-    1, 0.55, 1, 0.55, 1, 0.55, 1, 0.55, 1, 0.55, 1, 1, 1, 1, 1, 1.5),
-    ind = TRUE
-    )
-

plot of chunk unnamed-chunk-8

-

There is also another package: venneuler.

- - -
- - - - - - - - diff --git a/GraphicalTools/ggvis.Rmd b/GraphicalTools/ggvis.Rmd deleted file mode 100644 index 8b9e450..0000000 --- a/GraphicalTools/ggvis.Rmd +++ /dev/null @@ -1,237 +0,0 @@ ---- -title: "ggvis" -author: "João Neto" -date: October 2014 -output: - html_document: - toc: true - toc_depth: 3 - fig_width: 6 - fig_height: 6 -cache: yes ---- - -Refs: - -+ [http://cran.r-project.org/web/packages/ggvis/vignettes/overview.html](http://cran.r-project.org/web/packages/ggvis/vignettes/overview.html) - - -> package ggvis is used to turn a dataset into a visualisation, setting up default mappings between variables in the dataset and visual properties. It uses a syntax similar in spirit to ggplot2 and dplyr. - -> The goal is to combine the best of R (e.g. every modelling function you can imagine) and the best of the web (everyone has a web browser). Data manipulation and transformation are done in R, and the graphics are rendered in a web browser, using Vega [ref.(http://cran.r-project.org/web/packages/ggvis/vignettes/overview.html) - -```{r, warning=FALSE, message=FALSE} -library(ggvis) -library(dplyr) -``` - -Several examples: - -```{r} -head(mtcars) -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points(size := 25, shape := "diamond", stroke := "red", fill := NA) -mtcars %>% - ggvis(~mpg, ~disp, size = ~vs) %>% - layer_points() -mtcars %>% - ggvis(~mpg, ~disp, size = ~vs, opacity := 0.4) %>% - layer_points() -``` - -### Axis - -```{r} -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - add_axis("x", title = "Weight (lb/1000)", title_offset = 50, orient = "top") %>% - add_axis("y", title = "Miles/(US) gallon", subdivide = 2, values = seq(10,34,by=2)) - -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - add_axis("x", title = "") %>% - add_axis("x", title = "Weight (lb/1000)", offset = 60, grid = FALSE) %>% - hide_axis("y") - -# For axes, you can set the properties of the ticks (or majorTicks and minorTicks separately), the labels and axis. -mtcars %>% ggvis(~wt, ~mpg) %>% - layer_points() %>% - add_axis("x", properties = axis_props( - axis = list(stroke = "red", strokeWidth = 3), - grid = list(stroke = "blue"), - ticks = list(stroke = "blue", strokeWidth = 2), - labels = list(angle = 45, align = "left", fontSize = 10) - )) - -mtcars %>% ggvis(y = ~mpg) %>% - layer_points(prop("x", ~disp, scale = "xdisp")) %>% - layer_points(prop("x", ~wt, scale = "xwt"), fill := "blue") %>% - add_axis("x", "xdisp", orient = "bottom") %>% - add_axis("x", "xwt", orient = "top", - properties = axis_props(labels = list(fill = "blue"))) -``` - -### Legends - -Unlike ggplot2, by default, ggvis will not combine scales based on the same underlying variables into a single legend. Instead you must do this yourself by supplying the name of multiple scales to one legend: - -```{r} -mtcars %>% - ggvis(~wt, ~mpg, size = ~cyl) %>% - layer_points() %>% - add_legend(c("size")) -mtcars %>% - ggvis(~wt, ~mpg, size = ~cyl, fill=~cyl) %>% - layer_points() %>% - add_legend(c("size","fill")) -``` - -### Regression Lines - -```{r} -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - layer_smooths(span=0.5) # add a smooth loess curve using span% of the neighbors -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - layer_model_predictions(model = "lm", se = TRUE, stroke := "red") # add a regression line with 95% CI -# layer_smooths() is just compute_smooth() + layer_paths() -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - compute_smooth(mpg ~ wt) %>% - layer_paths(~pred_, ~resp_, strokeWidth := 1, stroke := "red") -mtcars %>% ggvis(~wt, ~mpg) %>% - layer_points(size := 5) %>% - layer_smooths(span = 1, stroke := "orange") %>% - layer_smooths(span = 0.3, stroke := "red") -``` - -### Interactive elements - -Behind the scenes, interactive plots are built with shiny, and you can currently only have one running at a time in a given R session. To finish with a plot, press the stop button in Rstudio, or close the browser window and then press Escape or Ctrl + C in R. - -```{r} -mtcars %>% - ggvis(~wt, ~mpg, - size := input_slider(10, 100, label = "Point size"), - opacity := input_slider(0, 1, label = "Opacity"), - stroke := input_select(c("GOLD" = "gold", "BLACK" = "black"), label="Select color"), - strokeWidth := input_numeric(label = "Stroke size", value = 5) - ) %>% - layer_points() -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points() %>% - layer_smooths(se = TRUE, span = input_slider(0.2, 1), stroke := "blue", strokeWidth := 5) -mtcars %>% ggvis(~wt, ~mpg) %>% layer_points() %>% - layer_model_predictions(model = "lm", - domain = input_slider(0, 10, value = c(1, 4))) # domain determines the interval of the regression -mtcars %>% ggvis(~wt, ~mpg) %>% - layer_points() %>% - add_tooltip(function(df) df$wt*100) -``` - -### Scatter plots with grouping - -```{r} -mtcars %>% - ggvis(~wt, ~mpg) %>% - layer_points(fill = ~factor(cyl)) -mtcars %>% - ggvis(~wt, ~mpg, fill = ~factor(cyl)) %>% - layer_points() %>% - group_by(cyl) %>% - layer_smooths(span = input_slider(0.66, 1, value=1)) -``` - -### Bar graphs - -```{r} -head(pressure) -pressure %>% - ggvis(~temperature, ~pressure) %>% - layer_bars(width = 12) -``` - -### Line graphs - -```{r} -pressure %>% - ggvis(~temperature, ~pressure) %>% - layer_lines() -pressure %>% - ggvis(~temperature, ~pressure) %>% - layer_points(shape := "square", stroke := "darkgreen", fill := "gold") %>% - layer_lines(stroke := "blue", strokeWidth := 1) -``` - -### Histograms - -```{r} -head(faithful) -faithful %>% - ggvis(~eruptions) %>% - layer_histograms() -faithful %>% - ggvis(~eruptions) %>% - layer_histograms(width=0.5, center=0) -mtcars %>% - ggvis(~wt) %>% - layer_histograms(width = input_slider(0, 2, step = 0.10, label = "width"), - center = input_slider(0, 2, step = 0.05, label = "center")) -cocaine %>% ggvis(~month, fill := "#fff8dc") %>% - layer_histograms(width = 1, center = 0) %>% - add_axis("x", title = "month") %>% - add_axis("y", title = "count") -# with grouping -mtcars %>% - ggvis(~mpg, fill = ~factor(cyl)) %>% - group_by(cyl) %>% - layer_histograms(width = 2, stack=TRUE) -``` - -### Box plots - -```{r} -mtcars %>% - ggvis(~factor(cyl), ~mpg) %>% - layer_boxplots() -``` - -### More Layers - -```{r} -mtcars %>% - arrange(wt) %>% - ggvis(~wt, ~mpg) %>% - layer_paths() # arrange+layer_paths is the same as layer_lines -t <- seq(0, 2 * pi, length = 100) -data.frame(x = sin(t), y = cos(t)) %>% - ggvis(~x, ~y) %>% - layer_paths(fill := "red") # with fill makes a polygon -mtcars %>% - arrange(wt) %>% - ggvis(~wt, ~mpg) %>% - layer_ribbons() -data.frame(x = 1:10, y = (1:10) ^ 2) %>% - ggvis(~x, ~y, y2 := 0) %>% - layer_ribbons() -set.seed(1014) -data.frame(x1 = runif(5), x2 = runif(5), y1 = runif(5), y2 = runif(5)) %>% - ggvis(~x1, ~y1, x2 = ~x2, y2 = ~y2, fillOpacity := 0.1) %>% - layer_rects() -data.frame(x = 3:1, y = c(1, 3, 2), label = c("a", "b", "c"), type=c("x","x","y")) %>% - ggvis(~x, ~y, text := ~label) %>% - layer_text(fontSize := 15, fontWeight := "bold", angle := 45) %>% - layer_text(text := ~type, dx := 10, dy := -10, stroke := "blue") -``` - diff --git a/GraphicalTools/ggvis.html b/GraphicalTools/ggvis.html deleted file mode 100644 index 65a4d4d..0000000 --- a/GraphicalTools/ggvis.html +++ /dev/null @@ -1,6754 +0,0 @@ - - - - - - - - - - - - - - -ggvis - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Refs:

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package ggvis is used to turn a dataset into a visualisation, setting up default mappings between variables in the dataset and visual properties. It uses a syntax similar in spirit to ggplot2 and dplyr.

-
-
-

The goal is to combine the best of R (e.g. every modelling function you can imagine) and the best of the web (everyone has a web browser). Data manipulation and transformation are done in R, and the graphics are rendered in a web browser, using Vega [ref.(http://cran.r-project.org/web/packages/ggvis/vignettes/overview.html)

-
-
library(ggvis)
-library(dplyr)
-

Several examples:

-
head(mtcars)
-
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
-## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
-## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
-## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
-## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
-## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
-## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1
-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points()
-

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mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points(size := 25, shape := "diamond", stroke := "red", fill := NA)
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mtcars %>% 
-  ggvis(~mpg, ~disp, size = ~vs) %>% 
-  layer_points()
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mtcars %>% 
-  ggvis(~mpg, ~disp, size = ~vs, opacity := 0.4) %>% 
-  layer_points()
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Axis

-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points() %>%
-  add_axis("x", title = "Weight (lb/1000)", title_offset = 50, orient = "top") %>%
-  add_axis("y", title = "Miles/(US) gallon", subdivide = 2, values = seq(10,34,by=2))
-

-
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- -
-
-

-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points() %>%
-  add_axis("x", title = "") %>%
-  add_axis("x", title = "Weight (lb/1000)", offset = 60, grid = FALSE) %>%
-  hide_axis("y")
-

-
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- -
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-

-
# For axes, you can set the properties of the ticks (or majorTicks and minorTicks separately), the labels and axis.
-mtcars %>% ggvis(~wt, ~mpg) %>%
-  layer_points() %>%
-  add_axis("x", properties = axis_props(
-    axis = list(stroke = "red", strokeWidth = 3),
-    grid = list(stroke = "blue"),
-    ticks = list(stroke = "blue", strokeWidth = 2),
-    labels = list(angle = 45, align = "left", fontSize = 10)
-  ))
-

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- -
-
-

-
mtcars %>% ggvis(y = ~mpg) %>%
-  layer_points(prop("x", ~disp, scale = "xdisp")) %>%
-  layer_points(prop("x", ~wt, scale = "xwt"), fill := "blue") %>%
-  add_axis("x", "xdisp", orient = "bottom") %>%
-  add_axis("x", "xwt", orient = "top",
-    properties = axis_props(labels = list(fill = "blue")))
-

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Legends

-

Unlike ggplot2, by default, ggvis will not combine scales based on the same underlying variables into a single legend. Instead you must do this yourself by supplying the name of multiple scales to one legend:

-
mtcars %>% 
-  ggvis(~wt, ~mpg, size = ~cyl) %>% 
-  layer_points() %>%
-  add_legend(c("size"))
-

-
-
- -
-
-

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mtcars %>% 
-  ggvis(~wt, ~mpg, size = ~cyl, fill=~cyl) %>% 
-  layer_points() %>%
-  add_legend(c("size","fill"))
-

-
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- -
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-

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-
-

Regression Lines

-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>%
-  layer_points() %>%
-  layer_smooths(span=0.5)  # add a smooth loess curve using span% of the neighbors
-

-
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- -
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-

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mtcars %>% 
-  ggvis(~wt, ~mpg) %>%
-  layer_points() %>%
-  layer_model_predictions(model = "lm", se = TRUE, stroke := "red") # add a regression line with 95% CI
-
## Guessing formula = mpg ~ wt
-

-
-
- -
-
-

-
# layer_smooths() is just compute_smooth() + layer_paths()
-mtcars %>%
-  ggvis(~wt, ~mpg) %>%
-  layer_points() %>%
-  compute_smooth(mpg ~ wt) %>%
-  layer_paths(~pred_, ~resp_, strokeWidth := 1, stroke := "red")
-

-
-
- -
-
-

-
mtcars %>% ggvis(~wt, ~mpg) %>%
-  layer_points(size := 5) %>%
-  layer_smooths(span = 1, stroke := "orange") %>%
-  layer_smooths(span = 0.3, stroke := "red")
-

-
-
- -
-
-

-
-
-

Interactive elements

-

Behind the scenes, interactive plots are built with shiny, and you can currently only have one running at a time in a given R session. To finish with a plot, press the stop button in Rstudio, or close the browser window and then press Escape or Ctrl + C in R.

-
mtcars %>% 
-  ggvis(~wt, ~mpg, 
-    size := input_slider(10, 100, label = "Point size"),
-    opacity := input_slider(0, 1, label = "Opacity"),
-    stroke := input_select(c("GOLD" = "gold", "BLACK" = "black"), label="Select color"),
-    strokeWidth := input_numeric(label = "Stroke size", value = 5)
-  ) %>% 
-  layer_points()
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points() %>%
-  layer_smooths(se = TRUE, span = input_slider(0.2, 1), stroke := "blue", strokeWidth := 5)
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
mtcars %>% ggvis(~wt, ~mpg) %>% layer_points() %>%
-  layer_model_predictions(model = "lm",
-    domain = input_slider(0, 10, value = c(1, 4)))  # domain determines the interval of the regression
-
## Guessing formula = mpg ~ wt
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
mtcars %>% ggvis(~wt, ~mpg) %>% 
-  layer_points() %>% 
-  add_tooltip(function(df) df$wt*100)
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
-
-

Scatter plots with grouping

-
mtcars %>% 
-  ggvis(~wt, ~mpg) %>% 
-  layer_points(fill = ~factor(cyl))
-

-
-
- -
-
-

-
mtcars %>% 
-  ggvis(~wt, ~mpg, fill = ~factor(cyl)) %>% 
-  layer_points() %>% 
-  group_by(cyl) %>% 
-  layer_smooths(span = input_slider(0.66, 1, value=1))
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
-
-

Bar graphs

-
head(pressure)
-
##   temperature pressure
-## 1           0   0.0002
-## 2          20   0.0012
-## 3          40   0.0060
-## 4          60   0.0300
-## 5          80   0.0900
-## 6         100   0.2700
-
pressure %>% 
-  ggvis(~temperature, ~pressure) %>%
-  layer_bars(width = 12)
-

-
-
- -
-
-

-
-
-

Line graphs

-
pressure %>% 
-  ggvis(~temperature, ~pressure) %>% 
-  layer_lines()
-

-
-
- -
-
-

-
pressure %>% 
-  ggvis(~temperature, ~pressure) %>%
-  layer_points(shape := "square", stroke := "darkgreen", fill := "gold") %>% 
-  layer_lines(stroke := "blue", strokeWidth := 1)
-

-
-
- -
-
-

-
-
-

Histograms

-
head(faithful)
-
##   eruptions waiting
-## 1     3.600      79
-## 2     1.800      54
-## 3     3.333      74
-## 4     2.283      62
-## 5     4.533      85
-## 6     2.883      55
-
faithful %>% 
-  ggvis(~eruptions) %>% 
-  layer_histograms()
-
## Guessing width = 0.1 # range / 35
-

-
-
- -
-
-

-
faithful %>% 
-  ggvis(~eruptions) %>% 
-  layer_histograms(width=0.5, center=0)
-

-
-
- -
-
-

-
mtcars %>% 
-  ggvis(~wt) %>% 
-  layer_histograms(width =  input_slider(0, 2, step = 0.10, label = "width"),
-                   center = input_slider(0, 2, step = 0.05, label = "center"))
-
## Warning: Can't output dynamic/interactive ggvis plots in a knitr document.
-## Generating a static (non-dynamic, non-interactive) version of the plot.
-

-
-
- -
-
-

-
cocaine %>% ggvis(~month, fill := "#fff8dc") %>%
-  layer_histograms(width = 1, center = 0) %>%
-  add_axis("x", title = "month") %>%
-  add_axis("y", title = "count")
-

-
-
- -
-
-

-
# with grouping
-mtcars %>% 
-  ggvis(~mpg, fill = ~factor(cyl)) %>% 
-  group_by(cyl) %>%
-  layer_histograms(width = 2, stack=TRUE)
-
## Warning: Unequal factor levels: coercing to character
-

-
-
- -
-
-

-
-
-

Box plots

-
mtcars %>% 
-  ggvis(~factor(cyl), ~mpg) %>% 
-  layer_boxplots()
-
## Warning: Unequal factor levels: coercing to character
-

-
-
- -
-
-

-
-
-

More Layers

-
mtcars %>% 
-  arrange(wt) %>% 
-  ggvis(~wt, ~mpg) %>%   
-  layer_paths() # arrange+layer_paths is the same as layer_lines
-

-
-
- -
-
-

-
t <- seq(0, 2 * pi, length = 100)
-data.frame(x = sin(t), y = cos(t)) %>% 
-  ggvis(~x, ~y) %>% 
-  layer_paths(fill := "red") # with fill makes a polygon
-

-
-
- -
-
-

-
mtcars %>% 
-  arrange(wt) %>% 
-  ggvis(~wt, ~mpg) %>%   
-  layer_ribbons()
-

-
-
- -
-
-

-
data.frame(x = 1:10, y = (1:10) ^ 2) %>%
-  ggvis(~x, ~y, y2 := 0) %>% 
-  layer_ribbons()
-

-
-
- -
-
-

-
set.seed(1014)
-data.frame(x1 = runif(5), x2 = runif(5), y1 = runif(5), y2 = runif(5)) %>% 
-  ggvis(~x1, ~y1, x2 = ~x2, y2 = ~y2, fillOpacity := 0.1) %>% 
-  layer_rects()
-

-
-
- -
-
-

-
data.frame(x = 3:1, y = c(1, 3, 2), label = c("a", "b", "c"), type=c("x","x","y")) %>% 
-  ggvis(~x, ~y, text := ~label) %>% 
-  layer_text(fontSize := 15, fontWeight := "bold", angle := 45) %>%
-  layer_text(text := ~type, dx := 10, dy := -10, stroke := "blue")
-

-
-
- -
-
-

-
- - -
- - - - - - - - diff --git a/GraphicalTools/googleVis.Rmd b/GraphicalTools/googleVis.Rmd deleted file mode 100644 index 314108e..0000000 --- a/GraphicalTools/googleVis.Rmd +++ /dev/null @@ -1,229 +0,0 @@ ---- -title: "googleVis egs" -author: "João Neto" -date: "Friday, September 05, 2014" -output: html_document ---- - -Refs: - -+ [http://lamages.blogspot.pt/2014/09/zoom-zoom-googlevis.html](http://lamages.blogspot.pt/2014/09/zoom-zoom-googlevis.html) - -+ [http://www.r-bloggers.com/google-charts-in-r-markdown/](http://www.r-bloggers.com/google-charts-in-r-markdown/) - -+ [GoogleVis package](http://cran.r-project.org/web/packages/googleVis/index.html) - -+ [GoogleVis demos](http://cran.r-project.org/web/packages/googleVis/vignettes/googleVis_examples.html) - -+ [Google Chart Gallery](https://developers.google.com/chart/interactive/docs/gallery) - -```{r, message=FALSE, warning=FALSE} -library(googleVis) -``` - - -```{r, results='asis'} -set.seed(2020) -x <- seq(0,100,by=0.5) -y <- (50-x)^2+rnorm(length(x),sd=100) - -curvy <- data.frame(x,y) - -gvScat <- gvisScatterChart(curvy, - options=list( - explorer="{actions: ['dragToZoom', 'rightClickToReset'], maxZoomIn:0.05}", - gvis.editor="Edit me!", - chartArea="{width:'85%',height:'80%'}", - hAxis="{title: 'Click&drag for zoom region, right-click to reset', titleTextStyle: {color: '#000000'}}", - vAxis="{title: 'Response y', titleTextStyle: {color: '#000000'}}", - backgroundColor="#EEEEEE", - title="Curvilinear Relationship", - titleTextStyle="{color:'red', fontName:'Courier', fontSize:12}", - width=550, height=500, - legend="none"), - chartid="ZoomZoom") - -print(gvScat,'chart') -``` - -## More egs - - -```{r, results='asis'} -df=data.frame(country=c("US", "GB", "BR"), - val1=c(10,13,14), - val2=c(23,12,32)) - -gvLine <- gvisLineChart(df) - -print(gvLine,'chart') - -gvIntensity <- gvisIntensityMap(df) - -print(gvIntensity,'chart') -``` - -```{r} -head(Exports) -``` - -```{r, results='asis'} -Geo=gvisGeoChart(Exports, locationvar="Country", - colorvar="Profit", - options=list(projection="kavrayskiy-vii")) -print(Geo,'chart') -``` - -Merge charts: - -```{r, results='asis'} -G <- gvisGeoChart(Exports, "Country", "Profit", - options=list(width=300, height=300)) -T <- gvisTable(Exports, - options=list(width=220, height=300)) - -GT <- gvisMerge(G,T, horizontal=TRUE) -print(GT,'chart') -``` - - -```{r} -head(Stock) -``` - -```{r, results='asis'} -gvAnno <- gvisAnnotationChart(Stock, - datevar="Date", - numvar="Value", - idvar="Device", - titlevar="Title", - annotationvar="Annotation", - options=list( - width=600, height=350, - fill=10, displayExactValues=TRUE, - colors="['#0000ff','#00ff00']") -) -plot(gvAnno, 'chart') - -AnnoTimeLine <- gvisAnnotatedTimeLine(Stock, - datevar="Date", - numvar="Value", - idvar="Device", - titlevar="Title", - annotationvar="Annotation", - options=list(displayAnnotations=TRUE, - width="600px", height="350px")) -plot(AnnoTimeLine, 'chart') - -datSK <- data.frame(From=c(rep("A",3), rep("B", 3)), - To=c(rep(c("X", "Y", "Z"),2)), - Weight=c(5,7,6,2,9,4)) - -gvSankey <- gvisSankey(datSK, from="From", to="To", weight="Weight", - options=list( - sankey="{link: { color: { fill: '#d799ae' } }, - node: { color: { fill: '#a61d4c' }, - label: { color: '#871b47' } }}")) -plot(gvSankey, 'chart') -``` - -In this org chart, double-click to expand/collapse: - - -```{r} -head(Regions) -``` - - -```{r, results='asis'} -gvOrg <- gvisOrgChart(Regions, - options=list(width=600, height=250, - size='large', allowCollapse=TRUE)) -plot(gvOrg, 'chart') -``` - - -```{r} -head(Population[,-5]) -``` - -```{r, results='asis'} -PopTable <- gvisTable(Population[,-5], - formats=list(Population="#,###", - '% of World Population'='#.#%'), - options=list(page='enable')) -plot(PopTable, 'chart') -``` - - -```{r} -head(Andrew) -``` - -```{r, results='asis'} -GeoMarker <- gvisGeoChart(Andrew, "LatLong", - sizevar='Speed_kt', - colorvar="Pressure_mb", - options=list(region="US")) -plot(GeoMarker, 'chart') -``` - -## Google Maps - -```{r, results='asis'} -AndrewMap <- gvisMap(Andrew, "LatLong" , "Tip", - options=list(showTip=TRUE, - showLine=TRUE, - enableScrollWheel=TRUE, - mapType='terrain', - useMapTypeControl=TRUE)) -plot(AndrewMap, 'chart') -``` - -## Flash charts - -These charts require Flash. - -```{r} -head(Fruits) -``` - -```{r, results='asis'} -Motion=gvisMotionChart(Fruits, - idvar="Fruit", - timevar="Year") -plot(Motion, 'chart') - -myStateSettings <-' -{"xZoomedDataMin":1199145600000,"colorOption":"2", -"duration":{"timeUnit":"Y","multiplier":1},"yLambda":1, -"yAxisOption":"4","sizeOption":"_UNISIZE", -"iconKeySettings":[],"xLambda":1,"nonSelectedAlpha":0, -"xZoomedDataMax":1262304000000,"iconType":"LINE", -"dimensions":{"iconDimensions":["dim0"]}, -"showTrails":false,"uniColorForNonSelected":false, -"xAxisOption":"_TIME","orderedByX":false,"playDuration":15000, -"xZoomedIn":false,"time":"2010","yZoomedDataMin":0, -"yZoomedIn":false,"orderedByY":false,"yZoomedDataMax":100} -' -M <- gvisMotionChart(Fruits, "Fruit", "Year", options=list(state=myStateSettings)) -plot(M, 'chart') -``` - -From [http://members.unine.ch/martin.hilpert/motion.html](http://members.unine.ch/martin.hilpert/motion.html): - -```{r} -url <- "http://members.unine.ch/martin.hilpert/mot.zip" -fn <- paste0(tempfile(), ".zip") -download.file(url, destfile = fn) -dat <- read.table(unzip(fn, files="mot/convdata.txt", - exdir=tempdir()), - header=TRUE) -library(googleVis) -plot(gvisMotionChart(dat, idvar="VERB", timevar="DECADE", - xvar="verbs", yvar="nouns", - sizevar="freq", colorvar="skewedness", - options=list(width=500, height=450), - chartid="Hilpert")) -``` - diff --git a/GraphicalTools/googleVis.html b/GraphicalTools/googleVis.html deleted file mode 100644 index 6e4dc27..0000000 --- a/GraphicalTools/googleVis.html +++ /dev/null @@ -1,5017 +0,0 @@ - - - - - - - - - - - - - - -googleVis egs - - - - - - - - - - - - - - - - - - - - -
- - - - - -

Refs:

- -
library(googleVis)
-
set.seed(2020)
-x <- seq(0,100,by=0.5)
-y <- (50-x)^2+rnorm(length(x),sd=100)
- 
-curvy <- data.frame(x,y) 
- 
-gvScat <- gvisScatterChart(curvy,
-                   options=list(
-                     explorer="{actions: ['dragToZoom', 'rightClickToReset'], maxZoomIn:0.05}",
-                     gvis.editor="Edit me!",
-                     chartArea="{width:'85%',height:'80%'}",
-                     hAxis="{title: 'Click&drag for zoom region, right-click to reset', titleTextStyle: {color: '#000000'}}",
-                     vAxis="{title: 'Response y',    titleTextStyle: {color: '#000000'}}",
-                     backgroundColor="#EEEEEE",
-                     title="Curvilinear Relationship",
-                     titleTextStyle="{color:'red', fontName:'Courier', fontSize:12}",  
-                     width=550, height=500,
-                     legend="none"),
-                     chartid="ZoomZoom")
- 
-print(gvScat,'chart')
- - - - - - - - - - - -
-
- -
-
-

More egs

-
df=data.frame(country=c("US", "GB", "BR"), 
-               val1=c(10,13,14), 
-               val2=c(23,12,32))
-
-gvLine <- gvisLineChart(df)
-
-print(gvLine,'chart')
- - - - - - - - - - - - -
-
- -
gvIntensity <- gvisIntensityMap(df)
-
-print(gvIntensity,'chart')
- - - - - - - - - - - - -
-
- - -
head(Exports)
-
##         Country Profit Online
-## 1       Germany      3   TRUE
-## 2        Brazil      4  FALSE
-## 3 United States      5   TRUE
-## 4        France      4   TRUE
-## 5       Hungary      3  FALSE
-## 6         India      2   TRUE
-
Geo=gvisGeoChart(Exports, locationvar="Country", 
-                 colorvar="Profit",
-                 options=list(projection="kavrayskiy-vii"))
-print(Geo,'chart')
- - - - - - - - - - - - -
-
- -

Merge charts:

-
G <- gvisGeoChart(Exports, "Country", "Profit", 
-                  options=list(width=300, height=300))
-T <- gvisTable(Exports, 
-               options=list(width=220, height=300))
-
-GT <- gvisMerge(G,T, horizontal=TRUE) 
-print(GT,'chart')
- - - - - - - - - - - - - - - - - - - -
- - - -
-
- -		 - - - -
-
- -
- - - -
head(Stock)
-
##         Date  Device  Value          Title          Annotation
-## 1 2008-01-01 Pencils   3000           <NA>                <NA>
-## 2 2008-01-02 Pencils  14045           <NA>                <NA>
-## 3 2008-01-03 Pencils   5502           <NA>                <NA>
-## 4 2008-01-04 Pencils  75284           <NA>                <NA>
-## 5 2008-01-05 Pencils  41476 Bought pencils Bought 200k pencils
-## 6 2008-01-06 Pencils 333222           <NA>                <NA>
-
gvAnno <- gvisAnnotationChart(Stock, 
-                            datevar="Date",
-                            numvar="Value", 
-                            idvar="Device",
-                            titlevar="Title", 
-                            annotationvar="Annotation",
-                            options=list(
-                              width=600, height=350,
-                              fill=10, displayExactValues=TRUE,
-                              colors="['#0000ff','#00ff00']")
-)
-plot(gvAnno, 'chart')
- - - - - - - - - - - - -
-
- -
AnnoTimeLine  <- gvisAnnotatedTimeLine(Stock, 
-                                       datevar="Date",
-                                       numvar="Value", 
-                                       idvar="Device",
-                                       titlevar="Title", 
-                                       annotationvar="Annotation",
-                                       options=list(displayAnnotations=TRUE,
-                                                    width="600px", height="350px"))
-plot(AnnoTimeLine, 'chart')
- - - - - - - - - - - - -
-
- -
datSK <- data.frame(From=c(rep("A",3), rep("B", 3)),
-                    To=c(rep(c("X", "Y", "Z"),2)),
-                    Weight=c(5,7,6,2,9,4))
-
-gvSankey <- gvisSankey(datSK, from="From", to="To", weight="Weight",
-                     options=list(
-                       sankey="{link:  { color: { fill: '#d799ae' } },
-                                node:  { color: { fill: '#a61d4c' },
-                                label: { color: '#871b47' } }}"))
-plot(gvSankey, 'chart')
- - - - - - - - - - - - -
-
- -

In this org chart, double-click to expand/collapse:

-
head(Regions)
-
##    Region Parent Val Fac
-## 1  Global   <NA>  10   2
-## 2 America Global   2   4
-## 3  Europe Global  99  11
-## 4    Asia Global  10   8
-## 5  France Europe  71   2
-## 6  Sweden Europe  89   3
-
gvOrg <- gvisOrgChart(Regions, 
-                    options=list(width=600, height=250,
-                                 size='large', allowCollapse=TRUE))
-plot(gvOrg, 'chart')
- - - - - - - - - - - - -
-
- - - -
head(Population[,-5])
-
##   Rank       Country Population % of World Population Mode       Date
-## 1    1         China 1339940000                 19.50 TRUE 2010-10-09
-## 2    2         India 1188650000                 17.30 TRUE 2010-10-09
-## 3    3 United States  310438000                  4.52 TRUE 2010-10-09
-## 4    4     Indonesia  237556363                  3.46 TRUE 2010-10-09
-## 5    5        Brazil  193626000                  2.82 TRUE 2010-10-09
-## 6    6      Pakistan  170745000                  2.48 TRUE 2010-10-09
-
PopTable <- gvisTable(Population[,-5], 
-                      formats=list(Population="#,###",
-                                   '% of World Population'='#.#%'),
-                      options=list(page='enable'))
-plot(PopTable, 'chart')
- - - - - - - - - - - - -
-
- - - -
head(Andrew)
-
##         Date/Time UTC  Lat  Long Pressure_mb Speed_kt            Category
-## 1 1992-08-16 18:00:00 10.8 -35.5        1010       25 Tropical Depression
-## 2 1992-08-17 00:00:00 11.2 -37.4        1009       30 Tropical Depression
-## 3 1992-08-17 06:00:00 11.7 -39.6        1008       30 Tropical Depression
-## 4 1992-08-17 12:00:00 12.3 -42.0        1006       35      Tropical Storm
-## 5 1992-08-17 18:00:00 13.1 -44.2        1003       35      Tropical Storm
-## 6 1992-08-18 00:00:00 13.6 -46.2        1002       40      Tropical Storm
-##      LatLong                                              Tip
-## 1 10.8:-35.5 Tropical Depression<BR>Pressure=1010<BR>Speed=25
-## 2 11.2:-37.4 Tropical Depression<BR>Pressure=1009<BR>Speed=30
-## 3 11.7:-39.6 Tropical Depression<BR>Pressure=1008<BR>Speed=30
-## 4   12.3:-42      Tropical Storm<BR>Pressure=1006<BR>Speed=35
-## 5 13.1:-44.2      Tropical Storm<BR>Pressure=1003<BR>Speed=35
-## 6 13.6:-46.2      Tropical Storm<BR>Pressure=1002<BR>Speed=40
-
GeoMarker <- gvisGeoChart(Andrew, "LatLong", 
-                          sizevar='Speed_kt',
-                          colorvar="Pressure_mb", 
-                          options=list(region="US"))
-plot(GeoMarker, 'chart')
- - - - - - - - - - - - -
-
- -
-
-

Google Maps

-
AndrewMap <- gvisMap(Andrew, "LatLong" , "Tip", 
-                     options=list(showTip=TRUE, 
-                                  showLine=TRUE, 
-                                  enableScrollWheel=TRUE,
-                                  mapType='terrain', 
-                                  useMapTypeControl=TRUE))
-plot(AndrewMap, 'chart')
- - - - - - - - - - - - -
-
- -
-
-

Flash charts

-

These charts require Flash.

-
head(Fruits)
-
##     Fruit Year Location Sales Expenses Profit       Date
-## 1  Apples 2008     West    98       78     20 2008-12-31
-## 2  Apples 2009     West   111       79     32 2009-12-31
-## 3  Apples 2010     West    89       76     13 2010-12-31
-## 4 Oranges 2008     East    96       81     15 2008-12-31
-## 5 Bananas 2008     East    85       76      9 2008-12-31
-## 6 Oranges 2009     East    93       80     13 2009-12-31
-
Motion=gvisMotionChart(Fruits, 
-                       idvar="Fruit", 
-                       timevar="Year")
-plot(Motion, 'chart')
- - - - - - - - - - - - -
-
- -
myStateSettings <-'
-{"xZoomedDataMin":1199145600000,"colorOption":"2",
-"duration":{"timeUnit":"Y","multiplier":1},"yLambda":1,
-"yAxisOption":"4","sizeOption":"_UNISIZE",
-"iconKeySettings":[],"xLambda":1,"nonSelectedAlpha":0,
-"xZoomedDataMax":1262304000000,"iconType":"LINE",
-"dimensions":{"iconDimensions":["dim0"]},
-"showTrails":false,"uniColorForNonSelected":false,
-"xAxisOption":"_TIME","orderedByX":false,"playDuration":15000,
-"xZoomedIn":false,"time":"2010","yZoomedDataMin":0,
-"yZoomedIn":false,"orderedByY":false,"yZoomedDataMax":100}
-'
-M <- gvisMotionChart(Fruits, "Fruit", "Year", options=list(state=myStateSettings))
-plot(M, 'chart')
- - - - - - - - - - - - -
-
- - - -
- - -
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-0.9502314815,20.8487084871,"female" -0.9706018519,23.8745387454,"female" -0.9696759259,23.8745387454,"female" diff --git a/bayes.packages/index.Rmd b/bayes.packages/index.Rmd deleted file mode 100644 index de4bfe9..0000000 --- a/bayes.packages/index.Rmd +++ /dev/null @@ -1,240 +0,0 @@ ---- -title: "Bayesian Model Packages" -author: "João Neto" -date: October 2014 -output: - html_document: - toc: true - toc_depth: 3 - fig_width: 6 - fig_height: 6 -cache: yes ---- - -## Bayesian First Aid - -> Bayesian First Aid is an attempt at implementing reasonable Bayesian alternatives to the classical hypothesis tests in R. For the rationale behind Bayesian First Aid see the [original announcement](http://sumsar.net/blog/2014/01/bayesian-first-aid/). The development of Bayesian First Aid can be followed on [GitHub](https://github.com/rasmusab/bayesian_first_aid). Bayesian First Aid is a work in progress and I'm grateful for any suggestion on how to improve it! [ref](http://sumsar.net/blog/2014/01/bayesian-first-aid-binomial-test/) - -The following code and tests in this chapter are taken from the package author's webpages, namely: - -+ [Binomial Test](http://sumsar.net/blog/2014/01/bayesian-first-aid-binomial-test/): bayes.binom.test(x, n) -+ [One Sample and Paired Samples t-test](http://sumsar.net/blog/2014/02/bayesian-first-aid-one-sample-t-test/): bayes.t.test(x) -+ [Pearson Correlation Test](http://sumsar.net/blog/2014/03/bayesian-first-aid-pearson-correlation-test/): bayes.cor.test(x, y) -+ [Test of Proportions](http://sumsar.net/blog/2014/06/bayesian-first-aid-prop-test/): bayes.prop.test(x, n) (check [part2](part2.html)) -+ [Poisson test](http://sumsar.net/blog/2014/09/bayesian-first-aid-poisson-test/): bayes.poisson.test(x, T) - -```{r, warning=FALSE, message=FALSE} -# To install: -## install.packages("devtools") -# library(devtools) -# install_github("rasmusab/bayesian_first_aid") - -library(BayesianFirstAid) -``` - -### Binomial Test - -We have $n$ trials with $x$ sucesses and $n-x$ failures. We assume that the tests are iid. - -The likelihood, the distribution of the data is considered a Binomial with parameter $\theta$ ($n$ is considered fixed): - -$$p(x|n, \theta) = {n \choose x} \theta^x (1-\theta)^{(n-x)}$$ - -The prior distribution of parameter $\theta$ used in the flat prior which is described by a Beta(1,1): - -$$\theta \sim \text{Beta}(1,1)$$ - -The Bayesian estimation: - -```{r} -# x: number of successes -# n: number of trials -# comp.theta: a fixed relative frequency of success to compare with the estimated relative frequency of success -# cred.mass: the amount of probability mass that will be contained in reported credible intervals -# n.iter: The number of iterations to run the MCMC sampling (default: 15000, max: 1e6-1) - -model <- bayes.binom.test(x=9, n=11, comp.theta=0.7, cred.mass = 0.95) -model -``` - -Versus the classical binomial test: - -```{r} -binom.test(x=9, n=11, p=0.7, conf.level=0.95) -``` - -To plot and summarize: - -```{r} -summary(model) -plot(model) -``` - -The posterior predictive distribution is the distribution of unobserved observation $y$ (a prediction) conditional on the observed data $x$ - -$$p(y|x,n) = \int_{\theta} p(y|\theta) p(\theta|x,n) d\theta = E_{\theta|x,n} [ p(y|\theta) ]$$ - - -`diagnostics` plots MCMC diagnostics based on the `code` package: - -```{r} -diagnostics(model) -``` - -`model_code` print out R and JAGS code that runs the model (copy-paste friendly): - -```{r} -model.code(model) -``` - -Eg, to change the prior just replace, in the model_string, the distribution of $\theta$ for something else (liek Jeffrey's prior `dbeta(0.5,0.5)`) and run the code yourself. - -### One Sample and Paired Samples t-test - -To replace the classical t-test, this test uses the [BEST](http://www.indiana.edu/~kruschke/BEST/) methodology which assumes the data $x=(x_1,x_2,\ldots,x_n)$ are distributed as a t distribution according to the following model: - -$$x_i \sim t(\mu,\sigma,\nu$$ - -$$\mu \sim \mathcal{N}(M_{\mu}, S_{\mu})$$ - -$$\sigma \sim U(L_{\sigma}, H_{\sigma})$$ - -$$\nu \sim \text{ShiftedExp}(\frac{1}{29}, \text{shift}=1)$$ - -$\nu$ is the degrees of freedom of the t distribution (lower values mean heavier tails). The value $\frac{1}{29}$ is used to try to balance nearly normal distributions ($\nu\gt 30$) with heavy tailed distributions ($\nu\lt 30$). - -For paired samples the test takes the difference between each paired sample and model just the paired differences using the one sample procedure. - -As an eg let's load a dataset with coffee yields and compare these yields in two different time periords (1960-80 amd 1980-2001) and see if the test recognize some statistical significant change: - -```{r} -d <- read.csv("roubik_2002_coffe_yield.csv") -head(d) -new.yield_61 <- d[,3][d$world=="new"] -new.yield_61 -new.yield_81 <- d[,4][d$world=="new"] -new.yield_81 - -model <- bayes.t.test(new.yield_61, new.yield_81, paired=TRUE) -model -``` - -The $95$\% credible interval does not include zero, so the test recognizes a statistical difference between the two samples. - -```{r} -summary(model) -plot(model) -``` - -The posterior predictive box presents a histogram with a smattering of t-distributions drawn from the posterior. If there is a large discrepancy between the model fit and the data then we need to think twice before proceeding. Herein it's ok. - -```{r} -diagnostics(model) -model.code(model) -``` - -### Pearson Correlation Test - -This is a measure of the linear correlation (dependence) between two variables $X_1$ and $X_2$, giving a value $\rho$ between +1 and -1 inclusive, where 1 is total positive correlation, 0 is no correlation, and -1 is total negative correlation - -$$\rho = \frac{\text{cov}(X_1,X_2)}{\sigma_{X_1} \sigma_{X_2}$$ - -Classical statistical inference based on Pearson's correlation coefficient aims at test the null hypothesis that $\rho=0$ and finding the p\% confidence interval around $r$ (the sample correlation) that contains $\rho$. - -The Pearson's correlation coefficient is which assumes bivariate normality. - -The model that a classical Pearson's correlation test assumes is that between two paired variables $X_{i1}$ and $X_{i2}$ it follows a bivariate normal distribution, ie, $X_i1 \sim \mathcal{N}(\mu_1,\sigma_1), X_i2 \sim \mathcal{N}(\mu_2,\sigma_2)$ and for each pair $(x_i,y_i)$ there is a linear dependency which is quantified by $\rho$. Here's an eg for $\rho=0.3$: - - - -The classical model pressuposes that $X=(X_1,X_2)^T$ has a multivariate normal distribution: - -$$X \sim \mathcal{N}(\mu,\Sigma)$$ - -where $\mu=(\mu_1,\mu_2)^T$ and - -$$\Sigma = -\left() \begin{array}{cc} -\sigma_1^2 & \rho\sigma_1\sigma_2 \\ -\rho\sigma_1\sigma_2 & \sigma_2^2 \end{array} \right)$$ - -This test is implemented by R function `cor.test`. - -The following Bayesian model replaces the normal for a bivariate t distribution which is more robust to outliers (it could also be a normal, of course, the Bayesian framework is much more flexible in this sense). - -The Bayesian model becomes - -$$X \sim t(\mu,\Sigma,nu)$$ - -$$\rho \sim U(-1,1)$$ - -$$\mu_x,\mu_y \sim \mathcal{N}(M_{\mu}, \S_{\mu})$$ - -$$\sigma_{x_1}, \sigma_{x_2}\sim U(L_{\sigma}, U_{\sigma})$$ - -$$\nu \sim \text{ShiftedExp}(\frac{1}{29}, \text{shift}=1)$$ - -Let's load some data: - -```{r} -d <- read.csv("2d4d_hone_2012.csv") -head(d) -plot(d$ratio_2d4d, d$grip_kg, col=unclass(d$sex), pch=18) -legend("topright",c("female","male"), col=1:2, pch=18) -``` - -There is a visual difference between the two variables concerning gender. Let's try to find some pattern with this test - -```{r} -model.male <- bayes.cor.test( ~ ratio_2d4d + grip_kg, data=d[d$sex=="male",], n.iter = 5000) -model.male -summary(model.male) -model.female <- bayes.cor.test( ~ ratio_2d4d + grip_kg, data=d[d$sex=="female",], n.iter = 5000) -model.female - -plot(model.male) -plot(model.female) -``` - -Both estimates indicate a slight negative correlation (the males more than the females). The two ellipses show the 50% (darker blue) and 95% (lighter blue) highest density regions. The red histograms show the marginal distributions of the data with a smatter of marginal densities drawn from the posterior. Looking at this plot we see that the model fits quite well, however, we could be concerned with the right skewness of the `ratio_2d4d` marginal which is not captured by the model (the t-distribution is symmetric). - -To take a look at the posterior difference in correlation between the male and the female group, we first extract the MCMC samples from the Bayesian First Aid fit object using the `as.data.frame` function: - -```{r} -female.mcmc <- as.data.frame(model.female) - male.mcmc <- as.data.frame(model.male) - -hist(male.mcmc$rho-female.mcmc$rho, breaks=50, xlim=c(-1,1), main=bquote(paste("Density for ", rho, " male minus ", rho, " female")), yaxt="n", ylab="") -``` - -And the entire code: - -```{r} -model.code(model.female) -``` - -For instance, if you wanted to replace $\rho \sim U(-1,1)$ with a Beta, such that $\rho \sim \text{Beta}(-1,1)$ we would replace - -```{r, eval=FALSE} -rho ~ dunif(-1,1) -``` - -with - -```{r, eval=FALSE} -rho_half_width ~ dbeta(1,1) -rho ~ 2*rho_half_width - 1 # shift and strech from [0,1] to[-1,1] -``` - -and replace the inits_lit variable: - -```{r, eval=FALSE} -# from -rho=cor(x, y, method="spearman") -# to -rho_half_width=( cor(x,y,method="spearman") + 1 ) / 2 -``` - -By changing the parameter values of `dbeta` we could define several priors, placing more probability mass at that value of `rho` we know is more probable. - -Goto [part2](part2.html) \ No newline at end of file diff --git a/bayes.packages/index.html b/bayes.packages/index.html deleted file mode 100644 index cf8c052..0000000 --- a/bayes.packages/index.html +++ /dev/null @@ -1,577 +0,0 @@ - - - - - - - - - - - - - - -Bayesian Model Packages - - - - - - - - - - - - - - - - - - - - -
- - - - - - -
-

Bayesian First Aid

-
-

Bayesian First Aid is an attempt at implementing reasonable Bayesian alternatives to the classical hypothesis tests in R. For the rationale behind Bayesian First Aid see the original announcement. The development of Bayesian First Aid can be followed on GitHub. Bayesian First Aid is a work in progress and I’m grateful for any suggestion on how to improve it! ref

-
-

The following code and tests in this chapter are taken from the package author’s webpages, namely:

- -
# To install:
-## install.packages("devtools")
-# library(devtools)
-# install_github("rasmusab/bayesian_first_aid")
-
-library(BayesianFirstAid)
-
-

Binomial Test

-

We have \(n\) trials with \(x\) sucesses and \(n-x\) failures. We assume that the tests are iid.

-

The likelihood, the distribution of the data is considered a Binomial with parameter \(\theta\) (\(n\) is considered fixed):

-

\[p(x|n, \theta) = {n \choose x} \theta^x (1-\theta)^{(n-x)}\]

-

The prior distribution of parameter \(\theta\) used in the flat prior which is described by a Beta(1,1):

-

\[\theta \sim \text{Beta}(1,1)\]

-

The Bayesian estimation:

-
# x: number of successes
-# n: number of trials
-# comp.theta: a fixed relative frequency of success to compare with the estimated relative frequency of success
-# cred.mass: the amount of probability mass that will be contained in reported credible intervals
-# n.iter: The number of iterations to run the MCMC sampling (default: 15000, max: 1e6-1)
-
-model <- bayes.binom.test(x=9, n=11, comp.theta=0.7, cred.mass = 0.95)
-model
-
## 
-##  Bayesian First Aid binomial test
-## 
-## data: 9 and 11
-## number of successes = 9, number of trials = 11
-## Estimated relative frequency of success:
-##   0.78 
-## 95% credible interval:
-##   0.55 0.96 
-## The relative frequency of success is more than 0.7 by a probability of 0.742 
-## and less than 0.7 by a probability of 0.258
-

Versus the classical binomial test:

-
binom.test(x=9, n=11, p=0.7, conf.level=0.95)
-
## 
-##  Exact binomial test
-## 
-## data:  9 and 11
-## number of successes = 9, number of trials = 11, p-value = 0.523
-## alternative hypothesis: true probability of success is not equal to 0.7
-## 95 percent confidence interval:
-##  0.4822 0.9772
-## sample estimates:
-## probability of success 
-##                 0.8182
-

To plot and summarize:

-
summary(model)
-
##   Data
-## number of successes = 9, number of trials = 11
-## 
-##   Model parameters and generated quantities
-## theta: the relative frequency of success
-## x_pred: predicted number of successes in a replication
-## 
-##   Measures
-##         mean    sd HDIlo HDIup %<comp %>comp
-## theta  0.767 0.113 0.545  0.96  0.258  0.742
-## x_pred 8.434 1.847 5.000 11.00  0.000  1.000
-## 
-## 'HDIlo' and 'HDIup' are the limits of a 95% HDI credible interval.
-## '%<comp' and '%>comp' are the probabilities of the respective parameter being
-## smaller or larger than 0.7.
-## 
-##   Quantiles
-##        q2.5%  q25% median   q75% q97.5%
-## theta  0.512 0.696  0.781  0.853  0.944
-## x_pred 4.000 7.000  9.000 10.000 11.000
-
plot(model)
-

plot of chunk unnamed-chunk-4

-

The posterior predictive distribution is the distribution of unobserved observation \(y\) (a prediction) conditional on the observed data \(x\)

-

\[p(y|x,n) = \int_{\theta} p(y|\theta) p(\theta|x,n) d\theta = E_{\theta|x,n} [ p(y|\theta) ]\]

-

diagnostics plots MCMC diagnostics based on the code package:

-
diagnostics(model)
-
## 
-## Iterations = 1:5000
-## Thinning interval = 1 
-## Number of chains = 3 
-## Sample size per chain = 5000 
-## 
-##   Diagnostic measures
-##         mean    sd mcmc_se n_eff Rhat
-## theta  0.767 0.113   0.001 14883    1
-## x_pred 8.434 1.847   0.015 14749    1
-## 
-## mcmc_se: the estimated standard error of the MCMC approximation of the mean.
-## n_eff: a crude measure of effective MCMC sample size.
-## Rhat: the potential scale reduction factor (at convergence, Rhat=1).
-## 
-##   Model parameters and generated quantities
-## theta: The relative frequency of success
-## x_pred: Predicted number of successes in a replication
-

plot of chunk unnamed-chunk-5

-

model_code print out R and JAGS code that runs the model (copy-paste friendly):

-
model.code(model)
-
## ### Model code for the Bayesian First Aid alternative to the binomial test ###
-## require(rjags)
-## 
-## # Setting up the data
-## x <- 9 
-## n <- 11 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   x ~ dbinom(theta, n)
-##   theta ~ dbeta(1, 1)
-##   x_pred ~ dbinom(theta, n)
-## }"
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = list(x = x, n = n), 
-##                     n.chains = 3, n.adapt=1000)
-## samples <- coda.samples(model, c("theta", "x_pred"), n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-

Eg, to change the prior just replace, in the model_string, the distribution of \(\theta\) for something else (liek Jeffrey’s prior dbeta(0.5,0.5)) and run the code yourself.

-
-
-

One Sample and Paired Samples t-test

-

To replace the classical t-test, this test uses the BEST methodology which assumes the data \(x=(x_1,x_2,\ldots,x_n)\) are distributed as a t distribution according to the following model:

-

\[x_i \sim t(\mu,\sigma,\nu\]

-

\[\mu \sim \mathcal{N}(M_{\mu}, S_{\mu})\]

-

\[\sigma \sim U(L_{\sigma}, H_{\sigma})\]

-

\[\nu \sim \text{ShiftedExp}(\frac{1}{29}, \text{shift}=1)\]

-

\(\nu\) is the degrees of freedom of the t distribution (lower values mean heavier tails). The value \(\frac{1}{29}\) is used to try to balance nearly normal distributions (\(\nu\gt 30\)) with heavy tailed distributions (\(\nu\lt 30\)).

-

For paired samples the test takes the difference between each paired sample and model just the paired differences using the one sample procedure.

-

As an eg let’s load a dataset with coffee yields and compare these yields in two different time periords (1960-80 amd 1980-2001) and see if the test recognize some statistical significant change:

-
d <- read.csv("roubik_2002_coffe_yield.csv")
-head(d)
-
##   world     country yield_61_to_80 yield_81_to_01
-## 1   new  Costa_Rica           9139          14620
-## 2   new     Bolivia           7686           8767
-## 3   new El_Salvador           9996           8729
-## 4   new   Guatemala           5488           8231
-## 5   new    Colombia           5920           7740
-## 6   new    Honduras           4096           7264
-
new.yield_61 <- d[,3][d$world=="new"]
-new.yield_61
-
##  [1] 9139 7686 9996 5488 5920 4096 4566 4965 5487 5227 2347 3089 1938
-
new.yield_81 <- d[,4][d$world=="new"]
-new.yield_81
-
##  [1] 14620  8767  8729  8231  7740  7264  6408  6283  5740  5116  4124
-## [12]  3240  2789
-
model <- bayes.t.test(new.yield_61, new.yield_81, paired=TRUE)
-model
-
## 
-##  Bayesian estimation supersedes the t test (BEST) - paired samples
-## 
-## data: new.yield_61 and new.yield_81, n = 13
-## 
-##   Estimates [95% credible interval]
-## mean paired difference: -1399 [-2462, -377]
-## sd of the paired differences: 1690 [915, 2727]
-## 
-## The mean difference is more than 0 by a probability of 0.006 
-## and less than 0 by a probability of 0.994
-

The \(95\)% credible interval does not include zero, so the test recognizes a statistical difference between the two samples.

-
summary(model)
-
##   Data
-## new.yield_61, n = 13
-## new.yield_81, n = 13
-## 
-##   Model parameters and generated quantities
-## mu_diff: the mean pairwise difference between new.yield_61 and new.yield_81 
-## sigma_diff: the scale of the pairwise difference, a consistent
-##   estimate of SD when nu is large.
-## nu: the degrees-of-freedom for the t distribution fitted to the pairwise difference
-## eff_size: the effect size calculated as (mu_diff - 0) / sigma_diff
-## diff_pred: predicted distribution for a new datapoint generated
-##   as the pairwise difference between new.yield_61 and new.yield_81 
-## 
-##   Measures
-##                mean      sd     HDIlo   HDIup %<comp %>comp
-## mu_diff    -1401.85  525.00 -2461.806 -376.69  0.994  0.006
-## sigma_diff  1757.19  487.99   915.427 2726.86  0.000  1.000
-## nu            29.21   27.57     1.011   84.65  0.000  1.000
-## eff_size      -0.85    0.36    -1.576   -0.18  0.994  0.006
-## diff_pred  -1420.79 2165.88 -5583.972 2803.76  0.781  0.219
-## 
-## 'HDIlo' and 'HDIup' are the limits of a 95% HDI credible interval.
-## '%<comp' and '%>comp' are the probabilities of the respective parameter being
-## smaller or larger than 0.
-## 
-##   Quantiles
-##                q2.5%      q25%    median      q75%   q97.5%
-## mu_diff    -2463.431 -1729.394 -1399.476 -1063.340 -377.569
-## sigma_diff  1002.421  1431.532  1689.791  2007.287 2868.776
-## nu             2.314     9.441    20.572    40.006  102.353
-## eff_size      -1.580    -1.079    -0.838    -0.608   -0.183
-## diff_pred  -5610.141 -2645.939 -1410.718  -183.086 2782.547
-
plot(model)
-

plot of chunk unnamed-chunk-8

-

The posterior predictive box presents a histogram with a smattering of t-distributions drawn from the posterior. If there is a large discrepancy between the model fit and the data then we need to think twice before proceeding. Herein it’s ok.

-
diagnostics(model)
-
## 
-## Iterations = 601:10600
-## Thinning interval = 1 
-## Number of chains = 3 
-## Sample size per chain = 10000 
-## 
-##   Diagnostic measures
-##                mean      sd mcmc_se n_eff  Rhat
-## mu_diff    -1401.85  525.00   4.291 15032 1.002
-## sigma_diff  1757.19  487.99   6.084  7160 1.014
-## nu            29.21   27.57   0.384  5203 1.001
-## eff_size      -0.85    0.36   0.003 14951 1.000
-## diff_pred  -1420.79 2165.88  12.971 27889 1.001
-## 
-## mcmc_se: the estimated standard error of the MCMC approximation of the mean.
-## n_eff: a crude measure of effective MCMC sample size.
-## Rhat: the potential scale reduction factor (at convergence, Rhat=1).
-## 
-##   Model parameters and generated quantities
-## mu_diff: the mean pairwise difference between new.yield_61 and new.yield_81 
-## sigma_diff: the scale of the pairwise difference, a consistent
-##   estimate of SD when nu is large.
-## nu: the degrees-of-freedom for the t distribution fitted to the pairwise difference
-## eff_size: the effect size calculated as (mu_diff - 0) / sigma_diff
-## diff_pred: predicted distribution for a new datapoint generated
-##   as the pairwise difference between new.yield_61 and new.yield_81
-

plot of chunk unnamed-chunk-9plot of chunk unnamed-chunk-9

-
model.code(model)
-
## ## Model code for Bayesian estimation supersedes the t test - paired samples ##
-## require(rjags)
-## 
-## # Setting up the data
-## x <- new.yield_61 
-## y <- new.yield_81 
-## pair_diff <- x - y
-## comp_mu <-  0 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   for(i in 1:length(pair_diff)) {
-##     pair_diff[i] ~ dt( mu_diff , tau_diff , nu )
-##   }
-##   diff_pred ~ dt( mu_diff , tau_diff , nu )
-##   eff_size <- (mu_diff - comp_mu) / sigma_diff
-##   
-##   mu_diff ~ dnorm( mean_mu , precision_mu )
-##   tau_diff <- 1/pow( sigma_diff , 2 )
-##   sigma_diff ~ dunif( sigma_low , sigma_high )
-##   # A trick to get an exponentially distributed prior on nu that starts at 1.
-##   nu <- nuMinusOne + 1 
-##   nuMinusOne ~ dexp(1/29)
-## }"
-## 
-## # Setting parameters for the priors that in practice will result
-## # in flat priors on mu and sigma.
-## mean_mu = mean(pair_diff, trim=0.2)
-## precision_mu = 1 / (mad(pair_diff)^2 * 1000000)
-## sigma_low = mad(pair_diff) / 1000 
-## sigma_high = mad(pair_diff) * 1000
-## 
-## # Initializing parameters to sensible starting values helps the convergence
-## # of the MCMC sampling. Here using robust estimates of the mean (trimmed)
-## # and standard deviation (MAD).
-## inits_list <- list(
-##   mu_diff = mean(pair_diff, trim=0.2),
-##   sigma_diff = mad(pair_diff),
-##   nuMinusOne = 4)
-## 
-## data_list <- list(
-##   pair_diff = pair_diff,
-##   comp_mu = comp_mu,
-##   mean_mu = mean_mu,
-##   precision_mu = precision_mu,
-##   sigma_low = sigma_low,
-##   sigma_high = sigma_high)
-## 
-## # The parameters to monitor.
-## params <- c("mu_diff", "sigma_diff", "nu", "eff_size", "diff_pred")
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = data_list,
-##                     inits = inits_list, n.chains = 3, n.adapt=1000)
-## update(model, 500) # Burning some samples to the MCMC gods....
-## samples <- coda.samples(model, params, n.iter=10000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-
-
-

Pearson Correlation Test

-

This is a measure of the linear correlation (dependence) between two variables \(X_1\) and \(X_2\), giving a value \(\rho\) between +1 and -1 inclusive, where 1 is total positive correlation, 0 is no correlation, and -1 is total negative correlation

-

\[\rho = \frac{\text{cov}(X_1,X_2)}{\sigma_{X_1} \sigma_{X_2}\]

-

Classical statistical inference based on Pearson’s correlation coefficient aims at test the null hypothesis that \(\rho=0\) and finding the p% confidence interval around \(r\) (the sample correlation) that contains \(\rho\).

-

The Pearson’s correlation coefficient is which assumes bivariate normality.

-

The model that a classical Pearson’s correlation test assumes is that between two paired variables \(X_{i1}\) and \(X_{i2}\) it follows a bivariate normal distribution, ie, \(X_i1 \sim \mathcal{N}(\mu_1,\sigma_1), X_i2 \sim \mathcal{N}(\mu_2,\sigma_2)\) and for each pair \((x_i,y_i)\) there is a linear dependency which is quantified by \(\rho\). Here’s an eg for \(\rho=0.3\):

-

-

The classical model pressuposes that \(X=(X_1,X_2)^T\) has a multivariate normal distribution:

-

\[X \sim \mathcal{N}(\mu,\Sigma)\]

-

where \(\mu=(\mu_1,\mu_2)^T\) and

-

\[\Sigma = -\left() \begin{array}{cc} -\sigma_1^2 & \rho\sigma_1\sigma_2 \\ -\rho\sigma_1\sigma_2 & \sigma_2^2 \end{array} \right)\]

-

This test is implemented by R function cor.test.

-

The following Bayesian model replaces the normal for a bivariate t distribution which is more robust to outliers (it could also be a normal, of course, the Bayesian framework is much more flexible in this sense).

-

The Bayesian model becomes

-

\[X \sim t(\mu,\Sigma,nu)\]

-

\[\rho \sim U(-1,1)\]

-

\[\mu_x,\mu_y \sim \mathcal{N}(M_{\mu}, \S_{\mu})\]

-

\[\sigma_{x_1}, \sigma_{x_2}\sim U(L_{\sigma}, U_{\sigma})\]

-

\[\nu \sim \text{ShiftedExp}(\frac{1}{29}, \text{shift}=1)\]

-

Let’s load some data:

-
d <- read.csv("2d4d_hone_2012.csv")
-head(d)
-
##   ratio_2d4d grip_kg  sex
-## 1     0.9427   54.19 male
-## 2     0.9336   52.16 male
-## 3     0.9460   51.15 male
-## 4     0.9527   51.15 male
-## 5     0.9178   50.14 male
-## 6     0.9386   50.16 male
-
plot(d$ratio_2d4d, d$grip_kg, col=unclass(d$sex), pch=18)
-legend("topright",c("female","male"), col=1:2, pch=18)
-

plot of chunk unnamed-chunk-10

-

There is a visual difference between the two variables concerning gender. Let’s try to find some pattern with this test

-
model.male <- bayes.cor.test( ~ ratio_2d4d + grip_kg, data=d[d$sex=="male",], n.iter = 5000)
-model.male
-
## 
-##  Bayesian First Aid Pearson's Correlation Coefficient Test
-## 
-## data: ratio_2d4d and grip_kg (n = 97)
-## Estimated correlation:
-##   -0.34 
-## 95% credible interval:
-##   -0.51 -0.15 
-## The correlation is more than 0 by a probability of <0.001 
-## and less than 0 by a probability of >0.999
-
summary(model.male)
-
##   Data
-## ratio_2d4d and grip_kg, n = 97
-## 
-##   Model parameters
-## rho: the correlation between ratio_2d4d and grip_kg 
-## mu[1]: the mean of ratio_2d4d 
-## sigma[1]: the scale of ratio_2d4d , a consistent
-##   estimate of SD when nu is large.
-## mu[2]: the mean of grip_kg 
-## sigma[2]: the scale of grip_kg 
-## nu: the degrees-of-freedom for the bivariate t distribution
-## 
-##   Measures
-##            mean     sd  HDIlo   HDIup %<comp %>comp
-## rho      -0.339  0.092 -0.511  -0.154  0.999  0.001
-## mu[1]     0.958  0.003  0.952   0.965  0.000  1.000
-## mu[2]    37.252  0.923 35.488  39.124  0.000  1.000
-## sigma[1]  0.032  0.003  0.028   0.037  0.000  1.000
-## sigma[2]  8.701  0.684  7.490  10.130  0.000  1.000
-## nu       47.783 31.402  6.589 110.502  0.000  1.000
-## 
-## 'HDIlo' and 'HDIup' are the limits of a 95% HDI credible interval.
-## '%<comp' and '%>comp' are the probabilities of the respective parameter being
-## smaller or larger than 0.
-## 
-##   Quantiles
-##           q2.5%   q25% median   q75%  q97.5%
-## rho      -0.506 -0.402 -0.345 -0.283  -0.143
-## mu[1]     0.951  0.956  0.958  0.960   0.965
-## mu[2]    35.442 36.646 37.243 37.870  39.086
-## sigma[1]  0.028  0.031  0.032  0.034   0.038
-## sigma[2]  7.458  8.228  8.667  9.140  10.112
-## nu       10.569 25.617 40.041 60.820 129.822
-
model.female <- bayes.cor.test( ~ ratio_2d4d + grip_kg, data=d[d$sex=="female",], n.iter = 5000)
-model.female
-
## 
-##  Bayesian First Aid Pearson's Correlation Coefficient Test
-## 
-## data: ratio_2d4d and grip_kg (n = 119)
-## Estimated correlation:
-##   -0.14 
-## 95% credible interval:
-##   -0.31 0.052 
-## The correlation is more than 0 by a probability of 0.064 
-## and less than 0 by a probability of 0.936
-
plot(model.male)
-

plot of chunk unnamed-chunk-11

-
plot(model.female)
-

plot of chunk unnamed-chunk-11

-

Both estimates indicate a slight negative correlation (the males more than the females). The two ellipses show the 50% (darker blue) and 95% (lighter blue) highest density regions. The red histograms show the marginal distributions of the data with a smatter of marginal densities drawn from the posterior. Looking at this plot we see that the model fits quite well, however, we could be concerned with the right skewness of the ratio_2d4d marginal which is not captured by the model (the t-distribution is symmetric).

-

To take a look at the posterior difference in correlation between the male and the female group, we first extract the MCMC samples from the Bayesian First Aid fit object using the as.data.frame function:

-
female.mcmc <- as.data.frame(model.female)
-  male.mcmc <- as.data.frame(model.male)
-
-hist(male.mcmc$rho-female.mcmc$rho, breaks=50, xlim=c(-1,1), main=bquote(paste("Density for ", rho, " male minus ", rho, " female")), yaxt="n", ylab="")
-

plot of chunk unnamed-chunk-12

-

And the entire code:

-
model.code(model.female)
-
## ## Model code for the Bayesian First Aid alternative to Pearson's correlation test. ##
-## require(rjags)
-## 
-## # Setting up the data
-## x <- d[d$sex == "female", ][ , "ratio_2d4d"] 
-## y <- d[d$sex == "female", ][ , "grip_kg"] 
-## xy <- cbind(x, y)
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   for(i in 1:n) {
-##     xy[i,1:2] ~ dmt(mu[], prec[ , ], nu) 
-##   }
-## 
-##   # JAGS parameterizes the multivariate t using precision (inverse of variance) 
-##   # rather than variance, therefore here inverting the covariance matrix.
-##   prec[1:2,1:2] <- inverse(cov[,])
-## 
-##   # Constructing the covariance matrix
-##   cov[1,1] <- sigma[1] * sigma[1]
-##   cov[1,2] <- sigma[1] * sigma[2] * rho
-##   cov[2,1] <- sigma[1] * sigma[2] * rho
-##   cov[2,2] <- sigma[2] * sigma[2]
-## 
-##   # Priors  
-##   rho ~ dunif(-1, 1)
-##   sigma[1] ~ dunif(sigmaLow, sigmaHigh) 
-##   sigma[2] ~ dunif(sigmaLow, sigmaHigh)
-##   mu[1] ~ dnorm(mean_mu, precision_mu)
-##   mu[2] ~ dnorm(mean_mu, precision_mu)
-##   nu <- nuMinusOne+1
-##   nuMinusOne ~ dexp(1/29)
-## }"
-## 
-## # Initializing the data list and setting parameters for the priors
-## # that in practice will result in flat priors on mu and sigma.
-## data_list = list(
-##   xy = xy, 
-##   n = length(x),
-##   mean_mu = mean(c(x, y), trim=0.2) ,
-##   precision_mu = 1 / (max(mad(x), mad(y))^2 * 1000000),
-##   sigmaLow = min(mad(x), mad(y)) / 1000 ,
-##   sigmaHigh = max(mad(x), mad(y)) * 1000)
-## 
-## # Initializing parameters to sensible starting values helps the convergence
-## # of the MCMC sampling. Here using robust estimates of the mean (trimmed)
-## # and standard deviation (MAD).
-## inits_list = list(mu=c(mean(x, trim=0.2), mean(y, trim=0.2)), rho=cor(x, y, method="spearman"), 
-##                   sigma = c(mad(x), mad(y)), nuMinusOne = 5)
-## 
-## # The parameters to monitor.
-## params <- c("rho", "mu", "sigma", "nu")
-##   
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = data_list,
-##                     inits = inits_list, n.chains = 3, n.adapt=1000)
-## update(model, 500) # Burning some samples to the MCMC gods....
-## samples <- coda.samples(model, params, n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-

For instance, if you wanted to replace \(\rho \sim U(-1,1)\) with a Beta, such that \(\rho \sim \text{Beta}(-1,1)\) we would replace

-
rho ~ dunif(-1,1)
-

with

-
rho_half_width ~ dbeta(1,1)
-rho ~ 2*rho_half_width - 1  # shift and strech from [0,1] to[-1,1]
-

and replace the inits_lit variable:

-
# from 
-rho=cor(x, y, method="spearman")
-# to
-rho_half_width=( cor(x,y,method="spearman") + 1 ) / 2
-

By changing the parameter values of dbeta we could define several priors, placing more probability mass at that value of rho we know is more probable.

-

Goto part2

-
-
- - -
- - - - - - - - diff --git a/bayes.packages/part2.Rmd b/bayes.packages/part2.Rmd deleted file mode 100644 index 808ef9d..0000000 --- a/bayes.packages/part2.Rmd +++ /dev/null @@ -1,278 +0,0 @@ ---- -title: "Bayesian Model Packages" -author: "João Neto" -date: October 2014 -output: - html_document: - toc: true - toc_depth: 3 - fig_width: 6 - fig_height: 6 -cache: yes ---- - -## Bayesian First Aid (cont.) - -```{r, warning=FALSE, message=FALSE,echo=FALSE} -library(BayesianFirstAid) -``` - -### Test of Proportions - -A lot of questions out there involves estimating the proportion or relative frequency of success of two or more groups (where success could be a saved life, a click on a link, or a happy baby) and there exists a little known R function that does just that, `prop.test`. Here we'll use its Bayesian version `bayes.prop.test`. - -This is an extension of the binomial test which estimates the underlying relative frequency of success given a number of trials. - -For $m$ different trials, in the i-th trial there were $x_1$ successes out of $n_i$ trials, so: - -$$x_i \sim \text{Binomial}(\theta_i, n_i)$$ - -$$\theta_i \sim \text{Beta}(1,1)$$ - -Here's an eg with two trials: - -```{r} -trial.1 <- c( 43, 275) -trial.2 <- c(170,1454) -model <- bayes.prop.test(trial.1, trial.2) -model -``` - -It seems that the first trial has more successes by around 7\%. However this is not very solid evidence since the 95\% confidence interval includes 0 even if barely. - -We can calculate the probability that the difference between the two trials is small (say 5\%): - -```{r} -ts <- as.data.frame(model) -head(ts) -diff <- mean(abs( ts$theta1 - ts$theta2 ) < 0.05) # check Kruschke's ROPE -diff -``` - -So, there's a `r round(100*diff,0)`\% that the relative frequency of successes in the two trials is equivalent, which is weak evidence for the 'no difference' hypothesis. - - -```{r} -plot(model) -diagnostics(model) -model.code(model) -``` - -Let's see an eg with four groups: - -```{r, fig.height=12, fig.width=12} -smokers <- c(83, 90, 129, 70) -patients <- c(86, 93, 136, 82) -model <- bayes.prop.test(smokers, patients) -model -plot(model) -``` - -The 4th group seems slighty different from the others. - -```{r} -model.code(model) -``` - -### Poisson Test - -Given a set of counts per time period, and assuming a Poisson distribution, the goal is to estimate the $\lambda$ parameter of the Poisson. It assumes that every count comes from equal periods of time, and that the parameter is fixed, ie, all counts com from the same distribution. - -```{r} -sales.per.period <- c(14,16,9,18,10,6,13) -poisson.test(x=sum(sales.per.period), T=length(sales.per.period),r=10) # r -- hypothesized rate -``` - -The bayes version uses the following model: - -$$x \sim \text{Poisson}(\lambda_{\text{total}})$$ - -$$\lambda_{\text{total}} = \lambda . T$$ - -$$\lambda \sim \text{Gamma}(0.5,0.00001)$$ - -The $\text{Gamma}(0.5,0.00001)$ is the JAGS-friendly approximation of the Jeffrey's prior for the parameter of the Poisson (which is $p(\lambda) \propto 1/\sqrt{\lambda}$). - -Using `bayes.poisson.text`: - -```{r} -model <- bayes.poisson.test(x=sum(sales.per.period), T=length(sales.per.period), r=10) -model -plot(model) -diagnostics(model) -model.code(model) -``` - -The test accepts two different counts and compare its ratios. In the following eg we are comparing if the first group, that was X-rayed, the cancer rate is 1.5 higher than in the 2nd group, the control group: - -```{r} -cancer.cases <- c(41,15) -person.per.thousand <- c(28.011,19.025) -model <- bayes.poisson.test(x=cancer.cases, T=person.per.thousand, r=1.5) -model -``` - -So, there is evidence, around 75\%, that the cancer rate after the patients being X-rayed, is higher than 1.5 times the control group. - -```{r} -plot(model) -diagnostics(model) -model.code(model) -``` - -It's possible to add Poisson tests for more than two groups. Just copy-paste the R and JAGS code above, and change the input data for longer vectors. Then update the `for(group_i in 1:2)` to the required group size. - -# Zelig package - -Zelig is a unified framework for a large range of statistical models. Here in we'll check [its](http://cran.r-project.org/web/packages/Zelig/vignettes/manual-bayes.pdf) bayesian models. - -```{r, warning=FALSE, message=FALSE} -library(MCMCpack) -library(Zelig) -``` - -## Bayesian Logistic Regression - -A logistic model for $p_i = P(Z_i=1|X_i)$ is - -$$logit(p_i) = \log(\frac{p_i}{1-p_i}) = \beta_0 + \beta_1 \log(x_i)$$ - -$$\beta_0, \beta_1 \sim U(-\infty,+\infty)$$ - -The model option for `zelig` is `model = "logit.bayes"`. Here's an eg of training and testing using the bayesian logistic regression (check [here](http://web.cse.ohio-state.edu/~kulis/teaching/788_sp12/scribe_notes/lecture6.pdf) for more info): - -```{r} -head(mtcars) - -set.seed(101) -n <- nrow(mtcars) -sample.set <- sample(1:n, 0.7*n) -train.set <- mtcars[sample.set,] -test.set <- mtcars[-sample.set,] - -# model the probability of a manual transmission in a vehicle based on its engine horsepower & weight -z.out <- zelig(am ~ hp + wt, model = "logit.bayes", data = train.set, verbose=FALSE, cite=FALSE) -# test a new record: -x.out <- setx(z.out, wt=test.set[1,"wt"], hp=test.set[1,"hp"]) # this is test.set[1,] -s.out <- sim(z.out, x = x.out) -summary(s.out) -test.set[1,"am"] # compare with real value - -# check the entire test set -ams <- rep(NA, nrow(test.set)) -for(i in 1:nrow(test.set)) { - - x.out <- setx(z.out, wt=test.set[i,"wt"], hp=test.set[i,"hp"]) - s.out <- sim(z.out, x = x.out) - - ams[i] <- which.max(s.out$stats$`Predicted Value: Y|X`)-1 -} -table(test.set$`am`, ams, dnn = c("real","predicted")) -``` - - - -To check more bayesian models from this package check [Zelig's manual](http://cran.r-project.org/web/packages/Zelig/vignettes/manual-bayes.pdf). - -# Laplace's Demon - -This is another package that offers many different kinds of MCMC. Check their [webpage](http://www.bayesian-inference.com/software) for more info. - -```{r, eval=FALSE} -# to install, download from http://www.bayesian-inference.com/softwaredownload -install.packages(pkgs="path\\LaplacesDemon_[version].tar.gz", repos=NULL, type="source") - -# check package documentation -vignette("BayesianInference") -vignette("LaplacesDemonTutorial") -vignette("Examples") -``` - -Let's implement the following model ([ref](http://www.sumsar.net/blog/2013/06/three-ways-to-run-bayesian-models-in-r/)): - -$$y_i \sim \mathcal{N}(\mu,\sigma)$$ -$$\mu \sim \mathcal{N}(0,100)$$ -$$\sigma \sim \text{LogNormal}(0,4)$$ - -and get some data: - -```{r} -set.seed(1337) -y <- rnorm(20,10,5) -``` - -There is no special mechanism for keeping the parameters inside a bounded range, therefore $\sigma$ is sampled on the log-scale and then exponentiated to make sure it is always positive. - -```{r, message=FALSE, results=FALSE} -library(LaplacesDemon) - -model <- function(theta, data) { - mu <- theta[1] - sigma <- exp(theta[2]) - log_lik <- sum( dnorm(data$y, mu, sigma, log=T) ) # sum ( log p(y_i|theta) ) - log_post <- log_lik + dnorm(mu, 0, 100, log=T) + dlnorm(sigma, 0, 4, log=T) - - # return list in package required format - list(LP=log_post, - Dev= -2*log_lik, - Monitor=c(log_post,sigma), - yhat=NA, - parm=theta) -} - -data.list <- list(N=length(y), y=y, mon.names=c("log_post","sigma"), parm.names=c("mu","log.sigma")) -mcmc.samples <- LaplacesDemon(Model=model, - Data=data.list, - Iterations=1e4, - Algorithm="HARM", # Hit-and-Run Metropolis, www.bayesian-inference.com/mcmcharm - Thinning=1 - ) -``` - -We can present the results from the sampling: - -```{r} -Consort(mcmc.samples) -plot(mcmc.samples, BurnIn=1e3, data.list) -``` - -The modelling with this package is less user-friendly since there is no declarative language like in BUGS, JAGS or STAN. However it has the possibility of lots of configuration options. diff --git a/bayes.packages/part2.html b/bayes.packages/part2.html deleted file mode 100644 index 56879b0..0000000 --- a/bayes.packages/part2.html +++ /dev/null @@ -1,795 +0,0 @@ - - - - - - - - - - - - - - -Bayesian Model Packages - - - - - - - - - - - - - - - - - - - - -
- - - - - - -
-

Bayesian First Aid (cont.)

-
-

Test of Proportions

-

A lot of questions out there involves estimating the proportion or relative frequency of success of two or more groups (where success could be a saved life, a click on a link, or a happy baby) and there exists a little known R function that does just that, prop.test. Here we’ll use its Bayesian version bayes.prop.test.

-

This is an extension of the binomial test which estimates the underlying relative frequency of success given a number of trials.

-

For \(m\) different trials, in the i-th trial there were \(x_1\) successes out of \(n_i\) trials, so:

-

\[x_i \sim \text{Binomial}(\theta_i, n_i)\]

-

\[\theta_i \sim \text{Beta}(1,1)\]

-

Here’s an eg with two trials:

-
trial.1 <- c( 43, 275)
-trial.2 <- c(170,1454)
-model <- bayes.prop.test(trial.1, trial.2)
-model
-
## 
-##  Bayesian First Aid propotion test
-## 
-## data: trial.1 out of trial.2
-## number of successes:    43,  275
-## number of trials:      170, 1454
-## Estimated relative frequency of success [95% credible interval]:
-##   Group 1: 0.26 [0.19, 0.32]
-##   Group 2: 0.19 [0.17, 0.21]
-## Estimated group difference (Group 1 - Group 2):
-##   0.07 [-0.0034, 0.13]
-## The relative frequency of success is larger for Group 1 by a probability
-## of 0.975 and larger for Group 2 by a probability of 0.025 .
-

It seems that the first trial has more successes by around 7%. However this is not very solid evidence since the 95% confidence interval includes 0 even if barely.

-

We can calculate the probability that the difference between the two trials is small (say 5%):

-
ts <- as.data.frame(model)
-head(ts)
-
##   theta1 theta2 x_pred1 x_pred2
-## 1 0.3004 0.1976      46     305
-## 2 0.2749 0.1769      58     279
-## 3 0.2518 0.1836      39     263
-## 4 0.2867 0.1751      48     258
-## 5 0.2024 0.1986      36     309
-## 6 0.2417 0.1900      47     282
-
diff <- mean(abs( ts$theta1 - ts$theta2 ) < 0.05) # check Kruschke's ROPE
-diff
-
## [1] 0.3277
-

So, there’s a 33% that the relative frequency of successes in the two trials is equivalent, which is weak evidence for the ‘no difference’ hypothesis.

-
plot(model)
-

plot of chunk unnamed-chunk-4

-
diagnostics(model)
-
## 
-## Iterations = 1:5000
-## Thinning interval = 1 
-## Number of chains = 3 
-## Sample size per chain = 5000 
-## 
-##   Diagnostic measures
-##                    mean     sd mcmc_se n_eff  Rhat
-## theta[1]          0.256  0.033   0.000 14727 1.000
-## theta[2]          0.190  0.010   0.000 14791 1.000
-## x_pred[1]        43.451  8.024   0.067 14311 1.000
-## x_pred[2]       275.637 20.968   0.175 14385 1.001
-## theta_diff[1,2]   0.066  0.035      NA    NA    NA
-## 
-## mcmc_se: the estimated standard error of the MCMC approximation of the mean.
-## n_eff: a crude measure of effective MCMC sample size.
-## Rhat: the potential scale reduction factor (at convergence, Rhat=1).
-## 
-##   Model parameters and generated quantities
-## theta: The relative frequency of success
-## x_pred: Predicted number of successes in a replication
-## theta_diff[i,j]: the difference between two groups (theta[i] - theta[j])
-

plot of chunk unnamed-chunk-4

-
model.code(model)
-
## ### Model code for the Bayesian First Aid  ###
-## ### alternative to the test of proportions ###
-## require(rjags)
-## 
-## # Setting up the data
-## x <- c(43, 275) 
-## n <- c(170, 1454) 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   for(i in 1:length(x)) {
-##     x[i] ~ dbinom(theta[i], n[i])
-##     theta[i] ~ dbeta(1, 1)
-##     x_pred[i] ~ dbinom(theta[i], n[i])
-##   }
-## }"
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = list(x = x, n = n), 
-##                     n.chains = 3, n.adapt=1000)
-## samples <- coda.samples(model, c("theta", "x_pred"), n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-## 
-## # You can extract the mcmc samples as a matrix and compare the thetas 
-## # of the groups. For example, the following shows the median and 95%
-## # credible interval for the difference between Group 1 and Group 2.
-## samp_mat <- as.matrix(samples)
-## quantile(samp_mat[, "theta[1]"] - samp_mat[, "theta[2]"], c(0.025, 0.5, 0.975))
-

Let’s see an eg with four groups:

-
smokers  <- c(83, 90, 129, 70)
-patients <- c(86, 93, 136, 82)
-model <- bayes.prop.test(smokers, patients)
-model
-
## 
-##  Bayesian First Aid propotion test
-## 
-## data: smokers out of patients
-## number of successes:   83,  90, 129,  70
-## number of trials:      86,  93, 136,  82
-## Estimated relative frequency of success [95% credible interval]:
-##   Group 1: 0.96 [0.91, 0.99]
-##   Group 2: 0.96 [0.92, 0.99]
-##   Group 3: 0.94 [0.90, 0.98]
-##   Group 4: 0.85 [0.77, 0.92]
-## Estimated pairwise group differences (row - column) with 95 % cred. intervals:
-##                         Group                        
-##            2               3               4       
-##   1        0             0.01            0.11      
-##     [-0.064, 0.055] [-0.045, 0.072]  [0.023, 0.2]  
-##   2                      0.02            0.11      
-##                     [-0.042, 0.072]  [0.025, 0.2]  
-##   3                                      0.09      
-##                                      [0.014, 0.18]
-
plot(model)
-

plot of chunk unnamed-chunk-5

-

The 4th group seems slighty different from the others.

-
model.code(model)
-
## ### Model code for the Bayesian First Aid  ###
-## ### alternative to the test of proportions ###
-## require(rjags)
-## 
-## # Setting up the data
-## x <- c(83, 90, 129, 70) 
-## n <- c(86, 93, 136, 82) 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   for(i in 1:length(x)) {
-##     x[i] ~ dbinom(theta[i], n[i])
-##     theta[i] ~ dbeta(1, 1)
-##     x_pred[i] ~ dbinom(theta[i], n[i])
-##   }
-## }"
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = list(x = x, n = n), 
-##                     n.chains = 3, n.adapt=1000)
-## samples <- coda.samples(model, c("theta", "x_pred"), n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-## 
-## # You can extract the mcmc samples as a matrix and compare the thetas 
-## # of the groups. For example, the following shows the median and 95%
-## # credible interval for the difference between Group 1 and Group 2.
-## samp_mat <- as.matrix(samples)
-## quantile(samp_mat[, "theta[1]"] - samp_mat[, "theta[2]"], c(0.025, 0.5, 0.975))
-
-
-

Poisson Test

-

Given a set of counts per time period, and assuming a Poisson distribution, the goal is to estimate the \(\lambda\) parameter of the Poisson. It assumes that every count comes from equal periods of time, and that the parameter is fixed, ie, all counts com from the same distribution.

-
sales.per.period <- c(14,16,9,18,10,6,13)
-poisson.test(x=sum(sales.per.period), T=length(sales.per.period),r=10) # r -- hypothesized rate
-
## 
-##  Exact Poisson test
-## 
-## data:  sum(sales.per.period) time base: length(sales.per.period)
-## number of events = 86, time base = 7, p-value = 0.06345
-## alternative hypothesis: true event rate is not equal to 10
-## 95 percent confidence interval:
-##   9.827 15.173
-## sample estimates:
-## event rate 
-##      12.29
-

The bayes version uses the following model:

-

\[x \sim \text{Poisson}(\lambda_{\text{total}})\]

-

\[\lambda_{\text{total}} = \lambda . T\]

-

\[\lambda \sim \text{Gamma}(0.5,0.00001)\]

-

The \(\text{Gamma}(0.5,0.00001)\) is the JAGS-friendly approximation of the Jeffrey’s prior for the parameter of the Poisson (which is \(p(\lambda) \propto 1/\sqrt{\lambda}\)).

-

Using bayes.poisson.text:

-
model <- bayes.poisson.test(x=sum(sales.per.period), T=length(sales.per.period), r=10)
-model
-
## 
-##  Bayesian Fist Aid poisson test - one sample
-## 
-## number of events: 86, time periods: 7
-## Estimated event rate:
-##   12 
-## 95% credible interval:
-##   9.7 15 
-## The event rate is more than 10 by a probability of 0.969 
-## and less than 10 by a probability of 0.031  .
-
plot(model)
-

plot of chunk unnamed-chunk-8

-
diagnostics(model)
-
## 
-## Iterations = 101:5100
-## Thinning interval = 1 
-## Number of chains = 3 
-## Sample size per chain = 5000 
-## 
-##   Diagnostic measures
-##         mean     sd mcmc_se n_eff  Rhat
-## lambda 12.35  1.325   0.011 15313 1.001
-## x_pred 86.45 13.083   0.104 15741 1.001
-## 
-## mcmc_se: the estimated standard error of the MCMC approximation of the mean.
-## n_eff: a crude measure of effective MCMC sample size.
-## Rhat: the potential scale reduction factor (at convergence, Rhat=1).
-## 
-##   Model parameters and generated quantities
-## lambda: the rate of the process.
-## x_pred: predicted event count during 7 periods.
-

plot of chunk unnamed-chunk-8

-
model.code(model)
-
## ### Model code for the Bayesian First Aid one sample Poisson test ###
-## require(rjags)
-## 
-## # Setting up the data
-## x <- 86 
-## t <- 7 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   x ~ dpois(lambda * t)
-##   lambda ~ dgamma(0.5, 0.00001)
-##   x_pred ~ dpois(lambda * t)
-## }"
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = list(x = x, t = t), n.chains = 3)
-## samples <- coda.samples(model, c("lambda", "x_pred"), n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-

The test accepts two different counts and compare its ratios. In the following eg we are comparing if the first group, that was X-rayed, the cancer rate is 1.5 higher than in the 2nd group, the control group:

-
cancer.cases <- c(41,15)
-person.per.thousand  <- c(28.011,19.025)
-model <- bayes.poisson.test(x=cancer.cases, T=person.per.thousand, r=1.5)
-model
-
## 
-##  Bayesian Fist Aid poisson test - two sample
-## 
-## number of events: 41 and 15, time periods: 28.011 and 19.025
-## 
-##   Estimates [95% credible interval]
-## Group 1 rate: 1.5 [1.0, 1.9]
-## Group 2 rate: 0.80 [0.42, 1.2]
-## Rate ratio (Group 1 rate / Group 2 rate):
-##               1.8 [1.1, 3.5]
-## 
-## The event rate of group 1 is more than 1.5 times that of group 2 by a probability 
-## of 0.757 and less than 1.5 times that of group 2 by a probability of 0.243 .
-

So, there is evidence, around 75%, that the cancer rate after the patients being X-rayed, is higher than 1.5 times the control group.

-
plot(model)
-

plot of chunk unnamed-chunk-10

-
diagnostics(model)
-
## 
-## Iterations = 101:5100
-## Thinning interval = 1 
-## Number of chains = 3 
-## Sample size per chain = 5000 
-## 
-##   Diagnostic measures
-##              mean    sd mcmc_se n_eff Rhat
-## lambda[1]   1.485 0.230   0.002 15000    1
-## lambda[2]   0.815 0.208   0.002 15000    1
-## x_pred[1]  41.547 9.128   0.075 15000    1
-## x_pred[2]  15.501 5.576   0.046 14814    1
-## rate_diff   0.670 0.310   0.003 15000    1
-## rate_ratio  1.860    NA   0.005 14512    1
-## 
-## mcmc_se: the estimated standard error of the MCMC approximation of the mean.
-## n_eff: a crude measure of effective MCMC sample size.
-## Rhat: the potential scale reduction factor (at convergence, Rhat=1).
-## 
-##   Model parameters and generated quantities
-## lambda[1]: the rate of the process of group 1.
-## lambda[2]: the rate of the process of group 2.
-## x_pred[1]: predicted event count of group 1 during 28.01 periods.
-## x_pred[2]: predicted event count of group 2 during 19.02 periods.
-## rate_diff: The difference lambda[1] - lambda[2].
-## rate_ratio: The ratio lambda[1] / lambda[2].
-

plot of chunk unnamed-chunk-10plot of chunk unnamed-chunk-10

-
model.code(model)
-
## ### Model code for the Bayesian First Aid two sample Poisson test ###
-## require(rjags)
-## 
-## # Setting up the data
-## x <- c(41, 15) 
-## t <- c(28.011, 19.025) 
-## 
-## # The model string written in the JAGS language
-## model_string <- "model {
-##   for(group_i in 1:2) {
-##     x[group_i] ~ dpois(lambda[group_i] * t[group_i])
-##     lambda[group_i] ~ dgamma(0.5, 0.00001)
-##     x_pred[group_i] ~ dpois(lambda[group_i] * t[group_i])
-##   }
-##   rate_diff <- lambda[1] - lambda[2]
-##   rate_ratio <- lambda[1] / lambda[2]
-## }"
-## 
-## # Running the model
-## model <- jags.model(textConnection(model_string), data = list(x = x, t = t), n.chains = 3)
-## samples <- coda.samples(model, c("lambda", "x_pred", "rate_diff", "rate_ratio"), n.iter=5000)
-## 
-## # Inspecting the posterior
-## plot(samples)
-## summary(samples)
-

It’s possible to add Poisson tests for more than two groups. Just copy-paste the R and JAGS code above, and change the input data for longer vectors. Then update the for(group_i in 1:2) to the required group size.

-
-
-
-

Zelig package

-

Zelig is a unified framework for a large range of statistical models. Here in we’ll check its bayesian models.

-
library(MCMCpack)
-library(Zelig)
-
-

Bayesian Logistic Regression

-

A logistic model for \(p_i = P(Z_i=1|X_i)\) is

-

\[logit(p_i) = \log(\frac{p_i}{1-p_i}) = \beta_0 + \beta_1 \log(x_i)\]

-

\[\beta_0, \beta_1 \sim U(-\infty,+\infty)\]

-

The model option for zelig is model = "logit.bayes". Here’s an eg of training and testing using the bayesian logistic regression (check here for more info):

-
head(mtcars)
-
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
-## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
-## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
-## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
-## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
-## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
-## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1
-
set.seed(101)
-n <- nrow(mtcars)
-sample.set <- sample(1:n, 0.7*n)
-train.set  <- mtcars[sample.set,]
-test.set   <- mtcars[-sample.set,]
-
-# model the probability of a manual transmission in a vehicle based on its engine horsepower & weight
-z.out <- zelig(am ~ hp + wt, model = "logit.bayes", data = train.set, verbose=FALSE, cite=FALSE)
-# test a new record:
-x.out <- setx(z.out, wt=test.set[1,"wt"], hp=test.set[1,"hp"]) # this is test.set[1,]
-s.out <- sim(z.out, x = x.out)
-summary(s.out)
-
## 
-## Model:  logit.bayes 
-## Number of simulations:  1000 
-## 
-## Values of X
-##            (Intercept) hp   wt
-## Merc 450SE           1 93 2.32
-## attr(,"assign")
-## [1] 0 1 2
-## 
-## Expected Value: E(Y|X) 
-##             mean  sd   50% 2.5% 97.5%
-## Merc 450SE 0.934 0.1 0.974 0.63     1
-## 
-## Predicted Value: Y|X 
-##                0     1
-## Merc 450SE 0.068 0.932
-
test.set[1,"am"] # compare with real value
-
## [1] 1
-
# check the entire test set
-ams <- rep(NA, nrow(test.set))
-for(i in 1:nrow(test.set)) {
-   
-  x.out <- setx(z.out, wt=test.set[i,"wt"], hp=test.set[i,"hp"])
-  s.out <- sim(z.out, x = x.out)
-  
-  ams[i] <- which.max(s.out$stats$`Predicted Value: Y|X`)-1
-}
-table(test.set$`am`, ams, dnn = c("real","predicted"))
-
##     predicted
-## real 0 1
-##    0 4 0
-##    1 1 5
- - -

To check more bayesian models from this package check Zelig’s manual.

-
-
-
-

Laplace’s Demon

-

This is another package that offers many different kinds of MCMC. Check their webpage for more info.

-
# to install, download from http://www.bayesian-inference.com/softwaredownload
-install.packages(pkgs="path\\LaplacesDemon_[version].tar.gz", repos=NULL, type="source")
-
-# check package documentation
-vignette("BayesianInference")
-vignette("LaplacesDemonTutorial")
-vignette("Examples")
-

Let’s implement the following model (ref):

-

\[y_i \sim \mathcal{N}(\mu,\sigma)\] \[\mu \sim \mathcal{N}(0,100)\] \[\sigma \sim \text{LogNormal}(0,4)\]

-

and get some data:

-
set.seed(1337)
-y <- rnorm(20,10,5)
-

There is no special mechanism for keeping the parameters inside a bounded range, therefore \(\sigma\) is sampled on the log-scale and then exponentiated to make sure it is always positive.

-
library(LaplacesDemon)
-
-model <- function(theta, data) {
-  mu       <- theta[1]
-  sigma    <- exp(theta[2])
-  log_lik  <- sum( dnorm(data$y, mu, sigma, log=T) )  # sum ( log p(y_i|theta) )
-  log_post <- log_lik + dnorm(mu, 0, 100, log=T) + dlnorm(sigma, 0, 4, log=T)
-  
-  # return list in package required format
-  list(LP=log_post, 
-       Dev= -2*log_lik, 
-       Monitor=c(log_post,sigma),
-       yhat=NA,
-       parm=theta)
-}
-
-data.list <- list(N=length(y), y=y, mon.names=c("log_post","sigma"), parm.names=c("mu","log.sigma"))
-mcmc.samples <- LaplacesDemon(Model=model, 
-                              Data=data.list, 
-                              Iterations=1e4, 
-                              Algorithm="HARM", # Hit-and-Run Metropolis, www.bayesian-inference.com/mcmcharm
-                              Thinning=1
-                             )
-
## 
-## Laplace's Demon was called on Mon Oct 13 12:50:10 2014
-## 
-## Performing initial checks...
-## WARNING: Initial Values were not supplied.
-## Suggestion: 1 possible instance(s) of for loops
-##      were found in the Model specification. Iteration speed will
-##      increase if for loops are vectorized in R or coded in a
-##      faster language such as C++ via the Rcpp package.
-## 
-## Laplace Approximation will be used on initial values.
-## Suggestion: 1  possible instance(s) of for loops
-##      were found in the Model specification. Iteration speed will
-##      increase if for loops are vectorized in R or coded in a
-##      faster language such as C++ via the Rcpp package.
-## Sample Size:  20 
-## Laplace Approximation begins...
-## Iteration:  10  of  100 ,   LP:  -91.2 
-## Iteration:  20  of  100 ,   LP:  -85.6 
-## Iteration:  30  of  100 ,   LP:  -82.8 
-## Iteration:  40  of  100 ,   LP:  -79 
-## Iteration:  50  of  100 ,   LP:  -72.9 
-## Estimating the Covariance Matrix
-## Creating Summary from Point-Estimates
-## Estimating Log of the Marginal Likelihood
-## Laplace Approximation is finished.
-## 
-## The covariance matrix from Laplace Approximation has been scaled
-## for Laplace's Demon, and the posterior modes are now the initial
-## values for Laplace's Demon.
-## 
-## Algorithm: Hit-And-Run Metropolis 
-## 
-## Laplace's Demon is beginning to update...
-## Iteration: 100Iteration: 100,   Proposal: Multivariate,   LP:-73.5
-## Iteration: 200Iteration: 200,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 300Iteration: 300,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 400Iteration: 400,   Proposal: Multivariate,   LP:-74.5
-## Iteration: 500Iteration: 500,   Proposal: Multivariate,   LP:-73
-## Iteration: 600Iteration: 600,   Proposal: Multivariate,   LP:-73.5
-## Iteration: 700Iteration: 700,   Proposal: Multivariate,   LP:-73.8
-## Iteration: 800Iteration: 800,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 900Iteration: 900,   Proposal: Multivariate,   LP:-72.5
-## Iteration: 1000Iteration: 1000,   Proposal: Multivariate,   LP:-74
-## Iteration: 1100Iteration: 1100,   Proposal: Multivariate,   LP:-73.9
-## Iteration: 1200Iteration: 1200,   Proposal: Multivariate,   LP:-73.8
-## Iteration: 1300Iteration: 1300,   Proposal: Multivariate,   LP:-73
-## Iteration: 1400Iteration: 1400,   Proposal: Multivariate,   LP:-74.3
-## Iteration: 1500Iteration: 1500,   Proposal: Multivariate,   LP:-74.8
-## Iteration: 1600Iteration: 1600,   Proposal: Multivariate,   LP:-74.2
-## Iteration: 1700Iteration: 1700,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 1800Iteration: 1800,   Proposal: Multivariate,   LP:-76.3
-## Iteration: 1900Iteration: 1900,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 2000Iteration: 2000,   Proposal: Multivariate,   LP:-74.2
-## Iteration: 2100Iteration: 2100,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 2200Iteration: 2200,   Proposal: Multivariate,   LP:-75.3
-## Iteration: 2300Iteration: 2300,   Proposal: Multivariate,   LP:-73.7
-## Iteration: 2400Iteration: 2400,   Proposal: Multivariate,   LP:-73.2
-## Iteration: 2500Iteration: 2500,   Proposal: Multivariate,   LP:-73.4
-## Iteration: 2600Iteration: 2600,   Proposal: Multivariate,   LP:-72.5
-## Iteration: 2700Iteration: 2700,   Proposal: Multivariate,   LP:-75.1
-## Iteration: 2800Iteration: 2800,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 2900Iteration: 2900,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 3000Iteration: 3000,   Proposal: Multivariate,   LP:-74.4
-## Iteration: 3100Iteration: 3100,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 3200Iteration: 3200,   Proposal: Multivariate,   LP:-73
-## Iteration: 3300Iteration: 3300,   Proposal: Multivariate,   LP:-72.5
-## Iteration: 3400Iteration: 3400,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 3500Iteration: 3500,   Proposal: Multivariate,   LP:-73.5
-## Iteration: 3600Iteration: 3600,   Proposal: Multivariate,   LP:-74.4
-## Iteration: 3700Iteration: 3700,   Proposal: Multivariate,   LP:-74.8
-## Iteration: 3800Iteration: 3800,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 3900Iteration: 3900,   Proposal: Multivariate,   LP:-74.1
-## Iteration: 4000Iteration: 4000,   Proposal: Multivariate,   LP:-73.9
-## Iteration: 4100Iteration: 4100,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 4200Iteration: 4200,   Proposal: Multivariate,   LP:-74.9
-## Iteration: 4300Iteration: 4300,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 4400Iteration: 4400,   Proposal: Multivariate,   LP:-73.8
-## Iteration: 4500Iteration: 4500,   Proposal: Multivariate,   LP:-72.6
-## Iteration: 4600Iteration: 4600,   Proposal: Multivariate,   LP:-73.9
-## Iteration: 4700Iteration: 4700,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 4800Iteration: 4800,   Proposal: Multivariate,   LP:-73
-## Iteration: 4900Iteration: 4900,   Proposal: Multivariate,   LP:-73.4
-## Iteration: 5000Iteration: 5000,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 5100Iteration: 5100,   Proposal: Multivariate,   LP:-73.3
-## Iteration: 5200Iteration: 5200,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 5300Iteration: 5300,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 5400Iteration: 5400,   Proposal: Multivariate,   LP:-75.7
-## Iteration: 5500Iteration: 5500,   Proposal: Multivariate,   LP:-73.8
-## Iteration: 5600Iteration: 5600,   Proposal: Multivariate,   LP:-73.2
-## Iteration: 5700Iteration: 5700,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 5800Iteration: 5800,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 5900Iteration: 5900,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 6000Iteration: 6000,   Proposal: Multivariate,   LP:-73.6
-## Iteration: 6100Iteration: 6100,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 6200Iteration: 6200,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 6300Iteration: 6300,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 6400Iteration: 6400,   Proposal: Multivariate,   LP:-74
-## Iteration: 6500Iteration: 6500,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 6600Iteration: 6600,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 6700Iteration: 6700,   Proposal: Multivariate,   LP:-74.9
-## Iteration: 6800Iteration: 6800,   Proposal: Multivariate,   LP:-73
-## Iteration: 6900Iteration: 6900,   Proposal: Multivariate,   LP:-73.6
-## Iteration: 7000Iteration: 7000,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 7100Iteration: 7100,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 7200Iteration: 7200,   Proposal: Multivariate,   LP:-73.1
-## Iteration: 7300Iteration: 7300,   Proposal: Multivariate,   LP:-73
-## Iteration: 7400Iteration: 7400,   Proposal: Multivariate,   LP:-72.6
-## Iteration: 7500Iteration: 7500,   Proposal: Multivariate,   LP:-73.6
-## Iteration: 7600Iteration: 7600,   Proposal: Multivariate,   LP:-74.6
-## Iteration: 7700Iteration: 7700,   Proposal: Multivariate,   LP:-73.6
-## Iteration: 7800Iteration: 7800,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 7900Iteration: 7900,   Proposal: Multivariate,   LP:-74.1
-## Iteration: 8000Iteration: 8000,   Proposal: Multivariate,   LP:-73.5
-## Iteration: 8100Iteration: 8100,   Proposal: Multivariate,   LP:-74.3
-## Iteration: 8200Iteration: 8200,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 8300Iteration: 8300,   Proposal: Multivariate,   LP:-72.5
-## Iteration: 8400Iteration: 8400,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 8500Iteration: 8500,   Proposal: Multivariate,   LP:-72.8
-## Iteration: 8600Iteration: 8600,   Proposal: Multivariate,   LP:-72.7
-## Iteration: 8700Iteration: 8700,   Proposal: Multivariate,   LP:-72.9
-## Iteration: 8800Iteration: 8800,   Proposal: Multivariate,   LP:-74.7
-## Iteration: 8900Iteration: 8900,   Proposal: Multivariate,   LP:-74.2
-## Iteration: 9000Iteration: 9000,   Proposal: Multivariate,   LP:-73.7
-## Iteration: 9100Iteration: 9100,   Proposal: Multivariate,   LP:-74.2
-## Iteration: 9200Iteration: 9200,   Proposal: Multivariate,   LP:-73.7
-## Iteration: 9300Iteration: 9300,   Proposal: Multivariate,   LP:-74.4
-## Iteration: 9400Iteration: 9400,   Proposal: Multivariate,   LP:-72.6
-## Iteration: 9500Iteration: 9500,   Proposal: Multivariate,   LP:-73.6
-## Iteration: 9600Iteration: 9600,   Proposal: Multivariate,   LP:-73.5
-## Iteration: 9700Iteration: 9700,   Proposal: Multivariate,   LP:-75
-## Iteration: 9800Iteration: 9800,   Proposal: Multivariate,   LP:-75.6
-## Iteration: 9900Iteration: 9900,   Proposal: Multivariate,   LP:-73.2
-## Iteration: 10000Iteration: 10000,   Proposal: Multivariate,   LP:-72.6
-## 
-## Assessing Stationarity
-## Assessing Thinning and ESS
-## Creating Summaries
-## Estimating Log of the Marginal Likelihood
-## Creating Output
-## 
-## Laplace's Demon has finished.
-

We can present the results from the sampling:

-
Consort(mcmc.samples)
-
## 
-## #############################################################
-## # Consort with Laplace's Demon                              #
-## #############################################################
-## Call:
-## LaplacesDemon(Model = model, Data = data.list, Iterations = 10000, 
-##     Thinning = 1, Algorithm = "HARM")
-## 
-## Acceptance Rate: 0.4179
-## Algorithm: Hit-And-Run Metropolis
-## Covariance Matrix: (NOT SHOWN HERE; diagonal shown instead)
-##        mu log.sigma 
-##   1.49688   0.02556 
-## 
-## Covariance (Diagonal) History: (NOT SHOWN HERE)
-## Deviance Information Criterion (DIC):
-##          All Stationary
-## Dbar 127.733    127.733
-## pD     1.866      1.866
-## DIC  129.599    129.599
-## Initial Values:
-##        mu log.sigma 
-##    12.719     1.699 
-## 
-## Iterations: 10000
-## Log(Marginal Likelihood): -62.64
-## Minutes of run-time: 0.03
-## Model: (NOT SHOWN HERE)
-## Monitor: (NOT SHOWN HERE)
-## Parameters (Number of): 2
-## Posterior1: (NOT SHOWN HERE)
-## Posterior2: (NOT SHOWN HERE)
-## Recommended Burn-In of Thinned Samples: 0
-## Recommended Burn-In of Un-thinned Samples: 0
-## Recommended Thinning: 40
-## Specs: (NOT SHOWN HERE)
-## Status is displayed every 100 iterations
-## Summary1: (SHOWN BELOW)
-## Summary2: (SHOWN BELOW)
-## Thinned Samples: 10000
-## Thinning: 1
-## 
-## 
-## Summary of All Samples
-##              Mean     SD     MCSE    ESS      LB  Median      UB
-## mu         12.355 1.2235 0.127777  103.6  10.079  12.343  14.871
-## log.sigma   1.740 0.1599 0.005314 1636.8   1.453   1.732   2.079
-## Deviance  127.733 1.9316 0.117931  264.3 125.826 127.141 132.812
-## log_post  -73.539 0.9981 0.063120  249.6 -76.262 -73.238 -72.561
-## sigma       5.774 0.9563 0.032264 1594.9   4.277   5.651   7.998
-## 
-## 
-## Summary of Stationary Samples
-##              Mean     SD     MCSE    ESS      LB  Median      UB
-## mu         12.355 1.2235 0.127777  103.6  10.079  12.343  14.871
-## log.sigma   1.740 0.1599 0.005314 1636.8   1.453   1.732   2.079
-## Deviance  127.733 1.9316 0.117931  264.3 125.826 127.141 132.812
-## log_post  -73.539 0.9981 0.063120  249.6 -76.262 -73.238 -72.561
-## sigma       5.774 0.9563 0.032264 1594.9   4.277   5.651   7.998
-## 
-## Demonic Suggestion
-## 
-## Due to the combination of the following conditions,
-## 
-## 1. Hit-And-Run Metropolis
-## 2. The acceptance rate (0.4179) is within the interval [0.15,0.5].
-## 3. At least one target MCSE is >= 6.27% of its marginal posterior
-##    standard deviation.
-## 4. Each target distribution has an effective sample size (ESS)
-##    of at least 100.
-## 5. Each target distribution became stationary by
-##    1 iteration.
-## 
-## Laplace's Demon has not been appeased, and suggests
-## copy/pasting the following R code into the R console,
-## and running it.
-## 
-## Initial.Values <- as.initial.values(mcmc.samples)
-## mcmc.samples <- LaplacesDemon(Model, Data=data.list, Initial.Values,
-##      Covar=NULL, Iterations=4e+05, Status=333333, Thinning=40,
-##      Algorithm="HARM", Specs=list(alpha.star=NA, B=NULL)
-## 
-## Laplace's Demon is finished consorting.
-
plot(mcmc.samples, BurnIn=1e3, data.list)
-

plot of chunk unnamed-chunk-18plot of chunk unnamed-chunk-18

-

The modelling with this package is less user-friendly since there is no declarative language like in BUGS, JAGS or STAN. However it has the possibility of lots of configuration options.

-
- - -
- - - - - - - - diff --git a/bayes.packages/roubik_2002_coffe_yield.csv b/bayes.packages/roubik_2002_coffe_yield.csv deleted file mode 100644 index 7067309..0000000 --- a/bayes.packages/roubik_2002_coffe_yield.csv +++ /dev/null @@ -1,29 +0,0 @@ -world,country,yield_61_to_80,yield_81_to_01 -new,Costa_Rica,9139,14620 -new,Bolivia,7686,8767 -new,El_Salvador,9996,8729 -new,Guatemala,5488,8231 -new,Colombia,5920,7740 -new,Honduras,4096,7264 -new,Nicaragua,4566,6408 -new,Brazil,4965,6283 -new,Peru,5487,5740 -new,Mexico,5227,5116 -new,Panama,2347,4124 -new,Ecuador,3089,3240 -new,Venezuela,1938,2789 -old,Vietnam,4251,13380 -old,Papua_NG,10522,11561 -old,Thailand,3509,9652 -old,Philippines,10028,9593 -old,Ethiopia,5667,8797 -old,Sri_Lanka,17064,7869 -old,India,5904,7354 -old,Malaysia,4001,7288 -old,Kenya,6604,6055 -old,Tanzania,4738,5432 -old,Indonesia,5716,5394 -old,Madagascar,3824,3576 -old,Cameroon,3525,3141 -old,Ivory_Coast,3393,2391 -old,Ghana,3213,2136 diff --git a/bayes.packages/zelig-manual-bayes.pdf b/bayes.packages/zelig-manual-bayes.pdf deleted file mode 100644 index 91b8f14d1017b3887911178f5219d2960e26daab..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 291461 zcma%?QaPU-o|58V>46gWm*pZVbjUBm_m9dhvsFVQz7j1&YMU5V{=nozjxvxqt(LHiMeZg z);YCgsyqGIHY0O-#+JS5m&EgDcN4$Y+sH-6!rC%9gOY50&Si0Hz{D+38mdnfH0>0N z4p$x@ipsgt<)qAyRe!BfrnlxKLo)YX$!#3Qcg3N1JeBSpk+lETR-DGgaWIV4@2f&= zomTb%Ig5CT*3?AngiO2wx<)6{f?XRU2d(nYIX~O<6A5#I1>Dsh;;P?jB3ceZh#l2A z-U)OP`LkB(S7oz_u7%}Do9rL+)CpcWam1Md&eviIW#~3y9=rG%MDlF^{*;Nst&U<# zUYsgk+9)-}kpq=R(N=LCB#VR94QoUQf6oFJEv|Ky>?ROVOCs<=BuERGu$`e>gSoe% zkiXk}%(&GQX{f5y?Te9IKdvu#__yg9;}*PCvQB#mWgV1>mcOy5J)(FNppe+3MeDab za-<3eYAn}s%fcM+=id9-vOCkz&{JKdrm3W17d_RN{`0x#0lilyU$}H-FLtl6)qgVX zT!NBA&G@fIsNm|g84iyY3@+OZl!RJL0r?M&x+$+@*qEe&XI0EEd-gBu#!{TJ>2CjEy?y+}&MlJ`&`ksiveA&M|5jeB@6GDGS z+vr8ah?%-M6~+;Ja!trG572oJW4ukDjY`2YSc(ZipOO_Jsc!irrO2r{Bg7$zj5x@R zkAXF}ql_B@{1j$m^u1vEKjCT47N?ijdZX7?*|TP5#ZOK&?oSN7fAD|@hu)XXf(|-o zz86=nM2}7$x@}$zP6tTyD2C%<mbD@O|XAR$Rvd~FKDtbX$)HtK*3|tY;t-7%t}x)O5hL~b^<^TC%NPMyusm; z3tP6t$FU)LMgTmr8WM7R_#*njjR^1PuP<1;yM1Ol-QVf}qF=h7Nd}!zWrAPh!4Q?9 zk|bu*!MfOi?^J?!NSrY#ESmUjdv^M3HLfAJPgNYDkUhQ3qK ze$w)Qd+%e~tajZrx@`~YcG4xobTm%zD^BMg@Xd%z#yK?_kG^{dIVGi3v`)z{`V1_S zSQ9f*L77IX1`u79R z+)IFUcy@yb36kc~>t6^cZ1*b@pv|4jb&ELQp`A*fhS(nJKpEpld*%;9pp|f*7jY%N9HL&K&v>6&2p%ZU6+RO$?ik`$w!M zdU-%=b_h-g-!Dn(3tpb^k{b7mdYV@U&@FnH@5D4XS-eG-a9Up|&)4Msfk186M8p51 zQ7RQ8w2ci?{d^=ld4Aae*z2+V7blx>PvAEFldsW^sx#T^VAE@#t0gOgS-DGcJav9Q zb*jM5c{w<-z>b6K;m2bnbjoCe|W5shOho(9itEa`=+$W6WHn`vY zM_Zpk_I=Az3`&8&U#x31;)r#cU zX_LKStj0`rN=%V!Z=B+JvRn>(WHBn;oPf;tZ~5EVW1q8YjP<@q@bts-`WwT7!t#3&g z4H$_;f)7vXXDsj;pKY2@9-eohmW73Z1lw~Z~v$EQGRbPSk9jIob z!rZetNx0~VI|*t&qPxvks?tVlRq^ImsvMn{rBXEDYE3XN&+ts+_YLu~k3>gBWuN;2 z#Aa(u(vQ_RVv(%0^ceBM+DfilyyKV~2rxL1057`m$zo(pH%_+KR9qqzNBM;(Cm(wRANNKN z8cT&PB1asXuB^zu=Erp-OMa>YU6q@$-cFVC;K?t^utXMqg|Ew#2I*wj)-nY9?L7xa zJ=Pt*mBzqN!l*d-8T6!ehsF-xJ;^^;^QIImlod#xR%S#n;i_G~0~XGbnHo>5W($<8 zTyUiBk9-wYkD`ZoQCWXR@avs~hsejk2ZGCAkika_axdqiA1%_kIJ@nhb6Rq|L-F!jbbmw}eek5Y-0NA0 z-%q2Cgvd{ZeJ_S(6}7&L-3$3lX))+^7&Sm?s*aGwKIEaK+Uzk5!cvX&4?u8;n5;NN zg5QbC4f%ZN6+f-JPUwr?1d3+tJ<$!J)7(3fkd6oKAMWfTR83f*^`PIuse;9>P-Gd; z!0i{yO-2P9am$M$i~GZEP$X)B+b31p}{tsePWeud8+ed)s$?p-gOz{}+M&nf}2iC`Jyp{{$&UR@VO- zq-HcU?T$nceCO&g2uXN|T(_>dfr?>Ctp6Y)aSH*Zg4c~XnV$~k5>Ej4-FtZ{FNoaP?KzW>hV#kH{v&MCMDFaAC-T5zPk43B~d)G!6M8VRA&|7n}E_Tqt>-rT8(Iv-lR-n z^)(4yVJH)UI+??)0@?kea&w((zTw4y4OfWBbpIEb$UT)^Kwt1^vfz&Hd__$P^f>s>Sx~{w zwTN>5yTPh`>6mzsqmdoI43d_hmE~R6^g8m9tZWLCsw}nkVO}cQBx=v;p%L`>)LxiZ zp@vel{b{Tk+*`~RI*Xb5J_%!I{T>|M4A6e#igp#>A^YSNlA;pv(uO4yPR|w=2X@EGA1qE{EOq(qRbGGTtU!XO*feEdCyMz9lP^j1AV?q z%pzb0A)}@bCb($&05|kQGz~J~ytr_^+UU+RE|tF!TRGqGDa*bI!2?Kl61XBA3_L#_ z)NQ4TUbO_aVe3};T7KAkojp%dVouiLy*k$hhm

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a/bootstrap/crop.data.csv b/bootstrap/crop.data.csv new file mode 100644 index 0000000..546b84f --- /dev/null +++ b/bootstrap/crop.data.csv @@ -0,0 +1,97 @@ +"density","block","fertilizer","yield" +"1","1","1",177.228692278688 +"2","2","1",177.550041265426 +"1","3","1",176.408461852371 +"2","4","1",177.703625478918 +"1","1","1",177.125486343584 +"2","2","1",176.778342481435 +"1","3","1",176.746301895632 +"2","4","1",177.061164221059 +"1","1","1",176.274949297277 +"2","2","1",177.967202929576 +"1","3","1",176.601299834494 +"2","4","1",177.030542802918 +"1","1","1",177.479507160588 +"2","2","1",176.874129801452 +"1","3","1",176.114388315927 +"2","4","1",176.008394511531 +"1","1","1",176.108312589654 +"2","2","1",178.35744091425 +"1","3","1",177.262445084271 +"2","4","1",176.918844938972 +"1","1","1",176.239015775225 +"2","2","1",176.573069754873 +"1","3","1",176.039297939843 +"2","4","1",176.817922165499 +"1","1","1",176.160586502816 +"2","2","1",177.226424131397 +"1","3","1",175.938533030004 +"2","4","1",177.16493668281 +"1","1","1",175.360839598647 +"2","2","1",177.276995681026 +"1","3","1",175.945443795425 +"2","4","1",175.882779618556 +"1","1","2",176.479340919814 +"2","2","2",176.0443421205 +"1","3","2",177.412461749009 +"2","4","2",177.360818239535 +"1","1","2",177.385499180836 +"2","2","2",176.975807696393 +"1","3","2",177.379778689577 +"2","4","2",177.99799506429 +"1","1","2",176.434862565867 +"2","2","2",176.933265092142 +"1","3","2",175.983480169992 +"2","4","2",177.034092659355 +"1","1","2",176.436762368181 +"2","2","2",176.06774497035 +"1","3","2",177.121048632786 +"2","4","2",177.197721367386 +"1","1","2",176.60372408049 +"2","2","2",177.208171431058 +"1","3","2",177.148828595107 +"2","4","2",176.819076695268 +"1","1","2",176.999066949946 +"2","2","2",178.134604582348 +"1","3","2",176.429156002757 +"2","4","2",176.668322935082 +"1","1","2",176.895866859859 +"2","2","2",177.779492860266 +"1","3","2",176.414495002246 +"2","4","2",176.878897743394 +"1","1","2",177.580683078112 +"2","2","2",176.957268920193 +"1","3","2",175.747545582883 +"2","4","2",177.352595079015 +"1","1","3",177.104186398865 +"2","2","3",178.079635168278 +"1","3","3",176.903422145535 +"2","4","3",177.540284161493 +"1","1","3",177.03270969652 +"2","2","3",178.28604192157 +"1","3","3",176.405410230471 +"2","4","3",176.430830126686 +"1","1","3",177.396330635021 +"2","2","3",176.92557577835 +"1","3","3",177.055045778695 +"2","4","3",177.344163946335 +"1","1","3",177.128367531761 +"2","2","3",177.168302204533 +"1","3","3",176.353940642858 +"2","4","3",179.060899036915 +"1","1","3",176.300517050366 +"2","2","3",177.59335237605 +"1","3","3",177.115245241837 +"2","4","3",177.794457435485 +"1","1","3",177.004038102495 +"2","2","3",178.036858366448 +"1","3","3",177.701366283038 +"2","4","3",177.632808263613 +"1","1","3",177.652274608017 +"2","2","3",177.100417857738 +"1","3","3",177.187967031073 +"2","4","3",177.405291855943 +"1","1","3",178.14164435679 +"2","2","3",177.710612540335 +"1","3","3",177.687264356834 +"2","4","3",177.118175977614 diff --git a/bootstrap/stat_resampling.Rmd b/bootstrap/stat_resampling.Rmd index ccfd13c..7b53a4f 100644 --- a/bootstrap/stat_resampling.Rmd +++ b/bootstrap/stat_resampling.Rmd @@ -19,13 +19,13 @@ library(magrittr) library(resampledata) ``` -Refs +References + [Chihara, Hesterberg - Mathematical Statistics with Resampling and R 2ed (2018)](https://sites.google.com/site/chiharahesterberg/home), caps 1--4 + [Cobb - The Intr Stats Course, A Ptolemaic Curriculum (2007)](https://escholarship.org/uc/item/6hb3k0nz) -We will some of the resampling with the [two buckets model](http://www.di.fc.ul.pt/~jpn/r/bootstrap/buckets.html): +We will do some of the resampling with the [two buckets model](http://www.di.fc.ul.pt/~jpn/r/bootstrap/buckets.html): ```{r} # multiplier == 0 represents infinite population (ie, no replacement) @@ -55,8 +55,8 @@ compute.p.value <- function(results, observed.effect, precision=3) { list(mc.p.value=round((r+1)/(n+1), precision), r=r, n=n) } -present_results <- function(results, observed.effect, label="", breaks=50) { - lst <- compute.p.value(results, observed.effect) +present_results <- function(results, observed.effect, label="", breaks=50, precision=3) { + lst <- compute.p.value(results, observed.effect, precision=precision) hist(results, breaks=breaks, prob=T, main=label, sub=paste0("MC p-value for H0: ", lst$mc.p.value), @@ -431,3 +431,83 @@ f.test <- observed.data %>% as.matrix %>% friedman.test f.test$p.value ``` +# Replacing One-Way ANOVA + +One-way ANOVA estimates how a quantitative dependent variable changes according to the levels of one of its categorical independent variables. + +```{r} +# data set from https://www.scribbr.com/statistics/anova-in-r/ +crop.data <- read.csv("crop.data.csv", header = TRUE, + colClasses = c("factor", "factor", "factor", "numeric")) + +summary(crop.data) +``` + +In this data set we have three categorical independent variables that might or not be significant to the value of its yield. + +The next code will sample the categorical variable while keeping the original values of yield to compute the F statistic (check previous section). We do it lots of time and keep all permuted effects in order to compare with the observed effect. + +```{r} +f.stat <- function(means, vars) { + var(means) / mean(vars) +} + +# assume data frame has two columns, the first is the independent variable +# the second is the dependent variable +anova.test <- function(df, size=2500) { + + vals <- sort(unique(df[,1])) + + permuted.effects <- replicate(size, + { + permuted.data <- data.frame( x = sample(df[,1]), + y = df[,2]) + means <- sapply(vals, function(i) permuted.data[permuted.data$x==i,2] %>% mean) + vars <- sapply(vals, function(i) permuted.data[permuted.data$x==i,2] %>% var) + f.stat(means, vars) + }) + + # observed effect + means <- sapply(vals, function(i) df[df[,1]==i,2] %>% mean) + vars <- sapply(vals, function(i) df[df[,1]==i,2] %>% var) + observed.effect <- f.stat(means, vars) + + list(permuted.effects = permuted.effects, + observed.effect = observed.effect) +} +``` + +Let's check the significance of fertilizer: + +```{r} +df <- crop.data[,c(3,4)] # select fertilizer and yield +results <- anova.test(df, 15000) +present_results(results$permuted.effects, results$observed.effect, precision=5) +``` + +Comparing with the classical test: + +```{r} +one.way <- aov(yield ~ fertilizer, data = crop.data) + +summary(one.way) +``` + +Let's try with the independent variable block: + +```{r} +df <- crop.data[,c(2,4)] # select density and yield +results <- anova.test(df,15000) +present_results(results$permuted.effects, results$observed.effect, precision=5) +``` + + +And the result from the classical test: + +```{r} +one.way <- aov(yield ~ block, data = crop.data) + +summary(one.way) +``` + +The results of both methods are similar. \ No newline at end of file diff --git a/bootstrap/stat_resampling.html b/bootstrap/stat_resampling.html index 703cf5f..830e35a 100644 --- a/bootstrap/stat_resampling.html +++ b/bootstrap/stat_resampling.html @@ -1,11 +1,10 @@ - + - @@ -331,6 +330,7 @@ border: none; display: inline-block; border-radius: 4px; + background-color: transparent; } .tabset-dropdown > .nav-tabs.nav-tabs-open > li { @@ -380,17 +380,18 @@

16/11/2019

  • Bootstrap and Confidence Intervals
  • Replacing Friedman Rank Sum Test
    • +
  • Replacing One-Way ANOVA
    • library(magrittr)
 library(resampledata)
    -

    Refs

    +

    References

    -

    We will some of the resampling with the two buckets model:

    +

    We will do some of the resampling with the two buckets model:

    # multiplier == 0 represents infinite population (ie, no replacement)
 make.bucket1 <- function(universe, multiplier=1) {
   if (multiplier>0)
@@ -418,8 +419,8 @@ 
    16/11/2019
    
   list(mc.p.value=round((r+1)/(n+1), precision), r=r, n=n)
 }
 
-present_results <- function(results, observed.effect, label="", breaks=50) {
-  lst <- compute.p.value(results, observed.effect)
+present_results <- function(results, observed.effect, label="", breaks=50, precision=3) {
+  lst <- compute.p.value(results, observed.effect, precision=precision)
   
   hist(results, breaks=breaks, prob=T, main=label,
        sub=paste0("MC p-value for H0: ", lst$mc.p.value),
@@ -477,7 +478,7 @@ 
    One-sided permutation test
    
 
 results <- bucket2(1e4)
 present_results(results, observed.effect, "Difference of Means", breaks=40)
    -

    +

    Since the p-value is 0.001 it is evidence that supports the alternative hypothesis, that there is a significant difference of means between the genres in this study.

    If these people were selected inside a bar, then we cannot say anything about the population, since the group is not a random sample.

    We can easily use any other statistic. The next eg uses just the mean of male drinking:

    @@ -491,7 +492,7 @@

    One-sided permutation test

    results <- bucket2(1e4) present_results(results, mean(group.M), "Difference of Means", breaks=30) -

    +

    We could choose statistics, like the median or the trimmed mean, to achieve more robust results, if large outliers are in the sample.

    - - - - - - - - - - - - - -

    Ref:

    - -
    -

    The caret package (short for Classification And REgression Training) is a set of functions that attempt to streamline the process for creating predictive models. The package contains tools for: data splitting pre-processing feature selection model tuning using resampling variable importance estimation as well as other functionality. ref

    -
    -
    # to install package with all dependencies:
-# install.packages("caret", dependencies = c("Depends", "Suggests"))
-library(caret)
    -

    The next functions help prepare the dataset for learning.

    -
    # calls caret::preProcess
-caret_preprocess <- function(df, ...) {
-  predict(preProcess(df, ...), df)
-}
-
-# pre: to perform classification
-# pre: assumes dependent variable is the last column
-# convert factors with a one hot encoding (make dummy vars with 0/1s)
-#  “fullrank=T†create only (n-1) columns for a factor with n different levels
-caret_oneHotEncoding <- function(df) {
-  dmy <- dummyVars(" ~ .", data=df, fullRank=TRUE)
-  res <- data.frame(predict(dmy, newdata = df))
-  res[,ncol(res)] <- as.factor(res[,ncol(res)]) # make dependent variable a factor
-  names(res)[ncol(res)] <- names(df)[ncol(df)]  # and keep its original name
-  res
-}
-
-# pre: assumes dependent variable is the last column
-caret_featureSelection <- function(train, test, n.pred) {
-  if (missing(n.pred)) n.pred=ncol(train)-1  # use all as predictors
-  control <- rfeControl(functions = rfFuncs,
-                        method = "repeatedcv",
-                        repeats = 3,
-                        verbose = FALSE)
-  
-  dependent.col <- ncol(train)
-  predictors    <- names(train)[-dependent.col]
-  rfe.profile   <- rfe(train[,predictors], train[,dependent.col], rfeControl = control)
-  rfe.profile$variables$var[1:n.pred]  # return the best predictors
-}
    -

    Now we are ready to read and preprocess the dataset:

    -
    library(dplyr)
-
-raw.data <- read.csv("train_u6lujuX_CVtuZ9i.csv", stringsAsFactors = T)
-glimpse(raw.data)
    -
    ## Observations: 614
-## Variables: 13
-## $ Loan_ID           <fctr> LP001002, LP001003, LP001005, LP001006, LP0...
-## $ Gender            <fctr> Male, Male, Male, Male, Male, Male, Male, M...
-## $ Married           <fctr> No, Yes, Yes, Yes, No, Yes, Yes, Yes, Yes, ...
-## $ Dependents        <fctr> 0, 1, 0, 0, 0, 2, 0, 3+, 2, 1, 2, 2, 2, 0, ...
-## $ Education         <fctr> Graduate, Graduate, Graduate, Not Graduate,...
-## $ Self_Employed     <fctr> No, No, Yes, No, No, Yes, No, No, No, No, N...
-## $ ApplicantIncome   <int> 5849, 4583, 3000, 2583, 6000, 5417, 2333, 30...
-## $ CoapplicantIncome <dbl> 0, 1508, 0, 2358, 0, 4196, 1516, 2504, 1526,...
-## $ LoanAmount        <int> NA, 128, 66, 120, 141, 267, 95, 158, 168, 34...
-## $ Loan_Amount_Term  <int> 360, 360, 360, 360, 360, 360, 360, 360, 360,...
-## $ Credit_History    <int> 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,...
-## $ Property_Area     <fctr> Urban, Rural, Urban, Urban, Urban, Urban, U...
-## $ Loan_Status       <fctr> Y, N, Y, Y, Y, Y, Y, N, Y, N, Y, Y, Y, N, Y...
    -
    dependentVar <- names(raw.data)[ncol(raw.data)]  # must be the last column
-
-# process data
-raw.data %>% 
-  dplyr::select(-Loan_ID) %>%                          # assumption: irrelevant data
-  caret_preprocess(method = c("knnImpute", "center", "scale")) %>% 
-  caret_oneHotEncoding -> my.data
-glimpse(my.data)
    -
    ## Observations: 614
-## Variables: 19
-## $ Gender.Female           <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
-## $ Gender.Male             <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
-## $ Married.No              <dbl> 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,...
-## $ Married.Yes             <dbl> 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,...
-## $ Dependents.0            <dbl> 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0,...
-## $ Dependents.1            <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,...
-## $ Dependents.2            <dbl> 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1,...
-## $ Dependents.3.           <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,...
-## $ Education.Not.Graduate  <dbl> 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,...
-## $ Self_Employed.No        <dbl> 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1,...
-## $ Self_Employed.Yes       <dbl> 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,...
-## $ ApplicantIncome         <dbl> 0.072931360, -0.134302453, -0.39342656...
-## $ CoapplicantIncome       <dbl> -0.55403561, -0.03870000, -0.55403561,...
-## $ LoanAmount              <dbl> 0.01621546, -0.21512721, -0.93953353, ...
-## $ Loan_Amount_Term        <dbl> 0.276411, 0.276411, 0.276411, 0.276411...
-## $ Credit_History          <dbl> 0.4324768, 0.4324768, 0.4324768, 0.432...
-## $ Property_Area.Semiurban <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,...
-## $ Property_Area.Urban     <dbl> 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1,...
-## $ Loan_Status             <fctr> 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1...
    -

    Next we partition the dataset into training and testing sets:

    -
    set.seed(123)
-inTrain <- createDataPartition(my.data[,ncol(my.data)], p=0.75, list=FALSE)  # train gets 75%
-train   <- my.data[ inTrain,]
-test    <- my.data[-inTrain,]
    -

    We can optionally perform feature selection:

    -
    predictors <- caret_featureSelection(train, test, n.pred=5)
-predictors
    -
    ## [1] "Credit_History"          "Loan_Amount_Term"       
-## [3] "ApplicantIncome"         "CoapplicantIncome"      
-## [5] "Property_Area.Semiurban"
    -

    And can choose some of the many models available on caret to perform classification:

    -
    model_gbm  <- train(train[,predictors], train[,dependentVar], method='gbm' , verbose=F) # Boosted Regression
-model_rf   <- train(train[,predictors], train[,dependentVar], method='rf'  , verbose=F) # Random Forest
-model_nnet <- train(train[,predictors], train[,dependentVar], method='nnet', verbose=F) # Neural Nets
-model_svm  <- train(train[,predictors], train[,dependentVar], method='svmRadial' , verbose=F) # Support Vector Machines
    -

    We can check variable importance:

    -
    par(mfrow=c(2,2))
-plot(varImp(object=model_gbm),   main="GBM - Variable Importance")
    -

    -
    plot(varImp(object=model_rf),    main="RF  - Variable Importance")
    -

    -
    plot(varImp(object=model_nnet),  main="GBM - Variable Importance")
    -

    -
    plot(varImp(object=model_svm),   main="SVM - Variable Importance")
    -

    -
    par(mfrow=c(1,1))
    -

    and make predictions:

    -
    library(pROC)
-
-predictions <- predict.train(object=model_gbm, test[,predictors], type="raw")
-confusionMatrix(predictions, test[,dependentVar])$table
    -
    ##           Reference
-## Prediction   0   1
-##          0  23   1
-##          1  25 104
    -
    roc(as.integer(test[,dependentVar]), as.integer(predictions))$auc
    -
    ## Area under the curve: 0.7348
    -

    Caret also allows for parameter tuning:

    -
    modelLookup(model='gbm') # which parameters can be tuned?
    -
    ##   model         parameter                   label forReg forClass
-## 1   gbm           n.trees   # Boosting Iterations   TRUE     TRUE
-## 2   gbm interaction.depth          Max Tree Depth   TRUE     TRUE
-## 3   gbm         shrinkage               Shrinkage   TRUE     TRUE
-## 4   gbm    n.minobsinnode Min. Terminal Node Size   TRUE     TRUE
-##   probModel
-## 1      TRUE
-## 2      TRUE
-## 3      TRUE
-## 4      TRUE
    -
    # making a grid of values
-grid <- expand.grid(n.trees           = c(10,20),
-                    shrinkage         = c(0.01,0.05,0.5),
-                    n.minobsinnode    = c(3,5,10),
-                    interaction.depth = c(1,5,10))
-
-# let's use, say, 5-Fold cross-validation repeated 3 times
-fitControl <- trainControl(method = "repeatedcv", 
-                           number = 5, 
-                           repeats = 3)
-
-# tune the model
-model_gbm2 <- train(train[,predictors], train[,dependentVar], method='gbm',
-                   # "RMSE" or "Rsquared" for regression; 
-                   # "Accuracy" or "Kappa" for classification
-                   metric= "Accuracy", 
-                   trControl=fitControl,
-                   tuneGrid=grid,
-                   verbose=FALSE)
-
-model_gbm2$results %>% 
-  dplyr::arrange(desc(Accuracy)) %>% 
-  head(6)
    -
    ##   shrinkage interaction.depth n.minobsinnode n.trees  Accuracy     Kappa
-## 1      0.05                 1              3      10 0.8047626 0.4653741
-## 2      0.05                 1              5      10 0.8047626 0.4653741
-## 3      0.05                 1             10      10 0.8047626 0.4653741
-## 4      0.05                 5             10      10 0.8047626 0.4653741
-## 5      0.05                10             10      10 0.8047626 0.4653741
-## 6      0.05                 1              3      20 0.8047626 0.4653741
-##   AccuracySD    KappaSD
-## 1  0.0228608 0.07111885
-## 2  0.0228608 0.07111885
-## 3  0.0228608 0.07111885
-## 4  0.0228608 0.07111885
-## 5  0.0228608 0.07111885
-## 6  0.0228608 0.07111885
    -
    plot(model_gbm2)
    -

    -
    model_gbm2$bestTune
    -
    ##    n.trees interaction.depth shrinkage n.minobsinnode
-## 19      10                 1      0.05              3
    -
    predictions <- predict.train(object=model_gbm2, test[,predictors], type="raw")
-confusionMatrix(predictions, test[,dependentVar])$table
    -
    ##           Reference
-## Prediction   0   1
-##          0  22   1
-##          1  26 104
    -
    roc(as.integer(test[,dependentVar]), as.integer(predictions))$auc
    -
    ## Area under the curve: 0.7244
    -

    To compare different models:

    -
    resamps <- resamples(list(GBM = model_gbm,
-                          RF  = model_rf,
-                          NN  = model_nnet,
-                          SVM = model_svm))
-resamps
    -
    ## 
-## Call:
-## resamples.default(x = list(GBM = model_gbm, RF = model_rf, NN
-##  = model_nnet, SVM = model_svm))
-## 
-## Models: GBM, RF, NN, SVM 
-## Number of resamples: 25 
-## Performance metrics: Accuracy, Kappa 
-## Time estimates for: everything, final model fit
    -
    summary(resamps)
    -
    ## 
-## Call:
-## summary.resamples(object = resamps)
-## 
-## Models: GBM, RF, NN, SVM 
-## Number of resamples: 25 
-## 
-## Accuracy 
-##       Min. 1st Qu. Median   Mean 3rd Qu.   Max. NA's
-## GBM 0.7588  0.7840 0.7955 0.7969  0.8098 0.8383    0
-## RF  0.7396  0.7818 0.7919 0.7935  0.8110 0.8409    0
-## NN  0.7471  0.7844 0.8023 0.8001  0.8171 0.8494    0
-## SVM 0.7011  0.7378 0.7722 0.7637  0.7892 0.8160    0
-## 
-## Kappa 
-##       Min. 1st Qu. Median   Mean 3rd Qu.   Max. NA's
-## GBM 0.3509  0.4216 0.4476 0.4508  0.4757 0.5873    0
-## RF  0.3124  0.4404 0.4880 0.4721  0.5148 0.5739    0
-## NN  0.2706  0.4531 0.4769 0.4634  0.4962 0.5461    0
-## SVM 0.2437  0.2970 0.3764 0.3536  0.3995 0.4550    0
    -
    bwplot(resamps, layout = c(2, 1))
    -

    -
    dotplot(resamps, metric = "Kappa")
    -

    -
    xyplot(resamps, what = "BlandAltman")
    -

    -
    splom(resamps)
    -

    -
    -

    Ensemble Learning

    -

    A company package caretEmsemble deals with ensembles of models, and a vignette can be read here. Check also How to Build an Ensemble Of Machine Learning Algorithms in R.

    -
    library(caretEnsemble)
-
-control <- trainControl(method="repeatedcv", number=10, repeats=3, classProbs=TRUE)
-models.names <- c('gbm', 'rf', 'nnet', 'svmRadial')
-
-# necessary to prevent invalid R variables names in caretList
-for (f in names(my.data)) 
-  if (class(my.data[[f]])=="factor") {
-    levels <- unique(c(my.data[[f]]))
-    my.data[[f]] <- factor(my.data[[f]], labels=make.names(levels))
-  }
-
-models <- caretList(Loan_Status ~ ., 
-                    data=my.data[,c(predictors[-2],dependentVar)],
-                    trControl=control, 
-                    methodList=models.names,
-                    verbose=FALSE)
    -

    Let’s see some comparisons:

    -
    results <- resamples(models)
-summary(results)
    -
    ## 
-## Call:
-## summary.resamples(object = results)
-## 
-## Models: gbm, rf, nnet, svmRadial 
-## Number of resamples: 30 
-## 
-## Accuracy 
-##             Min. 1st Qu. Median   Mean 3rd Qu.   Max. NA's
-## gbm       0.7377  0.7774 0.8033 0.8067  0.8387 0.8689    0
-## rf        0.7541  0.7714 0.7903 0.8002  0.8226 0.8548    0
-## nnet      0.7541  0.7774 0.8033 0.8051  0.8361 0.8689    0
-## svmRadial 0.7258  0.7774 0.8033 0.8013  0.8197 0.8548    0
-## 
-## Kappa 
-##             Min. 1st Qu. Median   Mean 3rd Qu.   Max. NA's
-## gbm       0.2945  0.4009 0.4641 0.4773  0.5663 0.6544    0
-## rf        0.2945  0.3959 0.4532 0.4651  0.5342 0.6174    0
-## nnet      0.2945  0.4115 0.4641 0.4723  0.5534 0.6544    0
-## svmRadial 0.2670  0.3801 0.4670 0.4563  0.5169 0.6235    0
    -
    dotplot(results)
    -

    -

    The models should have low correlation so that the ensemble works best:

    -
    modelCor(results)
    -
    ##                 gbm        rf      nnet svmRadial
-## gbm       1.0000000 0.8705049 0.9310803 0.7941055
-## rf        0.8705049 1.0000000 0.8533515 0.7818630
-## nnet      0.9310803 0.8533515 1.0000000 0.7887679
-## svmRadial 0.7941055 0.7818630 0.7887679 1.0000000
    -

    We see that there is high correlation, so the ensemble results will have little benefits.

    -

    Function caretStack find a linear combination of several models:

    -
    stack.glm <- caretStack(models, method="glm", metric="Accuracy", trControl=control)
-print(stack.glm)
    -
    ## A glm ensemble of 2 base models: gbm, rf, nnet, svmRadial
-## 
-## Ensemble results:
-## Generalized Linear Model 
-## 
-## 1842 samples
-##    4 predictor
-##    2 classes: 'X2', 'X1' 
-## 
-## No pre-processing
-## Resampling: Cross-Validated (10 fold, repeated 3 times) 
-## Summary of sample sizes: 1657, 1658, 1659, 1658, 1659, 1658, ... 
-## Resampling results:
-## 
-##   Accuracy   Kappa    
-##   0.8036486  0.4705906
-## 
-##
    -

    We see that the results were, unsurprisingly, not that better…

    -

    Let’s try a random forest to ensemble the models:

    -
    stack.rf <- caretStack(models, method="rf", metric="Accuracy", trControl=control)
-print(stack.rf)
    -
    ## A rf ensemble of 2 base models: gbm, rf, nnet, svmRadial
-## 
-## Ensemble results:
-## Random Forest 
-## 
-## 1842 samples
-##    4 predictor
-##    2 classes: 'X2', 'X1' 
-## 
-## No pre-processing
-## Resampling: Cross-Validated (10 fold, repeated 3 times) 
-## Summary of sample sizes: 1658, 1657, 1659, 1658, 1657, 1658, ... 
-## Resampling results across tuning parameters:
-## 
-##   mtry  Accuracy   Kappa    
-##   2     0.8002355  0.4873520
-##   3     0.7991484  0.4855304
-##   4     0.7962508  0.4799460
-## 
-## Accuracy was used to select the optimal model using  the largest value.
-## The final value used for the model was mtry = 2.
    -

    To predict we need also to rename the dependent variable:

    -
    predictions <- ifelse(predict(object=stack.glm, test[,predictors]) ==
-                          levels(my.data$Loan_Status)[[1]], "0" , "1")
-confusionMatrix(predictions, test[,dependentVar])$table
    -
    ##           Reference
-## Prediction   0   1
-##          0  26 104
-##          1  22   1
    -
    roc(as.integer(test[,dependentVar]), as.integer(predictions))$auc
    -
    ## Area under the curve: 0.2756
    -
    - - - - - - - - - - - - - diff --git a/caret/train_u6lujuX_CVtuZ9i.csv b/caret/train_u6lujuX_CVtuZ9i.csv deleted file mode 100644 index 899be49..0000000 --- a/caret/train_u6lujuX_CVtuZ9i.csv +++ /dev/null @@ -1,615 +0,0 @@ -Loan_ID,Gender,Married,Dependents,Education,Self_Employed,ApplicantIncome,CoapplicantIncome,LoanAmount,Loan_Amount_Term,Credit_History,Property_Area,Loan_Status -LP001002,Male,No,0,Graduate,No,5849,0,,360,1,Urban,Y -LP001003,Male,Yes,1,Graduate,No,4583,1508,128,360,1,Rural,N -LP001005,Male,Yes,0,Graduate,Yes,3000,0,66,360,1,Urban,Y -LP001006,Male,Yes,0,Not Graduate,No,2583,2358,120,360,1,Urban,Y -LP001008,Male,No,0,Graduate,No,6000,0,141,360,1,Urban,Y -LP001011,Male,Yes,2,Graduate,Yes,5417,4196,267,360,1,Urban,Y -LP001013,Male,Yes,0,Not Graduate,No,2333,1516,95,360,1,Urban,Y -LP001014,Male,Yes,3+,Graduate,No,3036,2504,158,360,0,Semiurban,N -LP001018,Male,Yes,2,Graduate,No,4006,1526,168,360,1,Urban,Y -LP001020,Male,Yes,1,Graduate,No,12841,10968,349,360,1,Semiurban,N -LP001024,Male,Yes,2,Graduate,No,3200,700,70,360,1,Urban,Y -LP001027,Male,Yes,2,Graduate,,2500,1840,109,360,1,Urban,Y -LP001028,Male,Yes,2,Graduate,No,3073,8106,200,360,1,Urban,Y -LP001029,Male,No,0,Graduate,No,1853,2840,114,360,1,Rural,N -LP001030,Male,Yes,2,Graduate,No,1299,1086,17,120,1,Urban,Y -LP001032,Male,No,0,Graduate,No,4950,0,125,360,1,Urban,Y -LP001034,Male,No,1,Not Graduate,No,3596,0,100,240,,Urban,Y -LP001036,Female,No,0,Graduate,No,3510,0,76,360,0,Urban,N -LP001038,Male,Yes,0,Not Graduate,No,4887,0,133,360,1,Rural,N -LP001041,Male,Yes,0,Graduate,,2600,3500,115,,1,Urban,Y -LP001043,Male,Yes,0,Not Graduate,No,7660,0,104,360,0,Urban,N -LP001046,Male,Yes,1,Graduate,No,5955,5625,315,360,1,Urban,Y -LP001047,Male,Yes,0,Not Graduate,No,2600,1911,116,360,0,Semiurban,N -LP001050,,Yes,2,Not Graduate,No,3365,1917,112,360,0,Rural,N -LP001052,Male,Yes,1,Graduate,,3717,2925,151,360,,Semiurban,N -LP001066,Male,Yes,0,Graduate,Yes,9560,0,191,360,1,Semiurban,Y -LP001068,Male,Yes,0,Graduate,No,2799,2253,122,360,1,Semiurban,Y -LP001073,Male,Yes,2,Not Graduate,No,4226,1040,110,360,1,Urban,Y -LP001086,Male,No,0,Not Graduate,No,1442,0,35,360,1,Urban,N -LP001087,Female,No,2,Graduate,,3750,2083,120,360,1,Semiurban,Y -LP001091,Male,Yes,1,Graduate,,4166,3369,201,360,,Urban,N -LP001095,Male,No,0,Graduate,No,3167,0,74,360,1,Urban,N -LP001097,Male,No,1,Graduate,Yes,4692,0,106,360,1,Rural,N -LP001098,Male,Yes,0,Graduate,No,3500,1667,114,360,1,Semiurban,Y -LP001100,Male,No,3+,Graduate,No,12500,3000,320,360,1,Rural,N -LP001106,Male,Yes,0,Graduate,No,2275,2067,,360,1,Urban,Y -LP001109,Male,Yes,0,Graduate,No,1828,1330,100,,0,Urban,N -LP001112,Female,Yes,0,Graduate,No,3667,1459,144,360,1,Semiurban,Y -LP001114,Male,No,0,Graduate,No,4166,7210,184,360,1,Urban,Y -LP001116,Male,No,0,Not Graduate,No,3748,1668,110,360,1,Semiurban,Y -LP001119,Male,No,0,Graduate,No,3600,0,80,360,1,Urban,N -LP001120,Male,No,0,Graduate,No,1800,1213,47,360,1,Urban,Y -LP001123,Male,Yes,0,Graduate,No,2400,0,75,360,,Urban,Y -LP001131,Male,Yes,0,Graduate,No,3941,2336,134,360,1,Semiurban,Y -LP001136,Male,Yes,0,Not Graduate,Yes,4695,0,96,,1,Urban,Y -LP001137,Female,No,0,Graduate,No,3410,0,88,,1,Urban,Y -LP001138,Male,Yes,1,Graduate,No,5649,0,44,360,1,Urban,Y -LP001144,Male,Yes,0,Graduate,No,5821,0,144,360,1,Urban,Y -LP001146,Female,Yes,0,Graduate,No,2645,3440,120,360,0,Urban,N -LP001151,Female,No,0,Graduate,No,4000,2275,144,360,1,Semiurban,Y -LP001155,Female,Yes,0,Not Graduate,No,1928,1644,100,360,1,Semiurban,Y -LP001157,Female,No,0,Graduate,No,3086,0,120,360,1,Semiurban,Y -LP001164,Female,No,0,Graduate,No,4230,0,112,360,1,Semiurban,N -LP001179,Male,Yes,2,Graduate,No,4616,0,134,360,1,Urban,N -LP001186,Female,Yes,1,Graduate,Yes,11500,0,286,360,0,Urban,N -LP001194,Male,Yes,2,Graduate,No,2708,1167,97,360,1,Semiurban,Y -LP001195,Male,Yes,0,Graduate,No,2132,1591,96,360,1,Semiurban,Y -LP001197,Male,Yes,0,Graduate,No,3366,2200,135,360,1,Rural,N -LP001198,Male,Yes,1,Graduate,No,8080,2250,180,360,1,Urban,Y -LP001199,Male,Yes,2,Not Graduate,No,3357,2859,144,360,1,Urban,Y -LP001205,Male,Yes,0,Graduate,No,2500,3796,120,360,1,Urban,Y -LP001206,Male,Yes,3+,Graduate,No,3029,0,99,360,1,Urban,Y -LP001207,Male,Yes,0,Not Graduate,Yes,2609,3449,165,180,0,Rural,N -LP001213,Male,Yes,1,Graduate,No,4945,0,,360,0,Rural,N -LP001222,Female,No,0,Graduate,No,4166,0,116,360,0,Semiurban,N -LP001225,Male,Yes,0,Graduate,No,5726,4595,258,360,1,Semiurban,N -LP001228,Male,No,0,Not Graduate,No,3200,2254,126,180,0,Urban,N -LP001233,Male,Yes,1,Graduate,No,10750,0,312,360,1,Urban,Y -LP001238,Male,Yes,3+,Not Graduate,Yes,7100,0,125,60,1,Urban,Y -LP001241,Female,No,0,Graduate,No,4300,0,136,360,0,Semiurban,N -LP001243,Male,Yes,0,Graduate,No,3208,3066,172,360,1,Urban,Y -LP001245,Male,Yes,2,Not Graduate,Yes,1875,1875,97,360,1,Semiurban,Y -LP001248,Male,No,0,Graduate,No,3500,0,81,300,1,Semiurban,Y -LP001250,Male,Yes,3+,Not Graduate,No,4755,0,95,,0,Semiurban,N -LP001253,Male,Yes,3+,Graduate,Yes,5266,1774,187,360,1,Semiurban,Y -LP001255,Male,No,0,Graduate,No,3750,0,113,480,1,Urban,N -LP001256,Male,No,0,Graduate,No,3750,4750,176,360,1,Urban,N -LP001259,Male,Yes,1,Graduate,Yes,1000,3022,110,360,1,Urban,N -LP001263,Male,Yes,3+,Graduate,No,3167,4000,180,300,0,Semiurban,N -LP001264,Male,Yes,3+,Not Graduate,Yes,3333,2166,130,360,,Semiurban,Y -LP001265,Female,No,0,Graduate,No,3846,0,111,360,1,Semiurban,Y -LP001266,Male,Yes,1,Graduate,Yes,2395,0,,360,1,Semiurban,Y -LP001267,Female,Yes,2,Graduate,No,1378,1881,167,360,1,Urban,N -LP001273,Male,Yes,0,Graduate,No,6000,2250,265,360,,Semiurban,N -LP001275,Male,Yes,1,Graduate,No,3988,0,50,240,1,Urban,Y -LP001279,Male,No,0,Graduate,No,2366,2531,136,360,1,Semiurban,Y -LP001280,Male,Yes,2,Not Graduate,No,3333,2000,99,360,,Semiurban,Y -LP001282,Male,Yes,0,Graduate,No,2500,2118,104,360,1,Semiurban,Y -LP001289,Male,No,0,Graduate,No,8566,0,210,360,1,Urban,Y -LP001310,Male,Yes,0,Graduate,No,5695,4167,175,360,1,Semiurban,Y -LP001316,Male,Yes,0,Graduate,No,2958,2900,131,360,1,Semiurban,Y -LP001318,Male,Yes,2,Graduate,No,6250,5654,188,180,1,Semiurban,Y -LP001319,Male,Yes,2,Not Graduate,No,3273,1820,81,360,1,Urban,Y -LP001322,Male,No,0,Graduate,No,4133,0,122,360,1,Semiurban,Y -LP001325,Male,No,0,Not Graduate,No,3620,0,25,120,1,Semiurban,Y -LP001326,Male,No,0,Graduate,,6782,0,,360,,Urban,N -LP001327,Female,Yes,0,Graduate,No,2484,2302,137,360,1,Semiurban,Y -LP001333,Male,Yes,0,Graduate,No,1977,997,50,360,1,Semiurban,Y -LP001334,Male,Yes,0,Not Graduate,No,4188,0,115,180,1,Semiurban,Y -LP001343,Male,Yes,0,Graduate,No,1759,3541,131,360,1,Semiurban,Y -LP001345,Male,Yes,2,Not Graduate,No,4288,3263,133,180,1,Urban,Y -LP001349,Male,No,0,Graduate,No,4843,3806,151,360,1,Semiurban,Y -LP001350,Male,Yes,,Graduate,No,13650,0,,360,1,Urban,Y -LP001356,Male,Yes,0,Graduate,No,4652,3583,,360,1,Semiurban,Y -LP001357,Male,,,Graduate,No,3816,754,160,360,1,Urban,Y -LP001367,Male,Yes,1,Graduate,No,3052,1030,100,360,1,Urban,Y -LP001369,Male,Yes,2,Graduate,No,11417,1126,225,360,1,Urban,Y -LP001370,Male,No,0,Not Graduate,,7333,0,120,360,1,Rural,N -LP001379,Male,Yes,2,Graduate,No,3800,3600,216,360,0,Urban,N -LP001384,Male,Yes,3+,Not Graduate,No,2071,754,94,480,1,Semiurban,Y -LP001385,Male,No,0,Graduate,No,5316,0,136,360,1,Urban,Y -LP001387,Female,Yes,0,Graduate,,2929,2333,139,360,1,Semiurban,Y -LP001391,Male,Yes,0,Not Graduate,No,3572,4114,152,,0,Rural,N -LP001392,Female,No,1,Graduate,Yes,7451,0,,360,1,Semiurban,Y -LP001398,Male,No,0,Graduate,,5050,0,118,360,1,Semiurban,Y -LP001401,Male,Yes,1,Graduate,No,14583,0,185,180,1,Rural,Y -LP001404,Female,Yes,0,Graduate,No,3167,2283,154,360,1,Semiurban,Y -LP001405,Male,Yes,1,Graduate,No,2214,1398,85,360,,Urban,Y -LP001421,Male,Yes,0,Graduate,No,5568,2142,175,360,1,Rural,N -LP001422,Female,No,0,Graduate,No,10408,0,259,360,1,Urban,Y -LP001426,Male,Yes,,Graduate,No,5667,2667,180,360,1,Rural,Y -LP001430,Female,No,0,Graduate,No,4166,0,44,360,1,Semiurban,Y -LP001431,Female,No,0,Graduate,No,2137,8980,137,360,0,Semiurban,Y -LP001432,Male,Yes,2,Graduate,No,2957,0,81,360,1,Semiurban,Y -LP001439,Male,Yes,0,Not Graduate,No,4300,2014,194,360,1,Rural,Y -LP001443,Female,No,0,Graduate,No,3692,0,93,360,,Rural,Y -LP001448,,Yes,3+,Graduate,No,23803,0,370,360,1,Rural,Y -LP001449,Male,No,0,Graduate,No,3865,1640,,360,1,Rural,Y -LP001451,Male,Yes,1,Graduate,Yes,10513,3850,160,180,0,Urban,N -LP001465,Male,Yes,0,Graduate,No,6080,2569,182,360,,Rural,N -LP001469,Male,No,0,Graduate,Yes,20166,0,650,480,,Urban,Y -LP001473,Male,No,0,Graduate,No,2014,1929,74,360,1,Urban,Y -LP001478,Male,No,0,Graduate,No,2718,0,70,360,1,Semiurban,Y -LP001482,Male,Yes,0,Graduate,Yes,3459,0,25,120,1,Semiurban,Y -LP001487,Male,No,0,Graduate,No,4895,0,102,360,1,Semiurban,Y -LP001488,Male,Yes,3+,Graduate,No,4000,7750,290,360,1,Semiurban,N -LP001489,Female,Yes,0,Graduate,No,4583,0,84,360,1,Rural,N -LP001491,Male,Yes,2,Graduate,Yes,3316,3500,88,360,1,Urban,Y -LP001492,Male,No,0,Graduate,No,14999,0,242,360,0,Semiurban,N -LP001493,Male,Yes,2,Not Graduate,No,4200,1430,129,360,1,Rural,N -LP001497,Male,Yes,2,Graduate,No,5042,2083,185,360,1,Rural,N -LP001498,Male,No,0,Graduate,No,5417,0,168,360,1,Urban,Y -LP001504,Male,No,0,Graduate,Yes,6950,0,175,180,1,Semiurban,Y -LP001507,Male,Yes,0,Graduate,No,2698,2034,122,360,1,Semiurban,Y -LP001508,Male,Yes,2,Graduate,No,11757,0,187,180,1,Urban,Y -LP001514,Female,Yes,0,Graduate,No,2330,4486,100,360,1,Semiurban,Y -LP001516,Female,Yes,2,Graduate,No,14866,0,70,360,1,Urban,Y -LP001518,Male,Yes,1,Graduate,No,1538,1425,30,360,1,Urban,Y -LP001519,Female,No,0,Graduate,No,10000,1666,225,360,1,Rural,N -LP001520,Male,Yes,0,Graduate,No,4860,830,125,360,1,Semiurban,Y -LP001528,Male,No,0,Graduate,No,6277,0,118,360,0,Rural,N -LP001529,Male,Yes,0,Graduate,Yes,2577,3750,152,360,1,Rural,Y -LP001531,Male,No,0,Graduate,No,9166,0,244,360,1,Urban,N -LP001532,Male,Yes,2,Not Graduate,No,2281,0,113,360,1,Rural,N -LP001535,Male,No,0,Graduate,No,3254,0,50,360,1,Urban,Y -LP001536,Male,Yes,3+,Graduate,No,39999,0,600,180,0,Semiurban,Y -LP001541,Male,Yes,1,Graduate,No,6000,0,160,360,,Rural,Y -LP001543,Male,Yes,1,Graduate,No,9538,0,187,360,1,Urban,Y -LP001546,Male,No,0,Graduate,,2980,2083,120,360,1,Rural,Y -LP001552,Male,Yes,0,Graduate,No,4583,5625,255,360,1,Semiurban,Y -LP001560,Male,Yes,0,Not Graduate,No,1863,1041,98,360,1,Semiurban,Y -LP001562,Male,Yes,0,Graduate,No,7933,0,275,360,1,Urban,N -LP001565,Male,Yes,1,Graduate,No,3089,1280,121,360,0,Semiurban,N -LP001570,Male,Yes,2,Graduate,No,4167,1447,158,360,1,Rural,Y -LP001572,Male,Yes,0,Graduate,No,9323,0,75,180,1,Urban,Y -LP001574,Male,Yes,0,Graduate,No,3707,3166,182,,1,Rural,Y -LP001577,Female,Yes,0,Graduate,No,4583,0,112,360,1,Rural,N -LP001578,Male,Yes,0,Graduate,No,2439,3333,129,360,1,Rural,Y -LP001579,Male,No,0,Graduate,No,2237,0,63,480,0,Semiurban,N -LP001580,Male,Yes,2,Graduate,No,8000,0,200,360,1,Semiurban,Y -LP001581,Male,Yes,0,Not Graduate,,1820,1769,95,360,1,Rural,Y -LP001585,,Yes,3+,Graduate,No,51763,0,700,300,1,Urban,Y -LP001586,Male,Yes,3+,Not Graduate,No,3522,0,81,180,1,Rural,N -LP001594,Male,Yes,0,Graduate,No,5708,5625,187,360,1,Semiurban,Y -LP001603,Male,Yes,0,Not Graduate,Yes,4344,736,87,360,1,Semiurban,N -LP001606,Male,Yes,0,Graduate,No,3497,1964,116,360,1,Rural,Y -LP001608,Male,Yes,2,Graduate,No,2045,1619,101,360,1,Rural,Y -LP001610,Male,Yes,3+,Graduate,No,5516,11300,495,360,0,Semiurban,N -LP001616,Male,Yes,1,Graduate,No,3750,0,116,360,1,Semiurban,Y -LP001630,Male,No,0,Not Graduate,No,2333,1451,102,480,0,Urban,N -LP001633,Male,Yes,1,Graduate,No,6400,7250,180,360,0,Urban,N -LP001634,Male,No,0,Graduate,No,1916,5063,67,360,,Rural,N -LP001636,Male,Yes,0,Graduate,No,4600,0,73,180,1,Semiurban,Y -LP001637,Male,Yes,1,Graduate,No,33846,0,260,360,1,Semiurban,N -LP001639,Female,Yes,0,Graduate,No,3625,0,108,360,1,Semiurban,Y -LP001640,Male,Yes,0,Graduate,Yes,39147,4750,120,360,1,Semiurban,Y -LP001641,Male,Yes,1,Graduate,Yes,2178,0,66,300,0,Rural,N -LP001643,Male,Yes,0,Graduate,No,2383,2138,58,360,,Rural,Y -LP001644,,Yes,0,Graduate,Yes,674,5296,168,360,1,Rural,Y -LP001647,Male,Yes,0,Graduate,No,9328,0,188,180,1,Rural,Y -LP001653,Male,No,0,Not Graduate,No,4885,0,48,360,1,Rural,Y -LP001656,Male,No,0,Graduate,No,12000,0,164,360,1,Semiurban,N -LP001657,Male,Yes,0,Not Graduate,No,6033,0,160,360,1,Urban,N -LP001658,Male,No,0,Graduate,No,3858,0,76,360,1,Semiurban,Y -LP001664,Male,No,0,Graduate,No,4191,0,120,360,1,Rural,Y -LP001665,Male,Yes,1,Graduate,No,3125,2583,170,360,1,Semiurban,N -LP001666,Male,No,0,Graduate,No,8333,3750,187,360,1,Rural,Y -LP001669,Female,No,0,Not Graduate,No,1907,2365,120,,1,Urban,Y -LP001671,Female,Yes,0,Graduate,No,3416,2816,113,360,,Semiurban,Y -LP001673,Male,No,0,Graduate,Yes,11000,0,83,360,1,Urban,N -LP001674,Male,Yes,1,Not Graduate,No,2600,2500,90,360,1,Semiurban,Y -LP001677,Male,No,2,Graduate,No,4923,0,166,360,0,Semiurban,Y -LP001682,Male,Yes,3+,Not Graduate,No,3992,0,,180,1,Urban,N -LP001688,Male,Yes,1,Not Graduate,No,3500,1083,135,360,1,Urban,Y -LP001691,Male,Yes,2,Not Graduate,No,3917,0,124,360,1,Semiurban,Y -LP001692,Female,No,0,Not Graduate,No,4408,0,120,360,1,Semiurban,Y -LP001693,Female,No,0,Graduate,No,3244,0,80,360,1,Urban,Y -LP001698,Male,No,0,Not Graduate,No,3975,2531,55,360,1,Rural,Y -LP001699,Male,No,0,Graduate,No,2479,0,59,360,1,Urban,Y -LP001702,Male,No,0,Graduate,No,3418,0,127,360,1,Semiurban,N -LP001708,Female,No,0,Graduate,No,10000,0,214,360,1,Semiurban,N -LP001711,Male,Yes,3+,Graduate,No,3430,1250,128,360,0,Semiurban,N -LP001713,Male,Yes,1,Graduate,Yes,7787,0,240,360,1,Urban,Y -LP001715,Male,Yes,3+,Not Graduate,Yes,5703,0,130,360,1,Rural,Y -LP001716,Male,Yes,0,Graduate,No,3173,3021,137,360,1,Urban,Y -LP001720,Male,Yes,3+,Not Graduate,No,3850,983,100,360,1,Semiurban,Y -LP001722,Male,Yes,0,Graduate,No,150,1800,135,360,1,Rural,N -LP001726,Male,Yes,0,Graduate,No,3727,1775,131,360,1,Semiurban,Y -LP001732,Male,Yes,2,Graduate,,5000,0,72,360,0,Semiurban,N -LP001734,Female,Yes,2,Graduate,No,4283,2383,127,360,,Semiurban,Y -LP001736,Male,Yes,0,Graduate,No,2221,0,60,360,0,Urban,N -LP001743,Male,Yes,2,Graduate,No,4009,1717,116,360,1,Semiurban,Y -LP001744,Male,No,0,Graduate,No,2971,2791,144,360,1,Semiurban,Y -LP001749,Male,Yes,0,Graduate,No,7578,1010,175,,1,Semiurban,Y -LP001750,Male,Yes,0,Graduate,No,6250,0,128,360,1,Semiurban,Y -LP001751,Male,Yes,0,Graduate,No,3250,0,170,360,1,Rural,N -LP001754,Male,Yes,,Not Graduate,Yes,4735,0,138,360,1,Urban,N -LP001758,Male,Yes,2,Graduate,No,6250,1695,210,360,1,Semiurban,Y -LP001760,Male,,,Graduate,No,4758,0,158,480,1,Semiurban,Y -LP001761,Male,No,0,Graduate,Yes,6400,0,200,360,1,Rural,Y -LP001765,Male,Yes,1,Graduate,No,2491,2054,104,360,1,Semiurban,Y -LP001768,Male,Yes,0,Graduate,,3716,0,42,180,1,Rural,Y -LP001770,Male,No,0,Not Graduate,No,3189,2598,120,,1,Rural,Y -LP001776,Female,No,0,Graduate,No,8333,0,280,360,1,Semiurban,Y -LP001778,Male,Yes,1,Graduate,No,3155,1779,140,360,1,Semiurban,Y -LP001784,Male,Yes,1,Graduate,No,5500,1260,170,360,1,Rural,Y -LP001786,Male,Yes,0,Graduate,,5746,0,255,360,,Urban,N -LP001788,Female,No,0,Graduate,Yes,3463,0,122,360,,Urban,Y -LP001790,Female,No,1,Graduate,No,3812,0,112,360,1,Rural,Y -LP001792,Male,Yes,1,Graduate,No,3315,0,96,360,1,Semiurban,Y -LP001798,Male,Yes,2,Graduate,No,5819,5000,120,360,1,Rural,Y -LP001800,Male,Yes,1,Not Graduate,No,2510,1983,140,180,1,Urban,N -LP001806,Male,No,0,Graduate,No,2965,5701,155,60,1,Urban,Y -LP001807,Male,Yes,2,Graduate,Yes,6250,1300,108,360,1,Rural,Y -LP001811,Male,Yes,0,Not Graduate,No,3406,4417,123,360,1,Semiurban,Y -LP001813,Male,No,0,Graduate,Yes,6050,4333,120,180,1,Urban,N -LP001814,Male,Yes,2,Graduate,No,9703,0,112,360,1,Urban,Y -LP001819,Male,Yes,1,Not Graduate,No,6608,0,137,180,1,Urban,Y -LP001824,Male,Yes,1,Graduate,No,2882,1843,123,480,1,Semiurban,Y -LP001825,Male,Yes,0,Graduate,No,1809,1868,90,360,1,Urban,Y -LP001835,Male,Yes,0,Not Graduate,No,1668,3890,201,360,0,Semiurban,N -LP001836,Female,No,2,Graduate,No,3427,0,138,360,1,Urban,N -LP001841,Male,No,0,Not Graduate,Yes,2583,2167,104,360,1,Rural,Y -LP001843,Male,Yes,1,Not Graduate,No,2661,7101,279,180,1,Semiurban,Y -LP001844,Male,No,0,Graduate,Yes,16250,0,192,360,0,Urban,N -LP001846,Female,No,3+,Graduate,No,3083,0,255,360,1,Rural,Y -LP001849,Male,No,0,Not Graduate,No,6045,0,115,360,0,Rural,N -LP001854,Male,Yes,3+,Graduate,No,5250,0,94,360,1,Urban,N -LP001859,Male,Yes,0,Graduate,No,14683,2100,304,360,1,Rural,N -LP001864,Male,Yes,3+,Not Graduate,No,4931,0,128,360,,Semiurban,N -LP001865,Male,Yes,1,Graduate,No,6083,4250,330,360,,Urban,Y -LP001868,Male,No,0,Graduate,No,2060,2209,134,360,1,Semiurban,Y -LP001870,Female,No,1,Graduate,No,3481,0,155,36,1,Semiurban,N -LP001871,Female,No,0,Graduate,No,7200,0,120,360,1,Rural,Y -LP001872,Male,No,0,Graduate,Yes,5166,0,128,360,1,Semiurban,Y -LP001875,Male,No,0,Graduate,No,4095,3447,151,360,1,Rural,Y -LP001877,Male,Yes,2,Graduate,No,4708,1387,150,360,1,Semiurban,Y -LP001882,Male,Yes,3+,Graduate,No,4333,1811,160,360,0,Urban,Y -LP001883,Female,No,0,Graduate,,3418,0,135,360,1,Rural,N -LP001884,Female,No,1,Graduate,No,2876,1560,90,360,1,Urban,Y -LP001888,Female,No,0,Graduate,No,3237,0,30,360,1,Urban,Y -LP001891,Male,Yes,0,Graduate,No,11146,0,136,360,1,Urban,Y -LP001892,Male,No,0,Graduate,No,2833,1857,126,360,1,Rural,Y -LP001894,Male,Yes,0,Graduate,No,2620,2223,150,360,1,Semiurban,Y -LP001896,Male,Yes,2,Graduate,No,3900,0,90,360,1,Semiurban,Y -LP001900,Male,Yes,1,Graduate,No,2750,1842,115,360,1,Semiurban,Y -LP001903,Male,Yes,0,Graduate,No,3993,3274,207,360,1,Semiurban,Y -LP001904,Male,Yes,0,Graduate,No,3103,1300,80,360,1,Urban,Y -LP001907,Male,Yes,0,Graduate,No,14583,0,436,360,1,Semiurban,Y -LP001908,Female,Yes,0,Not Graduate,No,4100,0,124,360,,Rural,Y -LP001910,Male,No,1,Not Graduate,Yes,4053,2426,158,360,0,Urban,N -LP001914,Male,Yes,0,Graduate,No,3927,800,112,360,1,Semiurban,Y -LP001915,Male,Yes,2,Graduate,No,2301,985.7999878,78,180,1,Urban,Y -LP001917,Female,No,0,Graduate,No,1811,1666,54,360,1,Urban,Y -LP001922,Male,Yes,0,Graduate,No,20667,0,,360,1,Rural,N -LP001924,Male,No,0,Graduate,No,3158,3053,89,360,1,Rural,Y -LP001925,Female,No,0,Graduate,Yes,2600,1717,99,300,1,Semiurban,N -LP001926,Male,Yes,0,Graduate,No,3704,2000,120,360,1,Rural,Y -LP001931,Female,No,0,Graduate,No,4124,0,115,360,1,Semiurban,Y -LP001935,Male,No,0,Graduate,No,9508,0,187,360,1,Rural,Y -LP001936,Male,Yes,0,Graduate,No,3075,2416,139,360,1,Rural,Y -LP001938,Male,Yes,2,Graduate,No,4400,0,127,360,0,Semiurban,N -LP001940,Male,Yes,2,Graduate,No,3153,1560,134,360,1,Urban,Y -LP001945,Female,No,,Graduate,No,5417,0,143,480,0,Urban,N -LP001947,Male,Yes,0,Graduate,No,2383,3334,172,360,1,Semiurban,Y -LP001949,Male,Yes,3+,Graduate,,4416,1250,110,360,1,Urban,Y -LP001953,Male,Yes,1,Graduate,No,6875,0,200,360,1,Semiurban,Y -LP001954,Female,Yes,1,Graduate,No,4666,0,135,360,1,Urban,Y -LP001955,Female,No,0,Graduate,No,5000,2541,151,480,1,Rural,N -LP001963,Male,Yes,1,Graduate,No,2014,2925,113,360,1,Urban,N -LP001964,Male,Yes,0,Not Graduate,No,1800,2934,93,360,0,Urban,N -LP001972,Male,Yes,,Not Graduate,No,2875,1750,105,360,1,Semiurban,Y -LP001974,Female,No,0,Graduate,No,5000,0,132,360,1,Rural,Y -LP001977,Male,Yes,1,Graduate,No,1625,1803,96,360,1,Urban,Y -LP001978,Male,No,0,Graduate,No,4000,2500,140,360,1,Rural,Y -LP001990,Male,No,0,Not Graduate,No,2000,0,,360,1,Urban,N -LP001993,Female,No,0,Graduate,No,3762,1666,135,360,1,Rural,Y -LP001994,Female,No,0,Graduate,No,2400,1863,104,360,0,Urban,N -LP001996,Male,No,0,Graduate,No,20233,0,480,360,1,Rural,N -LP001998,Male,Yes,2,Not Graduate,No,7667,0,185,360,,Rural,Y -LP002002,Female,No,0,Graduate,No,2917,0,84,360,1,Semiurban,Y -LP002004,Male,No,0,Not Graduate,No,2927,2405,111,360,1,Semiurban,Y -LP002006,Female,No,0,Graduate,No,2507,0,56,360,1,Rural,Y -LP002008,Male,Yes,2,Graduate,Yes,5746,0,144,84,,Rural,Y -LP002024,,Yes,0,Graduate,No,2473,1843,159,360,1,Rural,N -LP002031,Male,Yes,1,Not Graduate,No,3399,1640,111,180,1,Urban,Y -LP002035,Male,Yes,2,Graduate,No,3717,0,120,360,1,Semiurban,Y -LP002036,Male,Yes,0,Graduate,No,2058,2134,88,360,,Urban,Y -LP002043,Female,No,1,Graduate,No,3541,0,112,360,,Semiurban,Y -LP002050,Male,Yes,1,Graduate,Yes,10000,0,155,360,1,Rural,N -LP002051,Male,Yes,0,Graduate,No,2400,2167,115,360,1,Semiurban,Y -LP002053,Male,Yes,3+,Graduate,No,4342,189,124,360,1,Semiurban,Y -LP002054,Male,Yes,2,Not Graduate,No,3601,1590,,360,1,Rural,Y -LP002055,Female,No,0,Graduate,No,3166,2985,132,360,,Rural,Y -LP002065,Male,Yes,3+,Graduate,No,15000,0,300,360,1,Rural,Y -LP002067,Male,Yes,1,Graduate,Yes,8666,4983,376,360,0,Rural,N -LP002068,Male,No,0,Graduate,No,4917,0,130,360,0,Rural,Y -LP002082,Male,Yes,0,Graduate,Yes,5818,2160,184,360,1,Semiurban,Y -LP002086,Female,Yes,0,Graduate,No,4333,2451,110,360,1,Urban,N -LP002087,Female,No,0,Graduate,No,2500,0,67,360,1,Urban,Y -LP002097,Male,No,1,Graduate,No,4384,1793,117,360,1,Urban,Y -LP002098,Male,No,0,Graduate,No,2935,0,98,360,1,Semiurban,Y -LP002100,Male,No,,Graduate,No,2833,0,71,360,1,Urban,Y -LP002101,Male,Yes,0,Graduate,,63337,0,490,180,1,Urban,Y -LP002103,,Yes,1,Graduate,Yes,9833,1833,182,180,1,Urban,Y -LP002106,Male,Yes,,Graduate,Yes,5503,4490,70,,1,Semiurban,Y -LP002110,Male,Yes,1,Graduate,,5250,688,160,360,1,Rural,Y -LP002112,Male,Yes,2,Graduate,Yes,2500,4600,176,360,1,Rural,Y -LP002113,Female,No,3+,Not Graduate,No,1830,0,,360,0,Urban,N -LP002114,Female,No,0,Graduate,No,4160,0,71,360,1,Semiurban,Y -LP002115,Male,Yes,3+,Not Graduate,No,2647,1587,173,360,1,Rural,N -LP002116,Female,No,0,Graduate,No,2378,0,46,360,1,Rural,N -LP002119,Male,Yes,1,Not Graduate,No,4554,1229,158,360,1,Urban,Y -LP002126,Male,Yes,3+,Not Graduate,No,3173,0,74,360,1,Semiurban,Y -LP002128,Male,Yes,2,Graduate,,2583,2330,125,360,1,Rural,Y -LP002129,Male,Yes,0,Graduate,No,2499,2458,160,360,1,Semiurban,Y -LP002130,Male,Yes,,Not Graduate,No,3523,3230,152,360,0,Rural,N -LP002131,Male,Yes,2,Not Graduate,No,3083,2168,126,360,1,Urban,Y -LP002137,Male,Yes,0,Graduate,No,6333,4583,259,360,,Semiurban,Y -LP002138,Male,Yes,0,Graduate,No,2625,6250,187,360,1,Rural,Y -LP002139,Male,Yes,0,Graduate,No,9083,0,228,360,1,Semiurban,Y -LP002140,Male,No,0,Graduate,No,8750,4167,308,360,1,Rural,N -LP002141,Male,Yes,3+,Graduate,No,2666,2083,95,360,1,Rural,Y -LP002142,Female,Yes,0,Graduate,Yes,5500,0,105,360,0,Rural,N -LP002143,Female,Yes,0,Graduate,No,2423,505,130,360,1,Semiurban,Y -LP002144,Female,No,,Graduate,No,3813,0,116,180,1,Urban,Y -LP002149,Male,Yes,2,Graduate,No,8333,3167,165,360,1,Rural,Y -LP002151,Male,Yes,1,Graduate,No,3875,0,67,360,1,Urban,N -LP002158,Male,Yes,0,Not Graduate,No,3000,1666,100,480,0,Urban,N -LP002160,Male,Yes,3+,Graduate,No,5167,3167,200,360,1,Semiurban,Y -LP002161,Female,No,1,Graduate,No,4723,0,81,360,1,Semiurban,N -LP002170,Male,Yes,2,Graduate,No,5000,3667,236,360,1,Semiurban,Y -LP002175,Male,Yes,0,Graduate,No,4750,2333,130,360,1,Urban,Y -LP002178,Male,Yes,0,Graduate,No,3013,3033,95,300,,Urban,Y -LP002180,Male,No,0,Graduate,Yes,6822,0,141,360,1,Rural,Y -LP002181,Male,No,0,Not Graduate,No,6216,0,133,360,1,Rural,N -LP002187,Male,No,0,Graduate,No,2500,0,96,480,1,Semiurban,N -LP002188,Male,No,0,Graduate,No,5124,0,124,,0,Rural,N -LP002190,Male,Yes,1,Graduate,No,6325,0,175,360,1,Semiurban,Y -LP002191,Male,Yes,0,Graduate,No,19730,5266,570,360,1,Rural,N -LP002194,Female,No,0,Graduate,Yes,15759,0,55,360,1,Semiurban,Y -LP002197,Male,Yes,2,Graduate,No,5185,0,155,360,1,Semiurban,Y -LP002201,Male,Yes,2,Graduate,Yes,9323,7873,380,300,1,Rural,Y -LP002205,Male,No,1,Graduate,No,3062,1987,111,180,0,Urban,N -LP002209,Female,No,0,Graduate,,2764,1459,110,360,1,Urban,Y -LP002211,Male,Yes,0,Graduate,No,4817,923,120,180,1,Urban,Y -LP002219,Male,Yes,3+,Graduate,No,8750,4996,130,360,1,Rural,Y -LP002223,Male,Yes,0,Graduate,No,4310,0,130,360,,Semiurban,Y -LP002224,Male,No,0,Graduate,No,3069,0,71,480,1,Urban,N -LP002225,Male,Yes,2,Graduate,No,5391,0,130,360,1,Urban,Y -LP002226,Male,Yes,0,Graduate,,3333,2500,128,360,1,Semiurban,Y -LP002229,Male,No,0,Graduate,No,5941,4232,296,360,1,Semiurban,Y -LP002231,Female,No,0,Graduate,No,6000,0,156,360,1,Urban,Y -LP002234,Male,No,0,Graduate,Yes,7167,0,128,360,1,Urban,Y -LP002236,Male,Yes,2,Graduate,No,4566,0,100,360,1,Urban,N -LP002237,Male,No,1,Graduate,,3667,0,113,180,1,Urban,Y -LP002239,Male,No,0,Not Graduate,No,2346,1600,132,360,1,Semiurban,Y -LP002243,Male,Yes,0,Not Graduate,No,3010,3136,,360,0,Urban,N -LP002244,Male,Yes,0,Graduate,No,2333,2417,136,360,1,Urban,Y -LP002250,Male,Yes,0,Graduate,No,5488,0,125,360,1,Rural,Y -LP002255,Male,No,3+,Graduate,No,9167,0,185,360,1,Rural,Y -LP002262,Male,Yes,3+,Graduate,No,9504,0,275,360,1,Rural,Y -LP002263,Male,Yes,0,Graduate,No,2583,2115,120,360,,Urban,Y -LP002265,Male,Yes,2,Not Graduate,No,1993,1625,113,180,1,Semiurban,Y -LP002266,Male,Yes,2,Graduate,No,3100,1400,113,360,1,Urban,Y -LP002272,Male,Yes,2,Graduate,No,3276,484,135,360,,Semiurban,Y -LP002277,Female,No,0,Graduate,No,3180,0,71,360,0,Urban,N -LP002281,Male,Yes,0,Graduate,No,3033,1459,95,360,1,Urban,Y -LP002284,Male,No,0,Not Graduate,No,3902,1666,109,360,1,Rural,Y -LP002287,Female,No,0,Graduate,No,1500,1800,103,360,0,Semiurban,N -LP002288,Male,Yes,2,Not Graduate,No,2889,0,45,180,0,Urban,N -LP002296,Male,No,0,Not Graduate,No,2755,0,65,300,1,Rural,N -LP002297,Male,No,0,Graduate,No,2500,20000,103,360,1,Semiurban,Y -LP002300,Female,No,0,Not Graduate,No,1963,0,53,360,1,Semiurban,Y -LP002301,Female,No,0,Graduate,Yes,7441,0,194,360,1,Rural,N -LP002305,Female,No,0,Graduate,No,4547,0,115,360,1,Semiurban,Y -LP002308,Male,Yes,0,Not Graduate,No,2167,2400,115,360,1,Urban,Y -LP002314,Female,No,0,Not Graduate,No,2213,0,66,360,1,Rural,Y -LP002315,Male,Yes,1,Graduate,No,8300,0,152,300,0,Semiurban,N -LP002317,Male,Yes,3+,Graduate,No,81000,0,360,360,0,Rural,N -LP002318,Female,No,1,Not Graduate,Yes,3867,0,62,360,1,Semiurban,N -LP002319,Male,Yes,0,Graduate,,6256,0,160,360,,Urban,Y -LP002328,Male,Yes,0,Not Graduate,No,6096,0,218,360,0,Rural,N -LP002332,Male,Yes,0,Not Graduate,No,2253,2033,110,360,1,Rural,Y -LP002335,Female,Yes,0,Not Graduate,No,2149,3237,178,360,0,Semiurban,N -LP002337,Female,No,0,Graduate,No,2995,0,60,360,1,Urban,Y -LP002341,Female,No,1,Graduate,No,2600,0,160,360,1,Urban,N -LP002342,Male,Yes,2,Graduate,Yes,1600,20000,239,360,1,Urban,N -LP002345,Male,Yes,0,Graduate,No,1025,2773,112,360,1,Rural,Y -LP002347,Male,Yes,0,Graduate,No,3246,1417,138,360,1,Semiurban,Y -LP002348,Male,Yes,0,Graduate,No,5829,0,138,360,1,Rural,Y -LP002357,Female,No,0,Not Graduate,No,2720,0,80,,0,Urban,N -LP002361,Male,Yes,0,Graduate,No,1820,1719,100,360,1,Urban,Y -LP002362,Male,Yes,1,Graduate,No,7250,1667,110,,0,Urban,N -LP002364,Male,Yes,0,Graduate,No,14880,0,96,360,1,Semiurban,Y -LP002366,Male,Yes,0,Graduate,No,2666,4300,121,360,1,Rural,Y -LP002367,Female,No,1,Not Graduate,No,4606,0,81,360,1,Rural,N -LP002368,Male,Yes,2,Graduate,No,5935,0,133,360,1,Semiurban,Y -LP002369,Male,Yes,0,Graduate,No,2920,16.12000084,87,360,1,Rural,Y -LP002370,Male,No,0,Not Graduate,No,2717,0,60,180,1,Urban,Y -LP002377,Female,No,1,Graduate,Yes,8624,0,150,360,1,Semiurban,Y -LP002379,Male,No,0,Graduate,No,6500,0,105,360,0,Rural,N -LP002386,Male,No,0,Graduate,,12876,0,405,360,1,Semiurban,Y -LP002387,Male,Yes,0,Graduate,No,2425,2340,143,360,1,Semiurban,Y -LP002390,Male,No,0,Graduate,No,3750,0,100,360,1,Urban,Y -LP002393,Female,,,Graduate,No,10047,0,,240,1,Semiurban,Y -LP002398,Male,No,0,Graduate,No,1926,1851,50,360,1,Semiurban,Y -LP002401,Male,Yes,0,Graduate,No,2213,1125,,360,1,Urban,Y -LP002403,Male,No,0,Graduate,Yes,10416,0,187,360,0,Urban,N -LP002407,Female,Yes,0,Not Graduate,Yes,7142,0,138,360,1,Rural,Y -LP002408,Male,No,0,Graduate,No,3660,5064,187,360,1,Semiurban,Y -LP002409,Male,Yes,0,Graduate,No,7901,1833,180,360,1,Rural,Y -LP002418,Male,No,3+,Not Graduate,No,4707,1993,148,360,1,Semiurban,Y -LP002422,Male,No,1,Graduate,No,37719,0,152,360,1,Semiurban,Y -LP002424,Male,Yes,0,Graduate,No,7333,8333,175,300,,Rural,Y -LP002429,Male,Yes,1,Graduate,Yes,3466,1210,130,360,1,Rural,Y -LP002434,Male,Yes,2,Not Graduate,No,4652,0,110,360,1,Rural,Y -LP002435,Male,Yes,0,Graduate,,3539,1376,55,360,1,Rural,N -LP002443,Male,Yes,2,Graduate,No,3340,1710,150,360,0,Rural,N -LP002444,Male,No,1,Not Graduate,Yes,2769,1542,190,360,,Semiurban,N -LP002446,Male,Yes,2,Not Graduate,No,2309,1255,125,360,0,Rural,N -LP002447,Male,Yes,2,Not Graduate,No,1958,1456,60,300,,Urban,Y -LP002448,Male,Yes,0,Graduate,No,3948,1733,149,360,0,Rural,N -LP002449,Male,Yes,0,Graduate,No,2483,2466,90,180,0,Rural,Y -LP002453,Male,No,0,Graduate,Yes,7085,0,84,360,1,Semiurban,Y -LP002455,Male,Yes,2,Graduate,No,3859,0,96,360,1,Semiurban,Y -LP002459,Male,Yes,0,Graduate,No,4301,0,118,360,1,Urban,Y -LP002467,Male,Yes,0,Graduate,No,3708,2569,173,360,1,Urban,N -LP002472,Male,No,2,Graduate,No,4354,0,136,360,1,Rural,Y -LP002473,Male,Yes,0,Graduate,No,8334,0,160,360,1,Semiurban,N -LP002478,,Yes,0,Graduate,Yes,2083,4083,160,360,,Semiurban,Y -LP002484,Male,Yes,3+,Graduate,No,7740,0,128,180,1,Urban,Y -LP002487,Male,Yes,0,Graduate,No,3015,2188,153,360,1,Rural,Y -LP002489,Female,No,1,Not Graduate,,5191,0,132,360,1,Semiurban,Y -LP002493,Male,No,0,Graduate,No,4166,0,98,360,0,Semiurban,N -LP002494,Male,No,0,Graduate,No,6000,0,140,360,1,Rural,Y -LP002500,Male,Yes,3+,Not Graduate,No,2947,1664,70,180,0,Urban,N -LP002501,,Yes,0,Graduate,No,16692,0,110,360,1,Semiurban,Y -LP002502,Female,Yes,2,Not Graduate,,210,2917,98,360,1,Semiurban,Y -LP002505,Male,Yes,0,Graduate,No,4333,2451,110,360,1,Urban,N -LP002515,Male,Yes,1,Graduate,Yes,3450,2079,162,360,1,Semiurban,Y -LP002517,Male,Yes,1,Not Graduate,No,2653,1500,113,180,0,Rural,N -LP002519,Male,Yes,3+,Graduate,No,4691,0,100,360,1,Semiurban,Y -LP002522,Female,No,0,Graduate,Yes,2500,0,93,360,,Urban,Y -LP002524,Male,No,2,Graduate,No,5532,4648,162,360,1,Rural,Y -LP002527,Male,Yes,2,Graduate,Yes,16525,1014,150,360,1,Rural,Y -LP002529,Male,Yes,2,Graduate,No,6700,1750,230,300,1,Semiurban,Y -LP002530,,Yes,2,Graduate,No,2873,1872,132,360,0,Semiurban,N -LP002531,Male,Yes,1,Graduate,Yes,16667,2250,86,360,1,Semiurban,Y -LP002533,Male,Yes,2,Graduate,No,2947,1603,,360,1,Urban,N -LP002534,Female,No,0,Not Graduate,No,4350,0,154,360,1,Rural,Y -LP002536,Male,Yes,3+,Not Graduate,No,3095,0,113,360,1,Rural,Y -LP002537,Male,Yes,0,Graduate,No,2083,3150,128,360,1,Semiurban,Y -LP002541,Male,Yes,0,Graduate,No,10833,0,234,360,1,Semiurban,Y -LP002543,Male,Yes,2,Graduate,No,8333,0,246,360,1,Semiurban,Y -LP002544,Male,Yes,1,Not Graduate,No,1958,2436,131,360,1,Rural,Y -LP002545,Male,No,2,Graduate,No,3547,0,80,360,0,Rural,N -LP002547,Male,Yes,1,Graduate,No,18333,0,500,360,1,Urban,N -LP002555,Male,Yes,2,Graduate,Yes,4583,2083,160,360,1,Semiurban,Y -LP002556,Male,No,0,Graduate,No,2435,0,75,360,1,Urban,N -LP002560,Male,No,0,Not Graduate,No,2699,2785,96,360,,Semiurban,Y -LP002562,Male,Yes,1,Not Graduate,No,5333,1131,186,360,,Urban,Y -LP002571,Male,No,0,Not Graduate,No,3691,0,110,360,1,Rural,Y -LP002582,Female,No,0,Not Graduate,Yes,17263,0,225,360,1,Semiurban,Y -LP002585,Male,Yes,0,Graduate,No,3597,2157,119,360,0,Rural,N -LP002586,Female,Yes,1,Graduate,No,3326,913,105,84,1,Semiurban,Y -LP002587,Male,Yes,0,Not Graduate,No,2600,1700,107,360,1,Rural,Y -LP002588,Male,Yes,0,Graduate,No,4625,2857,111,12,,Urban,Y -LP002600,Male,Yes,1,Graduate,Yes,2895,0,95,360,1,Semiurban,Y -LP002602,Male,No,0,Graduate,No,6283,4416,209,360,0,Rural,N -LP002603,Female,No,0,Graduate,No,645,3683,113,480,1,Rural,Y -LP002606,Female,No,0,Graduate,No,3159,0,100,360,1,Semiurban,Y -LP002615,Male,Yes,2,Graduate,No,4865,5624,208,360,1,Semiurban,Y -LP002618,Male,Yes,1,Not Graduate,No,4050,5302,138,360,,Rural,N -LP002619,Male,Yes,0,Not Graduate,No,3814,1483,124,300,1,Semiurban,Y -LP002622,Male,Yes,2,Graduate,No,3510,4416,243,360,1,Rural,Y -LP002624,Male,Yes,0,Graduate,No,20833,6667,480,360,,Urban,Y -LP002625,,No,0,Graduate,No,3583,0,96,360,1,Urban,N -LP002626,Male,Yes,0,Graduate,Yes,2479,3013,188,360,1,Urban,Y -LP002634,Female,No,1,Graduate,No,13262,0,40,360,1,Urban,Y -LP002637,Male,No,0,Not Graduate,No,3598,1287,100,360,1,Rural,N -LP002640,Male,Yes,1,Graduate,No,6065,2004,250,360,1,Semiurban,Y -LP002643,Male,Yes,2,Graduate,No,3283,2035,148,360,1,Urban,Y -LP002648,Male,Yes,0,Graduate,No,2130,6666,70,180,1,Semiurban,N -LP002652,Male,No,0,Graduate,No,5815,3666,311,360,1,Rural,N -LP002659,Male,Yes,3+,Graduate,No,3466,3428,150,360,1,Rural,Y -LP002670,Female,Yes,2,Graduate,No,2031,1632,113,480,1,Semiurban,Y -LP002682,Male,Yes,,Not Graduate,No,3074,1800,123,360,0,Semiurban,N -LP002683,Male,No,0,Graduate,No,4683,1915,185,360,1,Semiurban,N -LP002684,Female,No,0,Not Graduate,No,3400,0,95,360,1,Rural,N -LP002689,Male,Yes,2,Not Graduate,No,2192,1742,45,360,1,Semiurban,Y -LP002690,Male,No,0,Graduate,No,2500,0,55,360,1,Semiurban,Y -LP002692,Male,Yes,3+,Graduate,Yes,5677,1424,100,360,1,Rural,Y -LP002693,Male,Yes,2,Graduate,Yes,7948,7166,480,360,1,Rural,Y -LP002697,Male,No,0,Graduate,No,4680,2087,,360,1,Semiurban,N -LP002699,Male,Yes,2,Graduate,Yes,17500,0,400,360,1,Rural,Y -LP002705,Male,Yes,0,Graduate,No,3775,0,110,360,1,Semiurban,Y -LP002706,Male,Yes,1,Not Graduate,No,5285,1430,161,360,0,Semiurban,Y -LP002714,Male,No,1,Not Graduate,No,2679,1302,94,360,1,Semiurban,Y -LP002716,Male,No,0,Not Graduate,No,6783,0,130,360,1,Semiurban,Y -LP002717,Male,Yes,0,Graduate,No,1025,5500,216,360,,Rural,Y -LP002720,Male,Yes,3+,Graduate,No,4281,0,100,360,1,Urban,Y -LP002723,Male,No,2,Graduate,No,3588,0,110,360,0,Rural,N -LP002729,Male,No,1,Graduate,No,11250,0,196,360,,Semiurban,N -LP002731,Female,No,0,Not Graduate,Yes,18165,0,125,360,1,Urban,Y -LP002732,Male,No,0,Not Graduate,,2550,2042,126,360,1,Rural,Y -LP002734,Male,Yes,0,Graduate,No,6133,3906,324,360,1,Urban,Y -LP002738,Male,No,2,Graduate,No,3617,0,107,360,1,Semiurban,Y -LP002739,Male,Yes,0,Not Graduate,No,2917,536,66,360,1,Rural,N -LP002740,Male,Yes,3+,Graduate,No,6417,0,157,180,1,Rural,Y -LP002741,Female,Yes,1,Graduate,No,4608,2845,140,180,1,Semiurban,Y -LP002743,Female,No,0,Graduate,No,2138,0,99,360,0,Semiurban,N -LP002753,Female,No,1,Graduate,,3652,0,95,360,1,Semiurban,Y -LP002755,Male,Yes,1,Not Graduate,No,2239,2524,128,360,1,Urban,Y -LP002757,Female,Yes,0,Not Graduate,No,3017,663,102,360,,Semiurban,Y -LP002767,Male,Yes,0,Graduate,No,2768,1950,155,360,1,Rural,Y -LP002768,Male,No,0,Not Graduate,No,3358,0,80,36,1,Semiurban,N -LP002772,Male,No,0,Graduate,No,2526,1783,145,360,1,Rural,Y -LP002776,Female,No,0,Graduate,No,5000,0,103,360,0,Semiurban,N -LP002777,Male,Yes,0,Graduate,No,2785,2016,110,360,1,Rural,Y -LP002778,Male,Yes,2,Graduate,Yes,6633,0,,360,0,Rural,N -LP002784,Male,Yes,1,Not Graduate,No,2492,2375,,360,1,Rural,Y -LP002785,Male,Yes,1,Graduate,No,3333,3250,158,360,1,Urban,Y -LP002788,Male,Yes,0,Not Graduate,No,2454,2333,181,360,0,Urban,N -LP002789,Male,Yes,0,Graduate,No,3593,4266,132,180,0,Rural,N -LP002792,Male,Yes,1,Graduate,No,5468,1032,26,360,1,Semiurban,Y -LP002794,Female,No,0,Graduate,No,2667,1625,84,360,,Urban,Y -LP002795,Male,Yes,3+,Graduate,Yes,10139,0,260,360,1,Semiurban,Y -LP002798,Male,Yes,0,Graduate,No,3887,2669,162,360,1,Semiurban,Y -LP002804,Female,Yes,0,Graduate,No,4180,2306,182,360,1,Semiurban,Y -LP002807,Male,Yes,2,Not Graduate,No,3675,242,108,360,1,Semiurban,Y -LP002813,Female,Yes,1,Graduate,Yes,19484,0,600,360,1,Semiurban,Y -LP002820,Male,Yes,0,Graduate,No,5923,2054,211,360,1,Rural,Y -LP002821,Male,No,0,Not Graduate,Yes,5800,0,132,360,1,Semiurban,Y -LP002832,Male,Yes,2,Graduate,No,8799,0,258,360,0,Urban,N -LP002833,Male,Yes,0,Not Graduate,No,4467,0,120,360,,Rural,Y -LP002836,Male,No,0,Graduate,No,3333,0,70,360,1,Urban,Y -LP002837,Male,Yes,3+,Graduate,No,3400,2500,123,360,0,Rural,N -LP002840,Female,No,0,Graduate,No,2378,0,9,360,1,Urban,N -LP002841,Male,Yes,0,Graduate,No,3166,2064,104,360,0,Urban,N -LP002842,Male,Yes,1,Graduate,No,3417,1750,186,360,1,Urban,Y -LP002847,Male,Yes,,Graduate,No,5116,1451,165,360,0,Urban,N -LP002855,Male,Yes,2,Graduate,No,16666,0,275,360,1,Urban,Y -LP002862,Male,Yes,2,Not Graduate,No,6125,1625,187,480,1,Semiurban,N -LP002863,Male,Yes,3+,Graduate,No,6406,0,150,360,1,Semiurban,N -LP002868,Male,Yes,2,Graduate,No,3159,461,108,84,1,Urban,Y -LP002872,,Yes,0,Graduate,No,3087,2210,136,360,0,Semiurban,N -LP002874,Male,No,0,Graduate,No,3229,2739,110,360,1,Urban,Y -LP002877,Male,Yes,1,Graduate,No,1782,2232,107,360,1,Rural,Y -LP002888,Male,No,0,Graduate,,3182,2917,161,360,1,Urban,Y -LP002892,Male,Yes,2,Graduate,No,6540,0,205,360,1,Semiurban,Y -LP002893,Male,No,0,Graduate,No,1836,33837,90,360,1,Urban,N -LP002894,Female,Yes,0,Graduate,No,3166,0,36,360,1,Semiurban,Y -LP002898,Male,Yes,1,Graduate,No,1880,0,61,360,,Rural,N -LP002911,Male,Yes,1,Graduate,No,2787,1917,146,360,0,Rural,N -LP002912,Male,Yes,1,Graduate,No,4283,3000,172,84,1,Rural,N -LP002916,Male,Yes,0,Graduate,No,2297,1522,104,360,1,Urban,Y -LP002917,Female,No,0,Not Graduate,No,2165,0,70,360,1,Semiurban,Y -LP002925,,No,0,Graduate,No,4750,0,94,360,1,Semiurban,Y -LP002926,Male,Yes,2,Graduate,Yes,2726,0,106,360,0,Semiurban,N -LP002928,Male,Yes,0,Graduate,No,3000,3416,56,180,1,Semiurban,Y -LP002931,Male,Yes,2,Graduate,Yes,6000,0,205,240,1,Semiurban,N -LP002933,,No,3+,Graduate,Yes,9357,0,292,360,1,Semiurban,Y -LP002936,Male,Yes,0,Graduate,No,3859,3300,142,180,1,Rural,Y -LP002938,Male,Yes,0,Graduate,Yes,16120,0,260,360,1,Urban,Y -LP002940,Male,No,0,Not Graduate,No,3833,0,110,360,1,Rural,Y -LP002941,Male,Yes,2,Not Graduate,Yes,6383,1000,187,360,1,Rural,N -LP002943,Male,No,,Graduate,No,2987,0,88,360,0,Semiurban,N -LP002945,Male,Yes,0,Graduate,Yes,9963,0,180,360,1,Rural,Y -LP002948,Male,Yes,2,Graduate,No,5780,0,192,360,1,Urban,Y -LP002949,Female,No,3+,Graduate,,416,41667,350,180,,Urban,N -LP002950,Male,Yes,0,Not Graduate,,2894,2792,155,360,1,Rural,Y -LP002953,Male,Yes,3+,Graduate,No,5703,0,128,360,1,Urban,Y -LP002958,Male,No,0,Graduate,No,3676,4301,172,360,1,Rural,Y -LP002959,Female,Yes,1,Graduate,No,12000,0,496,360,1,Semiurban,Y -LP002960,Male,Yes,0,Not Graduate,No,2400,3800,,180,1,Urban,N -LP002961,Male,Yes,1,Graduate,No,3400,2500,173,360,1,Semiurban,Y -LP002964,Male,Yes,2,Not Graduate,No,3987,1411,157,360,1,Rural,Y -LP002974,Male,Yes,0,Graduate,No,3232,1950,108,360,1,Rural,Y -LP002978,Female,No,0,Graduate,No,2900,0,71,360,1,Rural,Y -LP002979,Male,Yes,3+,Graduate,No,4106,0,40,180,1,Rural,Y -LP002983,Male,Yes,1,Graduate,No,8072,240,253,360,1,Urban,Y -LP002984,Male,Yes,2,Graduate,No,7583,0,187,360,1,Urban,Y -LP002990,Female,No,0,Graduate,Yes,4583,0,133,360,0,Semiurban,N diff --git a/index.htm b/index.htm index 7302052..50cb28d 100644 --- a/index.htm +++ b/index.htm @@ -26,53 +26,47 @@

    R Markdowns

    @@ -81,7 +75,11 @@

    Math

    -

    R Language & Libraries

    +

    R Language

    +

    R Libraries

    +
    -

    Some Bayesian Exercises & Tools

    +

    Links

    -

    Useful links

    - -
    +
    Disclaimer: This webpage started as a private collection of tutorials and notes until the web-crawlers made it public. Some code is mine, some is from other people. I tried to insert all relevant references but if I diff --git a/manipulate/manipulate.Rmd b/manipulate/manipulate.Rmd deleted file mode 100644 index 312b882..0000000 --- a/manipulate/manipulate.Rmd +++ /dev/null @@ -1,114 +0,0 @@ -Manipulate -======================================================== - -RStudio includes a manipulate package that enables the addition of interactive capabilities to standard R plots. This is accomplished by binding plot inputs to custom controls rather than static hard-coded values. - -Check [http://www.rstudio.com/ide/docs/advanced/manipulate](http://www.rstudio.com/ide/docs/advanced/manipulate) - -This egs do not work in HTML, we need to run them in RStudio. - -```{r} -library(manipulate) - -## Specify a custom label for a slider -manipulate( - barplot(seq(1,x,1/y)), - x = slider(0, 20, label = "Limit", step=2, initial=12), - y = slider(1, 4, label = "Precision", step=1, initial=4) -) - -## Filtering data with a picker -manipulate( - barplot(as.matrix(longley[,factor]), - beside = TRUE, main = factor), - factor = picker("GNP", "Unemployed", "Employed") -) - -## Picker with groups -manipulate( - barplot(as.matrix(mtcars[group,"mpg"]), beside=TRUE), - group = picker("Group 1" = 1:11, - "Group 2" = 12:22, - "Group 3" = 23:32) -) - -## Histogram w/ picker to select type -require(lattice) -require(stats) -manipulate( - histogram(~ height | voice.part, - data = singer, type = type), - type = picker("percent", "count", "density")) - -## Using checkboxes for boolean parameters -manipulate( - plot(cars, axes = axes, ann = label), - axes = checkbox(TRUE, "Draw Axes"), - label = checkbox(FALSE, "Draw Labels")) - -## Toggle boxplot outlier display using checkbox -manipulate( - boxplot(Freq ~ Class, data = Titanic, outline = outline), - outline = checkbox(FALSE, "Show outliers")) - - -## Combining controls - -manipulate( - plot(cars, xlim = c(0, x.max), type = type, ann = label), - x.max = slider(10, 25, step=5, initial = 25), - type = picker("Points" = "p", "Line" = "l", "Step" = "s"), - label = checkbox(TRUE, "Draw Labels")) - -manipulate( - plot(cars, xlim = c(x.min, x.max), type = type, - axes = axes, ann = label), - x.min = slider(0,15), - x.max = slider(15,30, initial = 25), - type = picker("p", "l", "b", "c", "o", "h", "s", "S", "n"), - axes = checkbox(TRUE, "Draw Axes"), - label = checkbox(FALSE, "Draw Labels")) - -# Button Eg -# When the user presses the button the manipulate expression will be executed with its associated value set to TRUE (in all other cases the value will be set to FALSE). -manipulate( - { - if(resetSeed) - set.seed(sample(1:1000)) - - hist(rnorm(n=100, mean=0, sd=3), breaks=bins) - }, - bins = slider(1, 20, step=1, initial =5, label="Bins"), - resetSeed = button("Reset Seed") -) - -# Using manipulate to make 3D rotations -manipulate( -{ - rotate <- angle - tilt <- angle.tilt - parallelness <- 5.0 - shadeval <- 0.05 - perspcex <- .7 - - xs <- seq(0,1,.05) - ys <- seq(0,1,.05) - f <- function(x,y) { - dnorm(x,.5,.25) + dnorm(y,.5,.125) - } - zs <- outer(xs,ys,f) - - persp(xs , ys , zs, - xlab="x" , ylab="y" , zlab="f(x,y)" , - main="Main Title" , cex=perspcex, lwd=0.1 , - xlim=c(0,1) , ylim=c(0,1) , zlim=c(-1,4), - theta=rotate , phi=tilt , d=parallelness , - shade=shadeval) -}, - angle = slider(-90,90,step=1,initial=-45, label="angle"), - angle.tilt = slider(-90,90,step=1,initial=30, label="tilt") -) - - -``` - diff --git a/manipulate/manipulate.html b/manipulate/manipulate.html deleted file mode 100644 index d498598..0000000 --- a/manipulate/manipulate.html +++ /dev/null @@ -1,320 +0,0 @@ - - - - - - -Manipulate - - - - - - - - - - - - - - - -

    Manipulate

    - -

    RStudio includes a manipulate package that enables the addition of interactive capabilities to standard R plots. This is accomplished by binding plot inputs to custom controls rather than static hard-coded values.

    - -

    Check http://www.rstudio.com/ide/docs/advanced/manipulate

    - -

    This egs do not work in HTML, we need to run them in RStudio.

    - -
    library(manipulate)
-
-## Specify a custom label for a slider
-manipulate(barplot(seq(1, x, 1/y)), x = slider(0, 20, label = "Limit", step = 2, 
-    initial = 12), y = slider(1, 4, label = "Precision", step = 1, initial = 4))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-## Filtering data with a picker
-manipulate(barplot(as.matrix(longley[, factor]), beside = TRUE, main = factor), 
-    factor = picker("GNP", "Unemployed", "Employed"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-## Picker with groups
-manipulate(barplot(as.matrix(mtcars[group, "mpg"]), beside = TRUE), group = picker(`Group 1` = 1:11, 
-    `Group 2` = 12:22, `Group 3` = 23:32))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-## Histogram w/ picker to select type
-require(lattice)
-
    - -
    ## Loading required package: lattice
-
    - -
    require(stats)
-manipulate(histogram(~height | voice.part, data = singer, type = type), type = picker("percent", 
-    "count", "density"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-## Using checkboxes for boolean parameters
-manipulate(plot(cars, axes = axes, ann = label), axes = checkbox(TRUE, "Draw Axes"), 
-    label = checkbox(FALSE, "Draw Labels"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-## Toggle boxplot outlier display using checkbox
-manipulate(boxplot(Freq ~ Class, data = Titanic, outline = outline), outline = checkbox(FALSE, 
-    "Show outliers"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-
-## Combining controls
-
-manipulate(plot(cars, xlim = c(0, x.max), type = type, ann = label), x.max = slider(10, 
-    25, step = 5, initial = 25), type = picker(Points = "p", Line = "l", Step = "s"), 
-    label = checkbox(TRUE, "Draw Labels"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-manipulate(plot(cars, xlim = c(x.min, x.max), type = type, axes = axes, ann = label), 
-    x.min = slider(0, 15), x.max = slider(15, 30, initial = 25), type = picker("p", 
-        "l", "b", "c", "o", "h", "s", "S", "n"), axes = checkbox(TRUE, "Draw Axes"), 
-    label = checkbox(FALSE, "Draw Labels"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-# Button Eg When the user presses the button the manipulate expression
-# will be executed with its associated value set to TRUE (in all other
-# cases the value will be set to FALSE).
-manipulate({
-    if (resetSeed) 
-        set.seed(sample(1:1000))
-
-    hist(rnorm(n = 100, mean = 0, sd = 3), breaks = bins)
-}, bins = slider(1, 20, step = 1, initial = 5, label = "Bins"), resetSeed = button("Reset Seed"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-# Using manipulate to make 3D rotations
-manipulate({
-    rotate <- angle
-    tilt <- angle.tilt
-    parallelness <- 5
-    shadeval <- 0.05
-    perspcex <- 0.7
-
-    xs <- seq(0, 1, 0.05)
-    ys <- seq(0, 1, 0.05)
-    f <- function(x, y) {
-        dnorm(x, 0.5, 0.25) + dnorm(y, 0.5, 0.125)
-    }
-    zs <- outer(xs, ys, f)
-
-    persp(xs, ys, zs, xlab = "x", ylab = "y", zlab = "f(x,y)", main = "Main Title", 
-        cex = perspcex, lwd = 0.1, xlim = c(0, 1), ylim = c(0, 1), zlim = c(-1, 
-            4), theta = rotate, phi = tilt, d = parallelness, shade = shadeval)
-}, angle = slider(-90, 90, step = 1, initial = -45, label = "angle"), angle.tilt = slider(-90, 
-    90, step = 1, initial = 30, label = "tilt"))
-
    - -
    ## Error: no such symbol rs_createUUID
-
    - -
    
-
    - - - - -