Update logistic regression

New update

Author: Rahul raoniar

11.2 Logistic Regression/Logistic_Diabetes_ROC_Computation.R

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+# Article 1
+# Shrikant I. Bangdiwala (2018): Regression: binary logistic, International Journal
+# of Injury Control and Safety Promotion, DOI: 10.1080/17457300.2018.1486503
+
+# Article 2
+# Leeper, T.J., 2017. Interpreting regression results using average marginal 
+# effects with R's margins. Tech. rep. URL https://cran. r-project.
+# org/web/packages/margins/index. html.
+
+
+
+#############################
+# Part 1: load Libraries
+#############################
+library(mlbench) # for PimaIndiansDiabetes2 dataset
+library(tidyverse) # or specifically you can use ggplot2 library
+                   # for plotting
+library(broom) # Make model summary tidy
+library(caret) # use to compute confusion matrix
+library(visreg) # For potting logodds and probabilitis
+library(margins) # Use to calculate Average Marginal Effects
+library(rcompanion) # Use to calculate pseudo R2
+library(ROCR) # Use to calculate Reciever Opering Curve
+
+
+
+#############################
+# Part 2: Gather and clean data
+#############################
+
+data(package = "mlbench")
+
+
+
+# load the diabetes dataset
+
+data(PimaIndiansDiabetes2)
+
+
+##########################
+# Variables of the dataset
+##########################
+
+# I1: pregnant:	 Number of times pregnant
+# I2: glucose:	 Plasma glucose concentration (glucose tolerance test)
+# I3: pressure:	 Diastolic blood pressure (mm Hg)
+# I4: triceps:	 Triceps skin fold thickness (mm)
+# I5: insulin:	 2-Hour serum insulin (mu U/ml)
+# I6: mass:	 Body mass index (weight in kg/(height in m)\^2)
+# I7: pedigree:	 Diabetes pedigree function
+# I8: age:	 Age (years)
+
+# D1: diabetes:	 Class variable (test for diabetes)
+
+
+head(PimaIndiansDiabetes2)
+
+
+# Save data to Diabetes
+
+Diabetes <- na.omit(PimaIndiansDiabetes2) # dataset for modeling
+
+head(Diabetes)
+
+str(Diabetes)
+
+
+
+
+# Changing levels neg = 0 and pos = 1
+
+head(Diabetes)
+
+levels(Diabetes$diabetes) <- 0:1
+
+head(Diabetes)
+
+
+###############################################
+# Part 3: Dividing randomly data samples into train and test dataset
+###############################################
+
+
+# Total number of rows in the credit data frame
+n <- nrow(Diabetes)
+
+# Number of rows for the training set (80% of the dataset)
+n_train <- round(0.80 * n) 
+
+# Create a vector of indices which is an 80% random sample
+set.seed(123)
+train_indices <- sample(1:n, n_train)
+
+# Subset the credit data frame to training indices only
+train <- Diabetes[train_indices, ]  
+
+# Exclude the training indices to create the test set
+test <- Diabetes[-train_indices, ]  
+
+####################################
+# Part 4: Fitting a logistic regression model
+####################################
+
+
+model_logi <- glm(diabetes~., data = train, family = "binomial")
+
+summary(model_logi) # see summary statistics
+
+
+# Make data tidy using broom package
+tidy(model_logi)
+
+glance(model_logi) # Check model fitting
+
+augment(model_logi) # obtain fitted values
+
+
+
+#####################################
+# Part 5: Calculating important statistics
+#####################################
+
+# Part 5 (A): Calculating the odd ratio
+
+(exp(coef(model_logi)))
+
+tidy(model_logi, exponentiate = TRUE, conf.level = 0.95) # odd ratio
+
+
+# Part 5 (B): Logodds and probability plots
+
+
+# Import and use visreg library
+
+# Logodds of diabetes wrt to glucose level
+visreg(model_logi, "glucose", xlab="Glucose level",
+       ylab="Log odds (diabetes)")
+
+# Logodds of diabetes wrt to pedigree level
+visreg(model_logi, "pedigree", xlab="pedigree level",
+       ylab="Log odds (diabetes)")
+
+
+
+
+# Probabilities of diabetes wrt glucose
+visreg(model_logi, "glucose", scale="response", rug=2, xlab="Glucose level",
+       ylab="P(diabetes)")
+
+# Probabilities of diabetes wrt pedigree
+visreg(model_logi, "pedigree", scale="response", rug=2, xlab="pedigree level",
+       ylab="P(diabetes)")
+
+
+
+
+# Part 5 (C): Calculate marginal effect
+
+
+######################################################
+
+# While the estimated coefficients from logistic regression 
+# are not easily interpretable
+
+# 1. Log odds: represents the change in the log of odds of 
+# outcome for a given change in a predictor  
+
+# 2. odds ratios: might provide a better summary of the effects of 
+# predictor on outcome variable (odds ratios are derived from
+# exponentiation of the estimated coefficients from logistic
+# regression). The Calculation and Interpretation of 
+# Odds Ratios may be somewhat more meaningful.
+
+# Marginal effects: Marginal effects are an alternative metric 
+# that can be used to describe the impact of a preditor on 
+# outcome variable. Marginal effects can be
+# described as the change in outcome as a
+# function of the change in the treatment 
+# (or independent variable of interest) holding all other
+# variables in the model constant. In linear regression,
+# the estimated regression coefficients are marginal effects
+# and are more easily interpreted (more on this later).
+
+
+# There are two way of computing Marginal Effects
+
+# a) Marginal Effect at Mean
+# b) Average Marginal Effect 
+
+# The magnitude of the marginal effect depends on the
+# values of the other variables and their coefficients.
+
+# The Marginal Effect at the Mean (MEM) is popular (i.e. compute the marginal
+# effects when all x's are at their mean) but many think that 
+# Average Marginal Effects (AMEs) are superior 
+
+
+# Use "margins" library for Average Marginal Effect compulation
+
+
+# Calculate average marginal effect
+effects_logit_dia = margins(model_logi)
+
+
+
+print(effects_logit_dia)
+
+
+# Summary of marginal effect
+summary(effects_logit_dia)
+
+
+
+# Plot marginal effect
+plot(effects_logit_dia)
+
+
+
+# Plot marginal effect using ggplot2 library
+
+effects_logit_diab = summary(effects_logit_dia)
+
+
+ggplot(data = effects_logit_diab) +
+  geom_point(mapping = aes(x = factor, y = AME)) +
+  geom_errorbar(mapping = aes(x = factor, ymin = lower, ymax = upper)) +
+  geom_hline(yintercept = 0) +
+  theme_minimal() +
+  theme(axis.text.x = element_text(angle = 45))
+
+
+#######################
+# Part 6: Model Evaluation
+#######################
+
+# Part 6 (A): Misclassification identification 
+#             using confusion matrix
+
+pred <- predict(model_logi, test, type="response") # predict using test data
+
+head(pred)
+
+predicted <- round(pred) # round of the value; >0.5 will convert to 1 
+      
+head(predicted)          # else 0
+
+# Side by side comparision
+
+head(data.frame(observed = test$diabetes, predicted = predicted))
+
+
+# Let's create a contigency table
+
+tab <- table(Predicted = predicted, Reference = test$diabetes)
+
+tab
+
+
+sum(diag(tab))/sum(tab)*100
+
+
+# Confusion matrix using caret package
+
+confusionMatrix(tab)
+
+
+
+
+
+# Part 6 (B):
+# Pseudo R2 and loglikelyhood ratio test
+
+# Import and use rcompanion library
+
+
+nagelkerke(model_logi)
+
+
+# Part 6 (C)
+# Compute the cutoff values
+# Use ROCR Package
+
+# Use the prediction function to generate a prediction result:
+
+
+pred.rocr <- prediction(pred, test$diabetes)
+
+eval <- performance(pred.rocr, "acc")
+
+plot(eval)
+
+
+
+# Identify best value (Cutoff vs Accuracy)
+
+max <- which.max(slot(eval, "y.values")[[1]])
+acc <- slot(eval, "y.values")[[1]][max] #y.values are accuracy measures
+cut <- slot(eval, "x.values")[[1]][max] # x.values are cutoff measures
+
+
+print(c(Accuracy = acc, Cutoff = cut))
+
+
+# Part 6 (D)
+# Receiver Operating Characteristic Curve computation
+# Import ROCR library
+
+# ROC (Receiver Operating Characteristic) Curve tells us about how good
+# the model can distinguish between two things
+
+# Use the performance function to obtain the performance measurement:
+
+perf.rocr <- performance(pred.rocr, measure = "auc",
+                         x.measure = "cutoff")
+
+perf.rocr@y.values[[1]] <- round(perf.rocr@y.values[[1]], digits = 4)
+
+perf.tpr.fpr.rocr <- performance(pred.rocr, "tpr", "fpr")
+
+# pos (actual) --and-- predicted (pos) ->correctly identified -> True pos
+# neg (actual) --and-- predicted (pos) ->Incorrectly identified -> False Pos
+# pos (actual) --and-- predicted (not pos) ->Incorrectly rejected -> False neg
+# neg (actual) --and-- predicted (not pos) ->Correctly rejected -> True neg
+
+
+# Visualize ROC curve using plot function
+
+plot(perf.tpr.fpr.rocr, colorize=T, 
+     main = paste("AUC:", (perf.rocr@y.values)))
+abline(a = 0, b = 1)