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.Rhistory
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library(tidyverse)
library(lme4)
library(rstan)
library(cowplot)
library(ggplot2)
library(lubridate)
library(ggridges)
library(kableExtra)
SalesTrans =
read_csv("C:/Users/ellen/Documents/UH/Fall 2020/Class Materials/Section II/Class 1/Data/Sales.csv")
Location =
read_csv("C:/Users/ellen/Documents/UH/Fall 2020/Class Materials/Section II/Class 1/Data/Location.csv")
MerGroup =
read_csv("C:/Users/ellen/Documents/UH/Fall 2020/Class Materials/Section II/Class 1/Data/MerGroup.csv")
SalesTrans = SalesTrans %>% inner_join(Location, by = "LocationID")
SalesTrans = SalesTrans %>% inner_join(MerGroup, by = "MerGroup")
LocationID = as.factor(SalesTrans$LocationID)
SalesTrans$ProductID = as.factor(SalesTrans$ProductID)
SalesTrans$Description = as.factor(SalesTrans$Description)
SalesTrans$MerGroup = as.factor(SalesTrans$MerGroup)
# breaking out Q4 to simplify exercise
SalesTrans$Qtr = quarter(SalesTrans$Tdate)
SalesTrans = filter(SalesTrans, Qtr == 4)
SalesTransSummary = SalesTrans %>%
group_by(Description, MerGroup, MfgPromo, Wk ) %>%
summarise(Volume = n(), TotSales = sum(Amount) )
SalesSummarySub = filter(SalesTransSummary,
Description %in% c("Arlington", "Boston", "San Jose", "Seattle"),
MerGroup %in% c("Accessories", "Beauty", "Cooking", "Men" ))
p = ggplot(SalesSummarySub, aes(Wk, TotSales, color = MerGroup)) +
geom_point(alpha = .2) +
geom_smooth(method = "lm", se = F, alpha = .05, linetype = "dashed", alpha = .5) +
facet_wrap(~Description) +
theme(panel.background = element_rect(fill = "white"))
p
Priors = lm(TotSales ~ Wk , data = SalesTransSummary)
lmI = as.numeric(Priors$coefficients[1])
lmS = as.numeric(Priors$coefficients[2])
# get adjusted level coefficients
# build stan model
stanMod <- '
data {
int<lower=0> N;
vector[N] x; // Wk
vector[N] y; // TotSales
int<lower=0> J; // Description
int Description[N];
int<lower=0> K; // MerGroup
int MerGroup[N];
vector[J] p_alpha;
vector[K] p_alpha2;
real<lower=0> p_alphaSigma;
real<lower=0> p_alphaSigma2;
vector[J] p_beta;
vector[K] p_beta2;
real<lower=0> p_betaSigma;
real<lower=0> p_betaSigma2;
}
parameters {
// random effects we found
vector[J] alpha; // intercept for Description
vector[K] alpha2; // intercept for MerGroup
vector[J] beta; // slope for Description
vector[K] beta2; // slope for MerGroup
real<lower=0> sigma; // to control sigma of y_hat
}
transformed parameters {
vector[N] y_hat;
for(i in 1:N)
y_hat[i]=alpha[Description[i]]+alpha2[MerGroup[i]]+(beta[Description[i]]*x[i])+(beta2[MerGroup[i]]*x[i]);
}
model {
target += normal_lpdf(alpha | p_alpha, p_alphaSigma);
target += normal_lpdf(alpha2 | p_alpha2, p_alphaSigma2);
target += normal_lpdf(beta | p_beta, p_betaSigma);
target += normal_lpdf(beta2 | p_beta2, p_betaSigma2);
target += normal_lpdf(sigma | 50, 50);
// y_hat: our prediction
target += normal_lpdf(y | y_hat, sigma);
}
'
fit <- stan(model_code = stanMod, data = list(
N = nrow(SalesTransSummary),
y = SalesTransSummary$TotSales,
x = SalesTransSummary$Wk,
J = length(unique(SalesTransSummary$Description)),
K = length(unique(SalesTransSummary$MerGroup)),
Description = as.numeric(SalesTransSummary$Description),
MerGroup = as.numeric(SalesTransSummary$MerGroup),
p_alpha = rep(lmI,10), # Description intercept
p_alpha2 = rep(lmI,10), # MerGroup intercept
#
p_alphaSigma = 500,
p_alphaSigma2 = 500,
p_beta = rep(lmS,10), # Description slope (lmer model)
p_beta2 = rep(lmS,10), # MerGroup slope (lmer model)
p_betaSigma = 10,
p_betaSigma2 = 10
), refresh = 0)
# Extract coefficients from stan model
sumFit <- data.frame(summary(fit))
# Description
Intercept1 <- summary(fit, pars = c("alpha"), probs = c(0.1, 0.9))$summary
# MerGroup
Intercept2 <- summary(fit, pars = c("alpha2"), probs = c(0.1, 0.9))$summary
# Description slope
Slope1 <- summary(fit, pars = c("beta"), probs = c(0.1, 0.9))$summary
# MerGroup slope
Slope2 <- summary(fit, pars = c("beta2"), probs = c(0.1, 0.9))$summary
# random effects for each Description
CoefMapD <- data.frame(Description = unique(SalesTransSummary$Description),
DIntercept = Intercept1[,1], DSlope = Slope1[,1])
# random effects for each MerGroup
CoefMapM <- data.frame(MerGroup = unique(SalesTransSummary$MerGroup), MIntercept = Intercept2[,1], MSlope = Slope2[,1])
# add all intercepts and all slopes cross each row
CoefMapB = crossing(CoefMapD, CoefMapM) %>%
mutate(Intercept = DIntercept + MIntercept, Slope = DSlope + MSlope)
CoefMapBSub <- filter(CoefMapB,
Description %in% c('Seattle', "Arlington", "San Jose", "Boston"),
MerGroup %in% c("Accessories", "Cooking", "Women", "Shoes"))
p1 <- p + geom_abline(data = CoefMapBSub,
aes(intercept=Intercept, slope=Slope, color=MerGroup))
p1
fit <- stan(model_code = stanMod, data = list(
N = nrow(SalesTransSummary),
y = SalesTransSummary$TotSales,
x = SalesTransSummary$Wk,
J = length(unique(SalesTransSummary$Description)),
K = length(unique(SalesTransSummary$MerGroup)),
Description = as.numeric(SalesTransSummary$Description),
MerGroup = as.numeric(SalesTransSummary$MerGroup),
p_alpha = as.numeric(CoefMapD[,2]), # Description intercept
p_alpha2 = as.numeric(CoefMapM[,2]), # MerGroup intercept
#
p_alphaSigma = 20000,
p_alphaSigma2 = 20000,
p_beta = as.numeric(CoefMapD[,3]), # Description slope (lmer model)
p_beta2 = as.numeric(CoefMapM[,3]), # MerGroup slope (lmer model)
p_betaSigma = 1000,
p_betaSigma2 = 1000
), refresh = 0)
# Extract coefficients from stan model
sumFit <- data.frame(summary(fit))
# Description
Intercept1 <- summary(fit, pars = c("alpha"), probs = c(0.1, 0.9))$summary
# MerGroup
Intercept2 <- summary(fit, pars = c("alpha2"), probs = c(0.1, 0.9))$summary
# Description slope
Slope1 <- summary(fit, pars = c("beta"), probs = c(0.1, 0.9))$summary
# MerGroup slope
Slope2 <- summary(fit, pars = c("beta2"), probs = c(0.1, 0.9))$summary
# random effects for each Description
CoefMapD2 <- data.frame(Description = unique(SalesTransSummary$Description),
DIntercept = Intercept1[,1], DSlope = Slope1[,1])
# random effects for each MerGroup
CoefMapM2 <- data.frame(MerGroup = unique(SalesTransSummary$MerGroup), MIntercept = Intercept2[,1], MSlope = Slope2[,1])
# add all intercepts and all slopes cross each row
CoefMapB2 = crossing(CoefMapD2, CoefMapM2) %>%
mutate(Intercept = DIntercept + MIntercept, Slope = DSlope + MSlope)
CoefMapBSub2 <- filter(CoefMapB2,
Description %in% c('Seattle', "Arlington", "San Jose", "Boston"),
MerGroup %in% c("Accessories", "Cooking", "Women", "Shoes"))
p2 <- p + geom_abline(data = CoefMapBSub2,
aes(intercept=Intercept, slope=Slope, color=MerGroup))
p2