# 3-way table:  Hypothetical DIF
# Edps 589
# Fall 2018
# C.J.Anderson
#

library(vcd)
library(vcdExtra)
library(MASS)
library(DescTools)

var.values <- expand.grid(response=c("yes","no"),
                          group=c("A","B"),
			              ability=c("low","middle","high"))
counts <- c(5, 15, 15, 5, 10, 10, 10, 10, 15, 5, 5, 15)	
dif <- cbind(var.values,counts)
dif

# 2-way marginal table
response.by.group <- xtabs(counts ~ response + group,data=dif) 
addmargins(response.by.group)

# 2-way marginal analysis:  
assocstats(response.by.group)             # Compute G2 and X2
( OR <- oddsratio(response.by.group)  )   # Compute odds ratio and view
summary(OR)                               # signficant test for odds ratio -- don't really 
                                          #   need because have X2 and G2 from assocstats()
exp(0)									  # odds ratio	 
exp(confint(OR) )                         # Confidnece interval of odds ratio


# 3-way  Table of data
#  -- partial or conditional tables
dif.tab <- xtabs(counts ~ response + group + ability,data=dif)
addmargins(dif.tab)

# 3-way contitional/partial table analysis 
assocstats(dif.tab)                    # Compute X2 and G2
( OR <- oddsratio(dif.tab)  )          # Compute odds ratio & view
logodds <- summary(OR)                 # Signficant test for odds ratios
exp(logodds[1:3]  )                     # Odds ratios
exp( confint(OR) )                     # Confidnece interval of odds ratios

# Breslow-Day test of homogeneity
BreslowDayTest(dif.tab, OR = NA, correct = FALSE)

# First: Test for homogenity (shouldn't be significant...p should = 1
WoolfTest(dif.tab)

# Shouldn't do this because WoolfTest significant...but if it wasn't....
# Test for conditional independence
CMHtest(dif.tab)

# If data are conditionally independent, estimate their Common odds ratio
mantelhaen.test(dif.tab,alternative = c("two.sided"),
                correct = TRUE, exact = FALSE, conf.level = 0.95)