#=======================================================
# R code that illustrates baseline category logit models
# using the alligator data described in section 6.3.2
#=======================================================

# Read aligator data from the web:
data="http://www.stat.ufl.edu/~aa/glm/data/Alligators.dat"
alligators = read.table(data, header = T)
alligators

# We will use teh VGAM library:
library(VGAM)

#======================
# Fit model 
#======================

# We fit a baseline category logit model with size and lake as
#main effects and fish (y1) as the reference category:
fit.main=vglm(cbind(y2,y3,y4,y5,y1)~size+factor(lake),
              family=multinomial, data=alligators)
summary(fit.main)

#============================
# Test if size has an effect:
#============================

# Fit model with only lake:
fit.lake=vglm(cbind(y2,y3,y4,y5,y1)~factor(lake),family=multinomial, data=alligators)
summary(fit.lake)

# Test if there is an effect of size 
G2=deviance(fit.lake)-deviance(fit.main)
G2
df.diff=df.residual(fit.lake)-df.residual(fit.main)
df.diff
1-pchisq(G2,df.diff)
# Size has a significant effect

#============================
# Test if lake has an effect:
#============================

# Fit model with only size:
fit.size=vglm(cbind(y2,y3,y4,y5,y1)~size,family=multinomial, data=alligators)
summary(fit.size)

# Test if there is an effect of lake 
G2=deviance(fit.size)-deviance(fit.main)
G2
df.diff=df.residual(fit.size)-df.residual(fit.main)
df.diff
1-pchisq(G2,df.diff)
# Lake has a significant effect