housing {MASS}

options(contrasts = c("contr.treatment", "contr.poly"))
 
# Surrogate Poisson models
house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family = poisson,
                  data = housing)
summary(house.glm0, cor = FALSE)
 
addterm(house.glm0, ~. + Sat:(Infl+Type+Cont), test = "Chisq")
 
house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
summary(house.glm1, cor = FALSE)
 
1 - pchisq(deviance(house.glm1), house.glm1$df.residual)
 
dropterm(house.glm1, test = "Chisq")
 
addterm(house.glm1, ~. + Sat:(Infl+Type+Cont)^2, test  =  "Chisq")
 
hnames <- lapply(housing[, -5], levels) # omit Freq
newData <- expand.grid(hnames)
newData$Sat <- ordered(newData$Sat)
house.pm <- predict(house.glm1, newData,
                    type = "response")  # poisson means
house.pm <- matrix(house.pm, ncol = 3, byrow = TRUE,
                   dimnames = list(NULL, hnames[[1]]))
house.pr <- house.pm/drop(house.pm %*% rep(1, 3))
cbind(expand.grid(hnames[-1]), round(house.pr, 2))
 
# Iterative proportional scaling
loglm(Freq ~ Infl*Type*Cont + Sat*(Infl+Type+Cont), data = housing)
 
 
# multinomial model
library(nnet)
(house.mult<- multinom(Sat ~ Infl + Type + Cont, weights = Freq,
                       data = housing))
house.mult2 <- multinom(Sat ~ Infl*Type*Cont, weights = Freq,
                        data = housing)
anova(house.mult, house.mult2)
 
house.pm <- predict(house.mult, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pm, 2))
 
# proportional odds model
house.cpr <- apply(house.pr, 1, cumsum)
logit <- function(x) log(x/(1-x))
house.ld <- logit(house.cpr[2, ]) - logit(house.cpr[1, ])
(ratio <- sort(drop(house.ld)))
mean(ratio)
 
(house.plr <- polr(Sat ~ Infl + Type + Cont,
                   data = housing, weights = Freq))
 
house.pr1 <- predict(house.plr, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pr1, 2))
 
Fr <- matrix(housing$Freq, ncol  =  3, byrow = TRUE)
2*sum(Fr*log(house.pr/house.pr1))
 
house.plr2 <- stepAIC(house.plr, ~.^2)
house.plr2$anova