Frequency Table from a Copenhagen Housing Conditions Survey
The housing data frame has 72 rows and 5 variables.
housing
SatSatisfaction of householders with their present housing circumstances, (High, Medium or Low, ordered factor).
InflPerceived degree of influence householders have on the management of the property (High, Medium, Low).
TypeType of rental accommodation, (Tower, Atrium, Apartment, Terrace).
ContContact residents are afforded with other residents, (Low, High).
FreqFrequencies: the numbers of residents in each class.
Madsen, M. (1976) Statistical analysis of multiple contingency tables. Two examples. Scand. J. Statist. 3, 97–106.
Cox, D. R. and Snell, E. J. (1984) Applied Statistics, Principles and Examples. Chapman & Hall.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
options(contrasts = c("contr.treatment", "contr.poly"))
# Surrogate Poisson models
house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family = poisson,
data = housing)
## IGNORE_RDIFF_BEGIN
summary(house.glm0, cor = FALSE)
## IGNORE_RDIFF_END
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$anovaPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.