Frequency Table from a Copenhagen Housing Conditions Survey

Description

The housing data frame has 72 rows and 5 variables.

Usage

housing

Format

Sat

Satisfaction of householders with their present housing circumstances, (High, Medium or Low, ordered factor).

Infl

Perceived degree of influence householders have on the management of the property (High, Medium, Low).

Type

Type of rental accommodation, (Tower, Atrium, Apartment, Terrace).

Cont

Contact residents are afforded with other residents, (Low, High).

Freq

Frequencies: the numbers of residents in each class.

Source

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.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

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