housing {MASS} | R Documentation

## Frequency Table from a Copenhagen Housing Conditions Survey

### Description

The `housing` data frame has 72 rows and 5 variables.

### Usage

    data(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.resid)

    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

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