housing                 package:MASS                 R Documentation

_F_r_e_q_u_e_n_c_y _T_a_b_l_e _f_r_o_m _a _C_o_p_e_n_h_a_g_e_n _H_o_u_s_i_n_g _C_o_n_d_i_t_i_o_n_s _S_u_r_v_e_y

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     housing

_F_o_r_m_a_t:


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

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

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

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

     '_F_r_e_q' Frequencies: the numbers of residents in each class.


_S_o_u_r_c_e:

     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.

_R_e_f_e_r_e_n_c_e_s:

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

_E_x_a_m_p_l_e_s:

     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

