polr {MASS}  R Documentation 
Fits a logistic or probit regression model to an ordered factor response. The default logistic case is proportional odds logistic regression, after which the function is named.
polr(formula, data, weights, start, ..., subset, na.action, contrasts = NULL, Hess = FALSE, model = TRUE, method = c("logistic", "probit", "cloglog", "cauchit"))
formula 
a formula expression as for regression models, of the form
response ~ predictors . The response should be a factor
(preferably an ordered
factor), which will be interpreted as an ordinal response, with levels
ordered as in the factor. A proportional odds model will be
fitted. The model must have an intercept: attempts to remove one will
lead to a warning and be ignored. An offset may be used. See the
documentation of formula for other details.

data 
an optional data frame in which to interpret the variables occurring
in formula .

weights 
optional case weights in fitting. Default to 1. 
start 
initial values for the parameters. 
... 
additional arguments to be passed to optim , most often a
control argument.

subset 
expression saying which subset of the rows of the data should be used in the fit. All observations are included by default. 
na.action 
a function to filter missing data. 
contrasts 
a list of contrasts to be used for some or all of the factors appearing as variables in the model formula. 
Hess 
logical for whether the Hessian (the observed information matrix) should be returned. 
model 
logical for whether the model matrix should be returned. 
method 
logistic or probit or complementary loglog or cauchit (corresponding to a Cauchy latent variable and only available in R >= 2.1.0). 
This model is what Agresti (2002) calls a cumulative link model. The basic interpretation is as a coarsened version of a latent variable Y_i which has a logistic or normal or extremevalue or Cauchy distribution with scale parameter one and a linear model for the mean. The ordered factor which is observed is which bin Y_i falls into with breakpoints
zeta_0 = Inf < zeta_1 < ... < zeta_K = Inf
This leads to the model
logit P(Y <= k  x) = zeta_k  eta
with logit replaced by probit for a normal latent variable, and eta being the linear predictor, a linear function of the explanatory variables. Note that it is quite common for other software to use the opposite sign for eta.
In the logistic case, the lefthand side of the last display is the log odds of category k or less, and since these are log odds which differ only by a constant for different k, the odds are proportional. Hence the term proportional odds logistic regression.
In the complementary loglog case, we have a proportional hazards model for grouped survival times.
There are methods for the standard modelfitting functions, including
predict
, summary
, vcov
,
anova
, model.frame
and an
extractAIC
method for use with stepAIC
. There
are also profile
and confint
methods.
A object of class "polr"
. This has components
coefficients 
the coefficients of the linear predictor. 
zeta 
the intercepts for the class boundaries. 
deviance 
the residual deviance. 
fitted.values 
a matrix, with a column for each level of the response. 
lev 
the names of the response levels. 
terms 
the terms structure describing the model. 
df.residual 
the number of residual degrees of freedoms, calculated using the weights. 
edf 
the (effective) number of degrees of freedom used by the model 
n, nobs 
the (effective) number of observations, calculated using the
weights. (nobs is for use by stepAIC . 
call 
the matched call. 
method 
the matched method used. 
convergence 
the convergence code returned by optim . 
niter 
the number of function and gradient evaluations used by
optim . 
Hessian 
(if Hess is true). 
model 
(if model is true). 
Agresti, A. (2002) Categorical Data. Second edition. Wiley.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
options(contrasts = c("contr.treatment", "contr.poly")) house.plr < polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing) house.plr summary(house.plr) ## slightly worse fit from summary(update(house.plr, method = "probit")) ## although it is not really appropriate, can fit summary(update(house.plr, method = "cloglog")) predict(house.plr, housing, type = "p") addterm(house.plr, ~.^2, test = "Chisq") house.plr2 < stepAIC(house.plr, ~.^2) house.plr2$anova anova(house.plr, house.plr2) house.plr < update(house.plr, Hess=TRUE) pr < profile(house.plr) confint(pr) plot(pr) pairs(pr)