```
polr(formula, data, weights, start, …, subset, na.action,
contrasts = NULL, Hess = FALSE, model = TRUE,
method = c("logistic", "probit", "loglog", "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.
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. This is in the format

`c(coefficients, zeta)`

: see the Values section.
…

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. Use this if you intend to call

`summary`

or
`vcov`

on the fit.
model

logical for whether the model matrix should be returned.

method

logistic or probit or (complementary) log-log or cauchit
(corresponding to a Cauchy latent variable).

`"polr"`

. This has components `terms`

structure describing the model.`nobs`

is for use by `stepAIC`

.`optim`

.`optim`

.`Hess`

is true). Note that this is a
numerical approximation derived from the optimization proces.`model`

is true).`beta`

). In the logistic case, the left-hand 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 `predict`

, `summary`

, `vcov`

,
`anova`

, `model.frame`

and an
`extractAIC`

method for use with `stepAIC`

(and
`step`

). There are also `profile`

and
`confint`

methods.`optim`

, `glm`

, `multinom`

.options(contrasts = c("contr.treatment", "contr.poly")) house.plr <- polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing) house.plr summary(house.plr, digits = 3) ## slightly worse fit from summary(update(house.plr, method = "probit", Hess = TRUE), digits = 3) ## although it is not really appropriate, can fit summary(update(house.plr, method = "loglog", Hess = TRUE), digits = 3) summary(update(house.plr, method = "cloglog", Hess = TRUE), digits = 3) 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)