Ordered Logistic or Probit Regression

DESCRIPTION:

Fits a proportional odd logistic regression model to an ordered factor response. The default logistic case is proportional odds logistic regression, after which the function is named.

USAGE:

polr(formula, data = NULL, weights, start, ..., subset,
     na.action = na.fail, contrasts = NULL, Hess = F,
     method = c("logistic", "probit", "cloglog"))

REQUIRED ARGUMENTS:

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.

OPTIONAL ARGUMENTS:

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 (currently ignored).
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.
method
logistic or probit or complementary log-log.

VALUE:

A object of class "polr".
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
the (effective) number of observations, calculated using the weights
call
the matched call.
convergence
the convergence message returned by nlminb.
niter
the number of iterations, function and gradient evaluations used by nlminb.
Hessian
(if Hess is true).

NOTE:

Agresti, A. (2002) Categorical Data. Second edition. Wiley.

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

SEE ALSO:

, , .

EXAMPLES:

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