Plackett-Luce Model Summaries — summaries • PlackettLuce

Obtain the coefficients, model summary or coefficient variance-covariance matrix for a model fitted by PlackettLuce.

Usage

# S3 method for PlackettLuce
coef(object, ref = 1L, log = TRUE, type = "all", ...)

# S3 method for PlackettLuce
summary(object, ref = 1L, ...)

# S3 method for PlackettLuce
vcov(object, ref = 1L, type = c("expected", "observed"), ...)

Arguments

object: An object of class "PlackettLuce" as returned by PlackettLuce.
ref: An integer or character string specifying the reference item (for which log worth will be set to zero). If NULL the sum of the log worth parameters is set to zero.
log: A logical indicating whether to return parameters on the log scale with the item specified by ref set to zero.
type: For coef, the type of coefficients to return: one of "ties", "worth" or "all". For vcov, the type of Fisher information to base the estimation on: either "expected" or "observed".
...: additional arguments, passed to vcov by summary.

Details

By default, parameters are returned on the log scale, as most suited for inference. If log = FALSE, the worth parameters are returned, constrained to sum to one so that they represent the probability that the corresponding item comes first in a ranking of all items, given that first place is not tied.

The variance-covariance matrix is returned for the worth and tie parameters on the log scale, with the reference as specified by ref. For models estimated by maximum likelihood, the variance-covariance is the inverse of the Fisher information of the log-likelihood.

For models with a normal or gamma prior, the variance-covariance is based on the Fisher information of the log-posterior. When adherence parameters have been estimated, the log-posterior is not linear in the parameters. In this case there is a difference between the expected and observed Fisher information. By default, vcov will return the variance-covariance based on the expected information, but type gives to option to use the observed information instead. For large samples, the difference between these options should be small. Note that the estimation of the adherence parameters is accounted for in the computation of the variance-covariance matrix, but only the sub-matrix corresponding to the worth and tie parameters is estimated.