# btmodel

0th

Percentile

##### Bradley-Terry Model Fitting Function

btmodel is a basic fitting function for simple Bradley-Terry models.

Keywords
regression
##### Usage
btmodel(y, weights = NULL, type = c("loglin", "logit"), ref = NULL,
undecided = NULL, position = NULL, start = NULL, vcov = TRUE, estfun =
FALSE, …)
##### Arguments
y

paircomp object with the response.

weights

an optional vector of weights (interpreted as case weights).

type

character. Should an auxiliary log-linear Poisson model or logistic binomial be employed for estimation? The latter is not available if undecided effects are estimated.

ref

character or numeric. Which object parameter should be the reference category, i.e., constrained to zero?

undecided

logical. Should an undecided parameter be estimated?

position

logical. Should a position effect be estimated?

start

numeric. Starting values when calling glm.fit.

vcov

logical. Should the estimated variance-covariance be included in the fitted model object?

estfun

logical. Should the empirical estimating functions (score/gradient contributions) be included in the fitted model object?

further arguments passed to functions.

##### Details

btmodel provides a basic fitting function for Bradley-Terry models, intended as a building block for fitting Bradley-Terry trees and Bradley-Terry mixtures in the psychotree package, respectively. While btmodel is intended for individual paired-comparison data, the eba package provides functions for aggregate data.

btmodel returns an object of class "btmodel" for which several basic methods are available, including print, plot, summary, coef, vcov, logLik, estfun and worth.

##### Value

btmodel returns an S3 object of class "btmodel", i.e., a list with components as follows.

y

paircomp object with the response

coefficients

estimated parameters on log-scale (without the first parameter which is always constrained to be 0),

vcov

covariance matrix of the parameters in the model,

loglik

log-likelihood of the fitted model,

df

number of estimated parameters,

weights

the weights used (if any),

n

number of observations (with non-zero weights),

type

character for model type (see above),

ref

character for reference category (see above),

undecided

logical for estimation of undecided parameter (see above),

position

logical for estimation of position effect (see above),

labels

character labels of the objects compared,

estfun

empirical estimating function (also known as scores or gradient contributions).

pcmodel, gpcmodel, rsmodel, raschmodel, plmodel, the eba package

##### Aliases
• btmodel
• btReg.fit
• print.btmodel
• summary.btmodel
• print.summary.btmodel
• coef.btmodel
• worth.btmodel
• deviance.btmodel
• logLik.btmodel
• vcov.btmodel
• estfun.btmodel
##### Examples
# NOT RUN {
o <- options(digits = 4)

## data
data("GermanParties2009", package = "psychotools")

bt <- btmodel(GermanParties2009$preference) summary(bt) plot(bt) options(digits = o$digits)