btreg: Bradley-Terry Regression Models

In prefmod2: Paired Comparison Models for Preferences

Description

Extended Bradley-Terry models with subject- and object-specific variables fitted by means of log-linear (or logistic) regression models.

Usage

btreg(formula, data, subset, na.action, weights, offset,
  type = c("loglin", "logit"), ref = NULL, undecided = NULL, position = NULL,
  model = FALSE, y = TRUE, x = FALSE, ...)

btreg.fit(x, y, z = NULL, weights = NULL, type = c("loglin", "logit"), ref = NULL,
  undecided = NULL, position = NULL, ...)

Arguments

formula	A symbolic description of the model to be fit. This should be of type y | z1 + z2 ~ x1 + x2 + x3 where y should be an object of class paircomp, x1, x2, x3 are subject-covariates (taken from data) and z1 and z2 are object-covariates (taken from covariates(y)).
data	an optional data frame containing the variables in the model.
subset	an optional subset specification.
na.action	A function which indicates what should happen when the data contain NAs, defaulting to na.action.
weights	an optional vector of weights, interpreted as case weights (integer only).
offset	an optional offset vector (currently ignored).
type	character. Should an auxiliary log-linear Poisson model or logistic binomial be employed for estimation? The latter is only available if not 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?
model	logical. Should the model frame be included in the fitted model object?
x	matrix. The regressor matrix pertaining to the subject covariates. This can be returned in btreg if x = TRUE.
y	paircomp object with the response. This can be returned in btreg if y = TRUE.
z	matrix. The regressor matrix pertaining to the object covariates. This can be returned in btreg if x = TRUE.
...	further arguments passed to functions.

Details

btreg is a convenient formula-based interface for fitting Bradley-Terry models. It essentially handles the formula parsing and argument preprocessing and then calls btreg.fit, the workhorse fitting function. This suitably aggregates the data and then calls glm.fit (currently) for parameter estimation and postprocesses the results.

Currently, the fitting function only supports simple Bradley-Terry models of type y ~ 1, i.e., without any covariates. This will be extended in future versions.

Value

An object of class "btreg", i.e., a list with components including

coefficients	a vector of estimated coefficients,
vcov	covariance matrix of all coefficients in the model,
loglik	log-likelihood of the fitted model,
df	degrees of freedom,
estfun	empirical estimating functions (gradients),
weights	case weights used,
n	number of observations (subjects),
type	type argument used,
ref	ref argument used,
undecided	undecided argument used,
position	position argument used,
labels	vector of object labels,
call	the original function call,
terms	the original model terms,
model	the full model frame (if model = TRUE),
y	the response paircomp vector (if y = TRUE),
x	regressor matrix of subject covariates (if x = TRUE),
z	regressor matrix of object covariates (if x = TRUE),

References

Critchlow DE, Fligner MA (1991). Paired Comparison, Triple Comparison, and Ranking Experiments as Generalized Linear Models, and their Implementation in GLIM. Psychometrika, 56(3), 517–533.

Dittrich R, Hatzinger R, Katzenbeisser W (1998). Modelling the Effect of Subject-Specific Covariates in Paired Comparison Studies with an Application to University Rankings. Journal of the Royal Statistical Society C, 47(4), 511–525.

See Also

plot.btreg

Examples

## CEMS university choice data
data("CEMSChoice", package = "psychotree")

## Bradley-Terry modeling
cems <- btreg(preference ~ 1, data = CEMSChoice)
cems
summary(cems)
plot(cems)
worth(cems)

prefmod2 documentation built on May 2, 2019, 5:20 p.m.