OptiPt {eba}R Documentation

Elimination-By-Aspects (EBA) Models

Description

Fits a probabilistic choice model by maximum likelihood estimation.

Usage

  OptiPt(M, A = 1:I, s = rep(1/J, J))

  summary.eba(object, ...)

Arguments

M a square matrix or a data frame consisting of absolute frequencies; row stimuli are chosen over column stimuli
A a list of vectors consisting of the stimulus aspects; the default is 1:I, where I is the number of stimuli
s the starting vector with default 1/J for all parameters, where J is the number of parameters
object an object of class eba, typically the result of a call to OptiPt
... additional arguments affecting the summary produced

Details

The probabilistic choice models which can be fitted to paired-comparison data are the Bradley-Terry-Luce (BTL) model, preference tree (Pretree) models, and elimination-by-aspects (EBA) models, the former being special cases of the latter.

A is usually a list of vectors, the first element of each being a number from 1 to I; additional elements specify the aspects shared by several stimuli. A must have as many elements as there are stimuli. When fitting a BTL model, A reduces to 1:I, i.e. there is only one aspect per stimulus.

The maximum likelihood estimation of the parameter values is carried out by nlm. The Hessian matrix, however, is approximated by fdHess{nlme}. The likelihood function L is called automatically.

Value

estimate a vector of parameter estimates
se a vector of standard errors of the parameter estimates
ci95 a vector of 95%-confidence intervals for the parameter estimates
logL.eba the log-likelihood of the fitted model
logL.sat the log-likelihood of the saturated (binomial) model
goodness.of.fit the goodness of fit statistic including the likelihood ratio fitted vs. saturated model (-2logL), the degrees of freedom, and the p-value of the corresponding chi2 distribution
u.scale the u-scale of the stimuli; one u-scale value is defined as the sum of aspect values (parameters) that characterize a given stimulus
hessian the Hessian matrix of the likelihood function
cov.p the covariance matrix of the model parameters
chi.alt the Pearson chi2 goodness of fit statistic
fitted the fitted paired-comparison matrix
y1 the data vector of the upper triangle matrix
y0 the data vector of the lower triangle matrix
n the number of observations per pair (y1 + y0)
mu the predicted choice probabilities for the upper triangle

Author(s)

Florian Wickelmaier

References

Wickelmaier, F., & Schmid, C. (2004). A Matlab function to estimate choice model parameters from paired-comparison data. Behavior Research Methods, Instruments, and Computers, 36, 29–40.

Bradley, R.A. (1984). Paired comparisons: some basic procedures and examples. In P.R. Krishnaiah & P.K. Sen (eds.), Handbook of Statistics, Volume 4. Amsterdam: Elsevier.

Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79, 281–299.

Tversky, A., & Sattath, S. (1979). Preference trees. Psychological Review, 86, 542–573.

See Also

strans, cov.u, wald.test, group.test, plot.eba, residuals.eba, nlm.

Examples

data(celebrities)  # absolute choice frequencies
A <- list(c(1,10), c(2,10), c(3,10), c(4,11), c(5,11), c(6,11),
          c(7,12), c(8,12), c(9,12))  # the structure of aspects
eba <- OptiPt(celebrities, A)  # Fit a preference tree

summary(eba)  # goodness of fit
plot(eba)  # residuals versus predicted values

ci <- 1.96 * sqrt(diag(cov.u(eba)))  # 95%-ci of the preference scale
a <- barplot(eba$u, ylim = c(0, .35))  # plot the scale
arrows(a, eba$u-ci, a, eba$u+ci, .05, 90, 3)  # error bars

[Package eba version 1.4-1 Index]