OptiPt {eba}R Documentation

Elimination-by-aspects 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
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
... additional arguments affecting the summary produced

Details

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. When fitting a BTL model, A reduces to 1:I, i.e. there is 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}.

Value

estimate a vector of parameter estimates
se a vector of the standard errors of the parameter estimates
ci95 the 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 (-2logL), the degrees of freedom, and the p-value of the corresponig chi2 distribution
u.scale the u-scale of the stimuli; one 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

Author(s)

Florian Wickelmaier wickelmaier@web.de

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, nlm.

Examples

data(rugr)  # 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(rugr,A)  # Fit a preference tree

summary(eba)  # goodness of fit
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

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