OptiPt {eba} | R Documentation |
Fits a probabilistic choice model by maximum likelihood estimation.
OptiPt(M, A = 1:I, s = rep(1/J, J)) summary.eba(object, ...)
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 |
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}
.
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 |
Florian Wickelmaier wickelmaier@web.de
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.
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