eba.order {eba} R Documentation

## Elimination-by-Aspects (EBA) Models with Order-Effect

### Description

Fits a (multi-attribute) probabilistic choice model that accounts for the effect of the presentation order within a pair.

### Usage

eba.order(M1, M2 = NULL, A = 1:I, s = c(rep(1/J, J), 1),
constrained = TRUE)

## S3 method for class 'eba.order'
summary(object, ...)


### Arguments

 M1, M2 two square matrices or data frames consisting of absolute choice frequencies in both within-pair orders; row stimuli are chosen over column stimuli. If M2 is empty (default), M1 is assumed to be a 3d array containing both orders A see eba s the starting vector with default 1/J for all J aspect parameters, and 1 for the order effect constrained see eba object an object of class eba.order, typically the result of a call to eba.order ... additional arguments

### Details

The choice models include a single multiplicative order effect, order, that is constant for all pairs (see Davidson and Beaver, 1977). An order effect < 1 (> 1) indicates a bias in favor of the first (second) interval. See eba for choice models without order effect.

Several likelihood ratio tests are performed (see also summary.eba).

EBA.order tests an order-effect EBA model against a saturated binomial model; this corresponds to a goodness of fit test of the former model.

Order tests an EBA model with an order effect constrained to 1 against an unconstrained order-effect EBA model; this corresponds to a test of the order effect.

Effect tests an order-effect indifference model (where all scale values are equal, but the order effect is free) against the order-effect EBA model; this corresponds to testing for a stimulus effect; order0 is the estimate of the former model.

Wickelmaier and Choisel (2006) describe a model that generalizes the Davidson-Beaver model and allows for an order effect in Pretree and EBA models.

### Value

 coefficients a vector of parameter estimates, the last component holds the order-effect estimate estimate same as coefficients 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 chi-square distribution u.scale the unnormalized utility scale of the stimuli; each utility 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 chi-square goodness of fit statistic fitted 3d array of the fitted paired-comparison matrices y1 the data vector of the upper triangle matrices y0 the data vector of the lower triangle matrices n the number of observations per pair (y1 + y0) mu the predicted choice probabilities for the upper triangles M1, M2 the data matrices

### Author(s)

Florian Wickelmaier

### References

Davidson, R.R., & Beaver, R.J. (1977). On extending the Bradley-Terry model to incorporate within-pair order effects. Biometrics, 33, 693–702.

Wickelmaier, F., & Choisel, S. (2006). Modeling within-pair order effects in paired-comparison judgments. In D.E. Kornbrot, R.M. Msetfi, & A.W. MacRae (eds.), Fechner Day 2006. Proceedings of the 22nd Annual Meeting of the International Society for Psychophysics (p. 89–94). St. Albans, UK: The ISP.

eba, group.test, plot.eba, residuals.eba, logLik.eba.
data(heaviness)                # weights judging data