eba.order {eba}R Documentation

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


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


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, ...)


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


see eba


the starting vector with default 1/J for all J aspect parameters, and 1 for the order effect


see eba


an object of class eba.order, typically the result of a call to eba.order


additional arguments


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.



a vector of parameter estimates, the last component holds the order-effect estimate


same as coefficients


the log-likelihood of the fitted model


the log-likelihood of the saturated (binomial) model


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


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


the Hessian matrix of the likelihood function


the covariance matrix of the model parameters


the Pearson chi-square goodness of fit statistic


3d array of the fitted paired-comparison matrices


the data vector of the upper triangle matrices


the data vector of the lower triangle matrices


the number of observations per pair (y1 + y0)


the predicted choice probabilities for the upper triangles

M1, M2

the data matrices


Florian Wickelmaier


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.

See Also

eba, group.test, plot.eba, residuals.eba, logLik.eba.


data(heaviness)                # weights judging data
ebao1 <- eba.order(heaviness)  # Davidson-Beaver model
summary(ebao1)                 # goodness of fit
plot(ebao1)                    # residuals versus predicted values
confint(ebao1)                 # confidence intervals for parameters

[Package eba version 1.10-0 Index]