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 eba.order
summary(object, …)
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
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
the data matrices
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.
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.
# NOT RUN {
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
# }
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