eba (version 1.5-2)

eba.order: 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, A = 1:I, s = c(rep(1/J, J), 1), constrained = TRUE)
## S3 method for class 'eba.order':
summary(object, \dots)

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

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

Value

• estimate
  a vector of parameter estimates, the last component holds the order-effect estimate
• se
  a vector of standard errors of the parameter estimates
• ci95
  a vector of 95% confidence intervals for the parameters
• 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 u-scale of the stimuli; one u-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
  the fitted paired-comparison matrix
• 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

Details

The choice models include a single multiplicative order effect, order, that is constant for all pairs (see Davidson & 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 & Choisel (2006) describe a model that generalizes the Davidson-Beaver model and allows for an order effect in Pretree and EBA models.

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.

See Also

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

Examples

data(heaviness)  # weights judging data
ebao1 <- eba.order(heaviness[,,1], heaviness[,,2])  # Davidson-Beaver model
summary(ebao1)   # goodness of fit
plot(ebao1)      # residuals versus predicted values