group.test {eba}

Group Effects in Elimination-by-Aspects (EBA) Models

Description

Tests for group effects in elimination-by-aspects (EBA) models.

Usage

group.test(groups, A = 1:I, s = rep(1/J, J), constrained = TRUE)

Arguments

groups

a 3d array containing one aggregate choice matrix per group

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

constrained

logical, if TRUE (default), EBA parameters are constrained to be positive

Details

The five tests are all based on likelihood ratios.

Overall compares a 1-parameter Poisson model to a saturated Poisson model, thereby testing the equality of the frequencies in each cell of the array. This test corresponds to simultaneously testing for a null effect of (1) the context induced by a given pair, (2) the grouping factor, (3) the stimuli, and (4) the imbalance between pairs. The deviances of the remaining tests sum to the total deviance associated with the overall test.

EBA.g tests an EBA group model against a saturated binomial group model, which corresponds to a goodness of fit test of the EBA group model.

Group tests an EBA model having its parameters restricted to be equal across groups (single set of parameters) against the EBA group model allowing its parameters to vary freely across groups (one set of parameters per group); this corresponds to testing for group differences.

Effect tests an indifference model (where all choice probabilities are equal to 0.5) against the restricted EBA model (single set of parameters), which corresponds to testing for a stimulus effect.

Imbalance tests for differences in the number of observations per pair by comparing the average sample size (1-parameter Poisson model) to the actual sample sizes (saturated Poisson model).

See Duineveld, Arents, and King (2000) for further details, and Choisel and Wickelmaier (2007) for an application.

Value

tests

a table displaying the likelihood ratio test statistics

References

Choisel, S., & Wickelmaier, F. (2007). Evaluation of multichannel reproduced sound: Scaling auditory attributes underlying listener preference. Journal of the Acoustical Society of America, 121, 388–400. doi: 10.1121/1.2385043

Duineveld, C.A.A., Arents, P., & King, B.M. (2000). Log-linear modelling of paired comparison data from consumer tests. Food Quality and Preference, 11, 63–70. doi: 10.1016/s0950-3293(99)00040-3

See Also

eba, wald.test.

Examples

## Bradley-Terry-Luce model
data(pork)          # Is there a difference between Judge 1 and Judge 2?
groups <- simplify2array(list(apply(pork[, , 1:5],  1:2, sum),
                              apply(pork[, , 6:10], 1:2, sum)))
group.test(groups)  # Yes, there is.

## Elimination-by-aspects model
data(drugrisk)   # Do younger and older males judge risk of drugs differently?
A2 <- list(c(1), c(2,7), c(3,7), c(4,7,8), c(5,7,8), c(6,7,8))
group.test(drugrisk[, , 3:4], A2)  # Yes.