group.test.RdTests for group effects in elimination-by-aspects (EBA) models.
group.test(groups, A = 1:I, s = rep(1/J, J), constrained = TRUE)
| groups | a 3d array containing one aggregate choice matrix per group |
|---|---|
| A | a list of vectors consisting of the stimulus aspects;
the default is |
| s | the starting vector with default |
| constrained | logical, if TRUE (default), EBA parameters are constrained to be positive |
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.
a table displaying the likelihood ratio test statistics
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
## 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.#> #> Testing for group effects in EBA models: #> #> Df1 Df2 logLik1 logLik2 Deviance Pr(>Chi) #> Overall 1 12 -21.110 -15.414 11.390 0.4112 #> EBA.g 4 6 -5.880 -4.973 1.814 0.4038 #> Group 2 4 -10.130 -5.880 8.500 0.0143 * #> Effect 0 2 -10.668 -10.130 1.076 0.5838 #> Imbalance 1 6 -10.442 -10.442 0.000 1.0000 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>## 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.#> #> Testing for group effects in EBA models: #> #> Df1 Df2 logLik1 logLik2 Deviance Pr(>Chi) #> Overall 1 60 -576.25 -134.63 883.23 < 2e-16 *** #> EBA.g 14 30 -60.49 -48.94 23.09 0.111307 #> Group 7 14 -74.08 -60.49 27.18 0.000309 *** #> Effect 0 7 -490.56 -74.08 832.96 < 2e-16 *** #> Imbalance 1 30 -85.69 -85.69 0.00 1.000000 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>