Testing the equality of scale values and discriminal dispersions in paired comparisons

Abstract

General normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley- Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of Comparative,General normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley- Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of ComparativeGeneral normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley-Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of Comparative Judgment.