A multiple-item model of paired comparisons: Separating chance from latentpreference

The authors develop a flexible model to analyze relative preference scores: the binomial/Dirichlet model. This model assumes that (I) individual respo ndents make independent draws from binomial distributions when stating thei r preferences and (2) the latent (unobserved) preference parameters vary ac ross respondents according to a Dirichlet distribution. Through the analysi s of 44 tests that include from two to five products each, the authors show that the model fits the data relatively well. A multinomial/Dirichlet exte nsion of the model that applies to repeat preference tests of two items pro vides a better fit than an alternative mixture model despite fewer paramete rs. To test two items and obtain an accuracy of +/-.05 with a 95% confidenc e interval for the mean preference intensities, a multinomial/Dirichlet mod el requires two paired comparisons (made at two points in time) per respond ent and a sample size of 400; these requirements represent half the require d number of preference measurements per respondent and half the required sa mple size of alternative methods. Although the illustrative examples refer to the comparison of known brands and unidentified products, the proposed m ethodology can be applied to many contexts, including the evaluation of pro duct profiles in conjoint analysis.