A Latent Class Approach to Modeling Pairwise Preferential Choice Data

Summary

Several probabilistic models have been proposed for representing two-way and three-way replicated paired comparisons data. Such data are usually obtained by having N subjects judge all n(n−1)/2 possible pairs of n stimuli. If the N subjects are grouped into T (T ≪ N) homogeneous groups, an n × n × T replicated paired comparisons data array is obtained. Examples of models for representing such three-way paired comparisons data are the wandering vector model and the wandering ideal point model. These models predict a different n(n−1)/2-variate Bernoulli distribution for each level t (1 ≤ t ≤ T) of the third way of the data array. By applying a latent class approach, the a priori grouping of the N subjects into T groups can be avoided. This is especially useful when one wants to estimate market segments from the preferential choice data. In the latent class formulation, a different multivariate Bernoulli distribution is predicted for each class and the data of an individual subject are assumed to be sampled from a finite mixture of these multivariate Bernoulli distributions. An EM algorithm for simultaneously estimating the mixture parameters and the choice model parameters is developed. The algorithm as well as a Monte Carlo significance test for the number of latent classes are illustrated on some real data.

Supported as “Bevoegdverklaard Navorser” of the Belgian N.F.W.O.