Mixture Models for Ordinal Data

Cumulative probability models are widely used for the analysis of ordinal data. In this article the authors propose cumulative probability mixture models that allow the assumptions of the cumulative probability model to hold within subsamples of the data. The subsamples are defined in terms of latent class membership. In the case of the ordered logit mixture model, on which the authors focus here, the assumption of a logistic distribution for an underlying latent dependent variable holds within each latent class, but because the sample then comprises a weighted sum of these distributions, the assumption of an underlying logistic distribution may not hold for the sample as a whole. The authors show that the latent classes can be allowed to vary in terms of both their location and scale and illustrate the approach using three examples.