Linear Logistic Latent Class Analysis for Polytomous Data

Abstract

For latent class analysis, a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones, a flexible model is presented in order to restrain the unknown class sizes (mixing weights) and the unknown latent response probabilities. Two systems of basic equations are stated such that they simultaneously allow parameter fixations, the equality of certain parameters as well as linear logistic constraints of each of the original parameters. The maximum likelihood equations for the parameters of this “linear logistic latent class analysis” are given, and their estimation by means of the EM algorithm is described. Further, the criteria for their local identifiability and statistical tests (Pearson- and likelihood-ratio-χ ²) for goodness of fit are outlined. The practical applicability of linear logistic latent class analysis is demonstrated by three examples: mixed logistic regression, a mixed Bradley-Terry model for paired comparisons with ties, and a local dependence latent class model in which the departure from stochastic independence is covered by a single additional parameter per class.

Key Words:

• Bioassay
• EM algorithm
• Local stochastic (in-)dependence
• Maximum likelihood method
• Mixed logistic regression
• Mixture multinomial
• Occupational mobility
• Paired comparisons with ties