A bayesian nonparametric approach for latent class regression analysis

Bayesian latent class regression analyses are usually carried out through embedding a multiple logistic regression procedure within the Gibbs sampler after the class assignments were imputed. Such practice often involves in heavy computation as posterior sample of the regression coefficients need to be generated indirectly using MCMC. As the number of classes increases to the range of 20 or more in research problems such as in disease etiology studies, the computation burden might become intolerable, especially when the relationships with the covariates are nonlinear and/or non-additive. Further, with so many parameters needed to be estimated, the identifiability issue of the model might prevent the approach converging to the correct estimation of the parameters. We proposed an innovative approach that linked covariates to the Dirichlet parameters of the posterior distribution of class assignment probability, instead of modeling the probability directly. This idea is like implementing a random partition models (RPMs) on the domain of the covariates. Following the general idea of Bayesian nonparametric approach, we will let the number of partitions be random too with possibility of going to infinity. That will result in a natural prior for the random partitions using Dirichlet mixture process. Gibbs samplers are then easily constructed. The actual computation can be further simplified through a connection between the Dirichlet mixture and the Kernel based density estimation. We will use examples from multiple pathogen disease etiology research to illustrate the advantages of the proposed method.