Modeling schizophrenic behavior using general mixture components

This article proposes a novel and general mixture component model, the features of which include a hierarchical structure with random effects, mixture components characterized by ANOVA-like linear regressions, and mixing mechanisms governed by logistic regressions. The model was developed as a consequence of attending to long-standing psychological theory about schizophrenic behavior. Scientifically revealing results are obtained by fitting the model to a data set concerning nonschizophrenic and schizophrenic eye-tracking behavior under different conditions. Included are descriptions of the algorithms for model fitting, specifically the ECM/SECM algorithms for large sample modal inference, and the Gibbs sampler for simulating the posterior distribution. For guidance on model comparison and selection, we use posterior predictive check distributions to obtain posterior predictive p-values for likelihood ratio statistics, which do not have asymptotic chi 2 reference distributions. These posterior predictive p-values suggest that all the mixture components in our model are necessary. The final model is selected using a combination of scientific parsimony, the posterior predictive p-values, and the posterior distributions of relevant parameters.