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 effect s, 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 nonschizop hrenic and schizophrenic eye-tracking behavior under different conditi ons. Included are description's of the algorithms for model fitting, s pecifically the ECM/SECM algorithms for large sample modal inference, and the Gibbs sampler for simulating the posterior distribution. For g uidance on model comparison and selection, we use posterior predictive check distributions to obtain posterior predictive p-values for likel ihood ratio statistics, which do not have asymptotic chi(2) reference distributions. These posterior predictive p-values suggest that all th e mixture components in our model are necessary. The final model is se lected using a combination of scientific parsimony, the posterior pred ictive p-values, and the posterior distributions of relevant parameter s.