The analysis of repeated-measures data on schizophrenic reaction times using mixture models

Reaction times for schizophrenic individuals in a simple visual tracking experiment can be substantially more variable than for non-schizophrenic individuals. Current psychological theory suggests that at least some of this extra variability arises from an attentional lapse that delays some, but not all, of each schizophrenic's reaction times. Based on this theory, we pursue models in which measurements from non-schizophrenics arise from a normal linear model with a separate mean for each individual, whereas measurements from schizophrenics arise from a mixture of (i) a component analogous to the distribution of response times for non-schizophrenics and (ii) a mean-shifted component. We fit four mixture models within this framework, where the distinctions between models arise from assumptions about the variance of the shifted observations and the exchangeability of schizophrenic individuals. Some of these models can be fit by maximum likelihood using the EM algorithm, and all can be fit using the ECM algorithm, where the covariance matrices associated with the parameters are calculated by the SEM and SECM algorithms, respectively. Bayesian model monitoring using posterior predictive checks is invoked to discard models that fail to reproduce certain observed features of the data and to stimulate the development of better models.