Testing the Within-State Distribution in Mixture Models for Responses and Response Times

Mixture models have been developed to enable detection of within-subject differences in responses and response times to psychometric test items. To enable mixture modeling of both responses and response times, a distributional assumption is needed for the within-state response time distribution. Since violations of the assumed response time distribution may bias the modeling results, choosing an appropriate within-state distribution is important. However, testing this distributional assumption is challenging as the latent within-state response time distribution is by definition different from the observed distribution. Therefore, existing tests on the observed distribution cannot be used. In this article, we propose statistical tests on the within-state response time distribution in a mixture modeling framework for responses and response times. We investigate the viability of the newly proposed tests in a simulation study, and we apply the test to a real data set.