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

• Activity Number: 380 - Advances in Statistical Learning for Large-Scale and Multidimensional Testing Data
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Dylan Molenaar*
• Companies: University of Amsterdam
• Keywords: mixture modeling; item response theory; response times

Abstract

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 within-state response time distribution is by definition different from the marginal distribution (i.e., aggregated over states). Therefore, existing tests on the marginal distribution (i.e., the observed response time distribution) cannot be used. In this paper, we propose statistical tests on the within-state response time distribution in a dynamical 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 dataset.