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 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.
Highlights
Research interest has grown in modeling response times next to the item responses in order to investigate individual differences in ability and speed
Suitable models to enable these inferences concerning individual differences in responses and response times include the model by Roskam (1987) and more recently the hierarchical model by van der Linden (2007, 2009), which was elaborated by Molenaar et al (2015a)
To enable mixture modeling of both the responses and response times, a distributional assumption is needed for the within-state response time distribution
Summary
Research interest has grown in modeling response times next to the item responses in order to investigate individual differences in ability and speed. Response times have been shown useful in detecting item preknowledge (McLeod et al, 2003), aberrant response patterns Wang, Xu, Shang, & Kuncel, 2018), and individual differences in the use of solution strategies. Van der Maas and Jansen (2003) showed that response times can give detailed information on the type and duration of different solution strategies children use to solve a balance scale task. Suitable models to enable these inferences concerning individual differences in responses and response times include the model by Roskam (1987) and more recently the hierarchical model by van der Linden (2007, 2009), which was elaborated by Molenaar et al (2015a)
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