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There has been a growing interest in psychological measurements that use the multiple-alternative forced-choice (MAFC) response format for its resistance to response biases. Although several models have been proposed for the data obtained from such measurements, none have succeeded in incorporating the response time information. Given that currently, many psychological measurements are performed via computers, it would be beneficial to develop a joint model involving an MAFC item response and response time. The present study proposes the first model that combines a cognitive process model that underlies the observed response time and the forced-choice item response model. Specifically, the proposed model is based on the linear ballistic accumulator model of response time, which is substantially extended by reformulating its parameters so as to incorporate the MAFC item responses. The model parameters are estimated by the Markov chain Monte Carlo (MCMC) algorithm. A simulation study confirmed that the proposed approach could appropriately recover the parameters. Two empirical applications are reported to demonstrate the use of the proposed model and compare it with existing models. The results showed that the proposed model could be a useful tool for jointly modeling the MAFC item responses and response times.

Linear Ballistic Accumulator Item Response Theory Model for Multidimensional Multiple-Alternative Forced-Choice Measurement of Personality