A Conditional Joint Modeling Approach for Locally Dependent Item Responses and Response Times

The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance structure to explain the local dependency between speed and accuracy. To obtain information about the population of test takers, the new model was embedded in the hierarchical framework proposed by van der Linden (2007). A fully Bayesian approach using a straightforward Markov chain Monte Carlo (MCMC) sampler was developed to estimate all parameters in the model. The deviance information criterion (DIC) and the Bayes factor (BF) were employed to compare the goodness of fit between the models with two different parameter structures. The Bayesian residual analysis method was also employed to evaluate the fit of the RT model. Based on the simulations, we conclude that (1) the new model noticeably improves the parameter recovery for both the item parameters and the examinees' latent traits when the assumptions of conditional independence between the item responses and the RTs are relaxed and (2) the proposed MCMC sampler adequately estimates the model parameters. The applicability of our approach is illustrated with an empirical example, and the model fit indices indicated a preference for the new model.