The case of dependency of responses and response times: A modeling approach based on standard latent trait models

When modeling responses and response times in tests with latent trait models, the assumption of conditional independence between responses and response times might be too strong in the case that both data are gained from reactions to the same item. In order to account for the possible dependency of responses and response times from the same item, a generalization of the model of van der Linden (2007) is proposed. The basic idea consists in the assumption of a latent continuous response that underlies the observed binary response. This latent response is assumed to be correlated with the corresponding response time. The main advantage of this approach consists in the fact that the marginal models for responses and response times follow well known, standard latent trait models. Model estimation can be accomplished by marginal maximum likelihood estimation. The adequacy of the estimation approach is demonstrated in a small scale simulation study. An empirical data application illustrates the practicability of the approach in practice.