response time, proportional hazard model, accelerated failure time model,

For computer-administered tests, response times can be recorded conjointly with the corresponding responses. This broadens the scope of potential modelling approaches because response times can be analysed in addition to analysing the responses themselves. For this purpose, we present a new latent trait model for response times on tests. This model is based on the Cox proportional hazards model. According to this model, latent variables alter a baseline hazard function. Two different approaches to item parameter estimation are described: the first approach uses a variant of the Cox model for discrete time, whereas the second approach is based on a profile likelihood function. Properties of each estimator will be compared in a simulation study. Compared to the estimator for discrete time, the profile likelihood estimator is more efficient, that is, has smaller variance. Additionally, we show how the fit of the model can be evaluated and how the latent traits can be estimated. Finally, the applicability of the model to an empirical data set is demonstrated.

The information matrix can equivalently be determined via the expectation of the Hessian matrix or the expectation of the outer product of the score vector. The identity of these two matrices, however, is only valid in case of a correctly specified model. Therefore, differences between the two versions of the observed information matrix indicate model misfit. The equality of both matrices can be tested with the so‐called information matrix test as a general test of misspecification. This test can be adapted to item response models in order to evaluate the fit of single items and the fit of the whole scale. The performance of different versions of the test is compared in a simulation study with existing tests of model fit, among them the  test of Orlando and Thissen, the score test of local independence due to Glas and Suarez‐Falcon, and the limited information approach of Maydeu‐Olivares and Joe. In general, the different versions of the information matrix test adhere to the nominal Type I error rate and have high power for detecting misspecified item characteristic curves. Additionally, some versions of the test can be used in order to detect violations of the local independence assumption.