Penalized partial likelihood inference of proportional hazards latent trait models.

The Cox proportional hazards model with a latent trait variable (Ranger & Ortner, 2012, Br. J. Math. Stat. Psychol., 65, 334) has shown promise in accounting for the dependency of response times from the same examinee. The model allows flexibility in shapes of response time distributions using the non-parametric baseline hazard rate while allowing parametric inference about the latent variable via exponential regression. The flexibility of the model, however, comes at the price of a significant increase in the complexity of estimating the model. The purpose of this study is to propose a new estimation approach to overcome this difficulty in model estimation. The new procedure is based on the penalized partial likelihood estimator in which the partial likelihood is maximized in the presence of a penalty function. The potential of the proposed method is corroborated by a series of simulation studies for fitting the proportional hazards latent trait model to psychological and educational testing data. The application of the estimation method to the hierarchical framework (van der Linden, 2007, Psychometrika, 72, 287) is also illustrated for jointly analysing response times and accuracy scores.