In this article, a new model for test response times is proposed that combines latent class analysis and the proportional hazards model with random effects in a similar vein as the mixture factor model. The model assumes the existence of different latent classes. In each latent class, the response times are distributed according to a class-specific proportional hazards model. The class-specific proportional hazards models relate the response times of each subject to his or her work pace, which is considered as a random effect. The latent class extension of the proportional hazards model allows for differences in response strategies between subjects. The differences can be captured in the hazard functions, which trace the progress individuals make over time when working on an item. The model can be calibrated with marginal maximum likelihood estimation. The fit of the model can either be assessed with information criteria or with a test of model fit. In a simulation study, the performance of the proposed approaches to model calibration and model evaluation is investigated. Finally, the model is used for a real data set.