We propose a latent trait model for the responses and response times on tests that separates capability from persistence.Core of the model is a race between a diffusion process and a censoring process.The diffusion process represents item-level cognitive processing and determines the processing time of a test taker.The censoring process sets the maximal time a test taker is willing to invest into an item.If the processing time is shorter than the maximal time, the response is generated differently; otherwise, the response is generated by different process.In the first version of the model, the response is generated by a random guess.In the second version of the model, the response is determined by the actual level of the diffusion process.We relate the diffusion process to the capability and response caution of a test taker and the censoring process to his willingness to invest time.Similar to models for rapid guessing, the proposed models take account of disengaged responding, but allow for individual differences in persistence and informed guessing.The model also provides a mathematical specification of persistence.In a simulation study, we investigate model fitting by marginal maximum likelihood estimation.We also apply the model to two empirical data sets.
Ranger et al. (Mon,) studied this question.