A Mixture Proportional Hazards Model With Random Effects for Response Times in Tests

Abstract

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.

Pace or Inverse Error Provide Facile Observational-Level Approximations to Logarithmic Response Time Residuals and Response Time in the Analysis of Computerized Assessments

“…Recall that while the correlation of average person pace and person speed approaches one, the observationallevel match between pace and RT is lower, perhaps because of "feeling-of-knowing" effects (Thompson et al, 2009). Finally, hazard estimation from survival analysis has also proven to be instructive (Ranger & Ortner, 2013) (Ranger & Kuhn, 2016).…”