A Latent Variable Model for Response Times with Individual-Specific Change-Points

Abstract

Response times collected in computerised assessments provide information about the underlying response process and may exhibit within-person variation over the course of a test. We propose a latent variable model for log response times that incorporates individual-specific change-points. The model extends the log-normal response time model by allowing an item-specific shift in the mean structure after an unobserved change-point. The change-point is treated as a discrete latent variable, and its distribution is modeled as a function of latent speed. Estimation is carried out using marginal maximum likelihood. The framework yields posterior distributions for change-point locations, allowing uncertainty to be quantified at the individual level, and supports statistical inference for the change-point effect parameters. A simulation study examines parameter recovery and change-point estimation under varying boundary conditions, prevalence of changers, sample sizes, and test lengths. The results show accurate recovery of item and structural parameters. The proposed model provides a unified approach to modeling response times with within-person changes in behaviour.