🤖 AI Summary
This study addresses the challenge that traditional models struggle to capture intra-individual variability in response times within computerized testing, where dynamic shifts in behavior may occur. To this end, we propose a novel latent variable model that incorporates individual-specific change points into log-response time modeling for the first time. Behavioral abrupt shifts are characterized through item-specific mean structure offsets, and the change point is treated as a discrete latent variable whose distribution is linked to an underlying speed factor. This unified framework enables simultaneous modeling of within-person dynamics and supports statistical inference and uncertainty quantification for both change point locations and effect parameters. Using marginal maximum likelihood estimation—integrating latent variable modeling, change point detection, and Bayesian posterior inference—simulation studies demonstrate that the model robustly and accurately recovers parameters and change point positions across varying sample sizes and test lengths.
📝 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.