Joint modeling with generalized item response theory model family and response time model: Enhancing model structural...

In this study, we propose a joint hierarchical model that combines a family of item response theory (IRT) models with a log-normal response time (RT) model to analyze item responses and response times. By incorporating RTs as auxiliary information, we improve the accuracy of latent trait estimation, thereby facilitating a deeper understanding of examinee performance. Additionally, we explore the use of either identical or distinct link functions across different items, allowing us to optimize IRT models for each item and improve overall model fit. We further investigate scenarios in which the joint distribution of speed and ability is nonlinear by integrating the generalized logit-linked IRT model with the log-normal random quadratic variable speed model. Compared to the traditional hierarchical model by van der Linden (Psychometrika, 72, 287-308 2007), this integration yields more accurate estimates of ability, item difficulty, and discrimination parameters. Additionally, Bayesian model comparison reveals that the new joint hierarchical model provides a better fit than various models combining item responses and RTs, particularly when the data are derived from a joint RT and two-parameter IRT model with both symmetric and asymmetric link functions. Finally, a comprehensive analysis of data from the computer-based Program for International Student Assessment (PISA) science examination from 2015 is conducted to illustrate the proposed methodology.