A unified framework for jointly modeling response times and item position effects in computer-based learning assessments

Current models for assessing response accuracy and response times in testing environments typically overlook variations in speed and ability within individuals. Instead, they often treat these as residual variances, missing the dynamic changes in individual performance throughout a test. Additionally, the influence of item position and the ordinal nature of response accuracy remain underexplored. This paper introduces a comprehensive modelling framework that integrates item responses, response times, and item position to better understand skill acquisition and latent speed changes. Our approach uses the Bivariate Generalised Linear Item Response Theory (B-GLIRT) model, capturing the dual impact of ability on response accuracy and the interplay between ability and speed on response times. We extend this model by incorporating random effects for item and individual-specific variations. The proposed model further explores how item positioning affects test performance and provides diagnostic insights into individual differences. The paper also discusses parameter estimation, model identification, and applications to real-world data, illustrating the practical implications of our findings in computer-based learning assessments.