A sparse latent class model incorporating response times

Diagnostic models (DM) have been widely used to classify respondents' latent attributes in cognitive and non-cognitive assessments. The integration of response times (RTs) with DM presents additional evidence to understand respondents' problem-solving behaviours. While recent research has explored using sparse latent class models (SLCM) to infer the latent structure of items based on item responses, the incorporation of RT data within these models remains underexplored. This study extends the SLCM framework to include RT, relaxing the conditional independence assumption between RT and latent attributes given individual speed. This adaptation provides a more flexible framework for jointly modelling RT and item responses. While the proposed model holds promise for applications in educational assessment, this study applied the model to the Fisher Temperament Inventory, yielding findings that provide a novel perspective on utilizing DM with RT in personality assessments. Additionally, a Gibbs sampling algorithm is proposed for parameter estimation. Results from Monte Carlo simulations demonstrate the algorithm's accuracy and efficiency.