A Latent Markov Model for Noninvariant Measurements: An Application to Interaction Log Data From Computer-Interactive Assessments.

The latent Markov model (LMM) has been increasingly used to analyze log data from computer-interactive assessments. An important consideration in applying the LMM to assessment data is measurement effects of items. In educational and psychological assessment, items exhibit distinct psychometric qualities and induce systematic variance to assessment outcome data. The current development in LMM, however, assumes that items have uniform effects and do not contribute to the variance of measurement outcomes. In this study, we propose a refinement of LMM that relaxes the measurement invariance constraint and examine empirical performance of the new framework through numerical experimentation. We modify the LMM for noninvariant measurements and refine the inferential scheme to accommodate the event-specific measurement effects. Numerical experiments are conducted to validate the proposed inference methods and evaluate the performance of the new framework. Results suggest that the proposed inferential scheme performs adequately well in retrieving the model parameters and state profiles. The new LMM framework demonstrated reliable and stable performance in modeling latent processes while appropriately accounting for items' measurement effects. Compared with the traditional scheme, the refined framework demonstrated greater relevance to real assessment data and yielded more robust inference results when the model was ill-specified. The findings from the empirical evaluations suggest that the new framework has potential for serving large-scale assessment data that exhibit distinct measurement effects.