Joint Modeling of Action Sequences and Action Times in Problem-solving Tasks

Process data refer to data recorded in computerized assessments that reflect the problem-solving processes of participants and provide greater insight into how they solve problems and how well they solve them. Action times, namely the amount of time required to complete an action sequence, are also included in such data along with action sequences. In this study, an action-level joint model of action sequences and action times was proposed, in which the sequential response model (SRM) was used as the measurement model for action sequences and a new proposed log-normal action time model was used as the measurement model for action times. The proposed action-level joint model can be regarded as an extension of the SRM by incorporating action times within the joint-hierarchical modeling framework and as an extension of the conventional item-level joint models in terms of process data analysis. Results of the empirical and simulation studies demonstrated that the model setup was justified, the model parameters could be interpreted, the parameter estimates were accurate, and that taking into account participants’ action times further was beneficial. Overall, the proposed action-level joint model provides a useful modeling framework for the analysis of process data in technology-enhanced assessments from the perspective of latent variable modeling.