A Mixture Modeling Approach to Detect Different Behavioral Patterns for Process Data

Process data recorded by computer-based assessments reflect how respondents solve problems and thus contain rich information about respondents as well as tasks. Considering that different respondents may exhibit different behavioral characteristics during problem-solving process, in this study, we propose a mixture one-parameter state response (Mix1P-SR) measurement model. This model assumes that respondents belong to discrete latent classes with different propensities towards responses to task states during the problem-solving process, and the varying response propensities are captured by different state parameters across classes. A Markov Chain Monte Carlo algorithm for the estimation of model parameters and classification of respondents is described. The simulation study shows that the Mix1P-SR model could recover parameters well on the premise that the average sequence length was not too short. Moreover, larger sample size, longer sequences, more uniform mixing proportions, and lower interclass similarity facilitated model convergence, model selection, and parameter estimation accuracy, with sequence length being particularly important. Based on the empirical data from PISA 2012, the Mix1P-SR model identified two latent classes of respondents. They had different patterns of state easiness parameters and exhibited different state response patterns, which affected their problem solving results. Implications for model application and future research directions are discussed.