Exploring Multiple Strategic Problem Solving Behaviors in Educational Psychology Research by Using Mixture Cognitive Diagnosis Model

A mixture cognitive diagnosis model (CDM), which is called mixture multiple strategy-Deterministic, Inputs, Noisy "and" Gate (MMS-DINA) model, is proposed to investigate individual differences in the selection of response categories in multiple-strategy items. The MMS-DINA model system is an effective psychometric and statistical approach consisting of multiple strategies for practical skills diagnostic testing, which not only allows for multiple strategies of problem solving, but also allows for different strategies to be associated with different levels of difficulty. A Markov chain Monte Carlo (MCMC) algorithm for parameter estimation is given to estimate model, and four simulation studies are presented to evaluate the performance of the MCMC algorithm. Based on the available MCMC outputs, two Bayesian model selection criteria are computed for guiding the choice of the single strategy DINA model and multiple strategy DINA models. An analysis of fraction subtraction data is provided as an illustration example.