Growth Modeling in a Diagnostic Classification Model (DCM) Framework–A Multivariate Longitudinal Diagnostic Classification Model

A multivariate longitudinal DCM is developed that is the composite of two components, the log-linear cognitive diagnostic model (LCDM) as the measurement model component that evaluates the mastery status of attributes at each measurement occasion, and a generalized multivariate growth curve model that describes the growth of each attribute over time. The proposed model represents an improvement in the current longitudinal DCMs given its ability to incorporate both balanced and unbalanced data and to measure the growth of a single attribute directly without assuming that attributes grow in the same pattern. One simulation study was conducted to evaluate the proposed model in terms of the convergence rates, the accuracy of classification, and parameter recoveries under different combinations of four design factors: the sample size, the growth patterns, the G matrix design, and the number of measurement occasions. The results revealed the following: (1) In general, the proposed model provided good convergence rates under different conditions. (2) Regarding the classification accuracy, the proposed model achieved good recoveries on the probabilities of attribute mastery. However, the correct classification rates depended on the cut point that was used to classify individuals. For individuals who truly mastered the attributes, the correct classification rates increased as the measurement occasions increased; however, for individuals who truly did not master the attributes, the correct classification rates decreased slightly as the numbers of measurement occasions increased. Cohen's kappa increased as the number of measurement occasions increased. (3) Both the intercept and main effect parameters in the LCDM were recovered well. The interaction effect parameters had a relatively large bias under the condition with a small sample size and fewer measurement occasions; however, the recoveries were improved as the sample size and the number of measurement occasions increased. (4) Overall, the proposed model achieved acceptable recoveries on both the fixed and random effects in the generalized growth curve model.