UC Berkeley

This dissertation proposes longitudinal growth curve cognitive diagnosis models (GC-CDM) to incorporate learning over time into the cognitive assessment framework. The approach was motivated by higher-order latent trait models (de la Torre & Douglas, 2004), which define a higher-order continuous latent trait that affects all the latent skills. The higher-order latent trait can be viewed as the more broadly defined general ability; and the skills can be viewed as the specific knowledge arising from the higher-order latent trait. GC-CDMs trace changes in the higher-order latent traits over time by using latent growth curve model with respondent-specific random intercept and random slope of time, and simultaneously trace students' skill mastery through the CDM measurement model.

GC-CDMs are estimated using marginal maximum likelihood (MML) estimation in Mplus. Relevant issues for estimating GC-CDMs are addressed, e.g., the high-dimensional computation problem, model specification for the relationship between the higher-order latent trait and the multiple skills, and model identification. In simulation studies, we use the DINA measurement model, and examine parameter recovery of the GC-DINA model under differing conditions. Particularly, the effects of the design of the Q-matrix, the number of respondents and the number of time points are discussed. Overall, MML estimation in Mplus shows good parameter recovery; especially, the average growth, which is the parameter of most interest, is well estimated in all conditions. We also illustrate the application of the GC-DINA model to real data using two datasets from multi-wave experiments designed to assess the effects of the Enhanced Anchored Instruction (EAI; Bottge et al., 2003) on mathematics achievement. In addition, the GC-DINA model is compared to the latent transition analysis DINA model (LTA-DINA) (Li et al., 2016; Kaya & Leite, 2016) and a longitudinal item response theory (IRT) model (Andersen, 1985) using a simulated data. The results suggest that the GC-DINA model and the LTA-DINA model are similar in terms of the predicted skill mastery; and the GC-DINA model and the longitudinal IRT model are similar in terms of the predicted higher-order latent trait.