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

Abstract

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.

Considerations for Fitting Dynamic Bayesian Networks With Latent Variables: A Monte Carlo Study

“…The relationship between DCMs and L-DCMs is similar to the relationship between LCA and LTA and between BN and DBN. L-DCMs represent a relatively new area of research but several recent examples exist in the literature (Kaya & Leite, 2017; Li et al, 2016; Madison & Bradshaw, 2018; Pan et al, 2020; Wang et al, 2018; Zhan et al, 2019). Several of these studies have included sample size as a manipulated factor.…”

A Longitudinal Diagnostic Model with Hierarchical Learning Trajectories

“…To provide theoretical support for the concept of a longitudinal learning diagnosis, several longitudinal learning diagnosis models (LDMs) have been proposed in recent years (for a review, see Pan, Qin, & Kingston, 2020; Zhan, 2020b). Existing longitudinal LDMs can be divided into two main types: latent transition analysis‐based models (e.g., Kaya & Leite, 2017; Li, Cohen, Bottge, & Templin, 2016; Madison & Bradshaw, 2018; Wang, Yang, Culpepper, & Douglas, 2018; Wen, Liu, & Zhao, 2020; Zhang & Wang, 2019) and higher‐order latent structure‐based models (e.g., Lee, 2017; Lin, Xing, & Park, 2020; Huang, 2017; Pan et al., 2020; Zhan, 2020c; Zhan, Jiao, Liao et al., 2019). The former estimates the transition probabilities from one latent attribute (profile) to another or the same latent attribute (profile).…”

Variational Bayes Inference for Hidden Markov Diagnostic Classification Models

“…For example, Huang (2017) proposed a multilevel generalized deterministic input noisy and-gate model (G-DINA; de la Torre, 2011) that captures changes in discrete latent attributes via a multilevel structure where the discrete attributes are assumed to come from a common continuous latent trait. Pan et al (2020) extended Huang (2017) and employed a multivariate normal distribution for the higher order traits and assessed proficiency changes under the log-linear cognitive diagnostic model (LCDM; Henson et al, 2009). Zhan, Jiao, Liao, et al (2019) employed a similar strategy in the development of a higher-order longitudinal variant of the DINA model (Junker & Sijtsma, 2001;Macready & Dayton, 1977;Maris, 1999), and Zhan, Jiao, Man, et al (2019) demonstrated how to estimate the longitudinal DINA model under a Bayesian setting.…”