Extending exploratory diagnostic classification models: Inferring the effect of covariates

Area of Science:

• Educational Measurement and Statistics
• Cognitive Science
• Bayesian Modeling

Background:

• Diagnostic models are crucial for formative assessments, classifying student knowledge via attributes.
• Student learning context and background knowledge significantly influence skill mastery.
• Current methods primarily incorporate covariates into confirmatory diagnostic models (restricted latent class models).

Purpose of the Study:

• To develop novel methods for integrating student covariates into exploratory restricted latent class models (RLCMs).
• To jointly infer latent structure and assess covariate effects on performance and skill mastery.
• To provide a flexible framework for analyzing the impact of background knowledge on attribute mastery.

Main Methods:

• A novel Bayesian formulation for exploratory RLCMs with covariates.
• Implementation of a Markov chain Monte Carlo (MCMC) algorithm using Metropolis-within-Gibbs for posterior distribution approximation.
• Monte Carlo simulations to evaluate the accuracy and performance of the proposed methods.

Main Results:

• The proposed methods accurately estimate model parameters and covariate effects.
• The application demonstrates the utility of the methods in examining student background knowledge in probability.
• The study validates the effectiveness of incorporating covariates in exploratory diagnostic models.

Conclusions:

• The developed Bayesian approach offers a robust framework for including covariates in exploratory RLCMs.
• These methods enhance the understanding of how student background influences skill acquisition.
• The findings support the use of advanced diagnostic models for personalized education and intervention evaluation.