A cognitive diagnosis model for latent classification of bounded continuous variables.

Area of Science:

• Psychometrics
• Statistical Modeling
• Social Sciences

Background:

• Cognitive Diagnosis Models (CDMs) are established for classifying latent attributes using dichotomous, polytomous, or continuous responses.
• Existing CDMs have limitations when applied to bounded continuous variables common in social sciences.

Purpose of the Study:

• Introduce a novel Bounded DINA (B-DINA) model to extend CDMs for bounded continuous responses.
• Provide a Bayesian estimation framework for the B-DINA model.
• Demonstrate the model's utility in classifying complex datasets.

Main Methods:

• Developed the Bounded DINA (B-DINA) model utilizing a Beta distribution for bounded continuous data.
• Implemented a Bayesian estimation framework, addressing label-switching nonidentifiability.
• Assessed model fit using posterior predictive p-values (PPP) and conducted simulation studies for parameter recovery.

Main Results:

• The B-DINA model effectively classifies entities using bounded continuous indicators.
• The model reveals meaningful relationships between observed indicators and latent attributes.
• Simulation studies confirmed good parameter recovery and model performance.

Conclusions:

• The proposed Bounded DINA (B-DINA) model offers a robust tool for latent attribute classification with bounded continuous data.
• This approach has broad applicability across social sciences and policy analysis where such data are prevalent.