Determining the number of attributes in the GDINA model.

Exploratory cognitive diagnosis models have been widely used in psychology, education and other fields. This paper focuses on determining the number of attributes in a widely used cognitive diagnosis model, the GDINA model. Under some conditions of cognitive diagnosis models, we prove that there exists a special structure for the covariance matrix of observed data. Due to the special structure of the covariance matrix, an estimator based on eigen-decomposition is proposed for the number of attributes for the GDINA model. The performance of the proposed estimator is verified by simulation studies. Finally, the proposed estimator is applied to two real data sets Examination for the Certificate of Proficiency in English (ECPE) and Big Five Personality (BFP).