The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model
arXiv:1711.03174 · doi:10.1007/s11336-018-9619-8
Abstract
Cognitive Diagnosis Models (CDMs) are useful statistical tools in cognitive diagnosis assessment. However, as many other latent variable models, the CDMs often suffer from the non-identifiability issue. This work gives the sufficient and necessary condition for the identifiability of the basic DINA model, which not only addresses the open problem in Xu and Zhang (2016, Psychomatrika, 81:625-649) on the minimal requirement for the identifiability, but also sheds light on the study of more general CDMs, which often cover the DINA as a submodel. Moreover, we show the identifiability condition ensures the consistent estimation of the model parameters. From a practical perspective, the identifiability condition only depends on the Q-matrix structure and is easy to verify, which would provide a guideline for designing statistically valid and estimable cognitive diagnosis tests.
References in corpus (2)
Cited by in corpus (13)
- On the Identifiability of Diagnostic Classification Models
- Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models
- Partial Identifiability of Restricted Latent Class Models
- Sufficient and Necessary Conditions for the Identifiability of the -matrix
- Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Models
- Scalable Bayesian Approach for the DINA Q-matrix Estimation Combining Stochastic Optimization and Variational Inference
- Partial-Mastery Cognitive Diagnosis Models
- Identifiability of Hierarchical Latent Attribute Models
- Identifiability of Latent Class Models with Covariates
- A Joint MLE Approach to Large-Scale Structured Latent Attribute Analysis
- Identifiability and consistency of network inference using the hub model and variants
- Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses
- Identifiability of Bifactor Models