A re-formulation of the DINA model and a direct derivation of estimation algorithms

• Yamaguchi Kazuhiro

  Hosei University The Japan Society for the Promotion of Science

Bibliographic Information

Other Title

• DINA モデルの再定式化と推定アルゴリズムの直接的導出

Abstract

In this study, we focused on the deterministic input noisy and-gate (DINA) model, which is one of the most fundamental diagnostic classification models, and re-formulated the model to easily derive parameter estimation algorithms. The formulation of this study was characterized by a latent indicator variable to represent individual attribute mastery patterns, which is another form of latent class. The expectation-maximization (EM) algorithm for maximum likelihood (ML) and maximum a posteriori estimation, as well as the Gibbs sampling algorithm, were easily derived because of the re-formulation. In addition, a numerical method to obtain standard errors of maximum likelihood estimation was introduced. A simulation study showed that the re-derived EM algorithm could recover true values, and the standard error estimation method provided appropriate values. The estimation method derived in this study indicated the same estimated values as a previous study method that used real data.

Journal

• Japanese Journal for Research on Testing

  Japanese Journal for Research on Testing 15 (1), 21-44, 2019

  The Japan Association for Research on Testing

Keywords

• diagnostic classification model, cognitive diagnostic model, DINA model, EM algorithm, standard error

Details

• CRID: 1390001288156730240
• NII Article ID: 130007691333
• DOI: 10.24690/jart.15.1_21
• ISSN: 24337447
• ISSN: 18809618
• Text Lang: ja
• Data Source:
  • JaLC
  • CiNii Articles
  • KAKEN
  • Crossref
• Abstract License Flag: Disallowed