A note on computing Louis’ observed information matrix identity for IRT and cognitive diagnostic models

Chen Wei Liu*, Robert Philip Chalmers

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

Using Louis’ formula, it is possible to obtain the observed information matrix and the corresponding large-sample standard error estimates after the expectation–maximization (EM) algorithm has converged. However, Louis’ formula is commonly de-emphasized due to its relatively complex integration representation, particularly when studying latent variable models. This paper provides a holistic overview that demonstrates how Louis’ formula can be applied efficiently to item response theory (IRT) models and other popular latent variable models, such as cognitive diagnostic models (CDMs). After presenting the algebraic components required for Louis’ formula, two real data analyses, with accompanying numerical illustrations, are presented. Next, a Monte Carlo simulation is presented to compare the computational efficiency of Louis’ formula with previously existing methods. Results from these presentations suggest that Louis’ formula should be adopted as a standard method when computing the observed information matrix for IRT models and CDMs fitted with the EM algorithm due to its computational efficiency and flexibility.

原文英語
頁(從 - 到)118-138
頁數21
期刊British Journal of Mathematical and Statistical Psychology
74
發行號1
DOIs
出版狀態已發佈 - 2021 二月

ASJC Scopus subject areas

  • 統計與概率
  • 藝術與人文(雜項)
  • 心理學(全部)

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