A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models

Chen Wei Liu*, Björn Andersson, Anders Skrondal

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)

摘要

In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy “And” gate model using a constrained Metropolis–Hastings Robbins–Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka’s fraction–subtraction data and Certificate of Proficiency in English data.

原文英語
頁(從 - 到)322-357
頁數36
期刊Psychometrika
85
發行號2
DOIs
出版狀態已發佈 - 2020 六月 1

ASJC Scopus subject areas

  • 心理學(全部)
  • 應用數學

指紋

深入研究「A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models」主題。共同形成了獨特的指紋。

引用此