高维诊断分类模型的高效Metropolis-Hastings-Robbins-Monro算法。

IF 1 4区 心理学 Q4 PSYCHOLOGY, MATHEMATICAL
Applied Psychological Measurement Pub Date : 2022-11-01 Epub Date: 2022-09-08 DOI:10.1177/01466216221123981
Chen-Wei Liu
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引用次数: 0

摘要

期望最大化(EM)算法是用于具有预先指定的Q矩阵的诊断分类模型(DCM)的参数估计的常用技术;然而,它在其期望步骤中需要O(2K)计算,这在属性数量K较大时显著减慢了计算。本研究提出了一种有效的Metropolis Hastings-Robbins-Monro(eMHRM)算法,在蒙特卡罗期望步骤中只需要O(K+1)次计算。此外,项目参数和结构参数通过Robbins-Monro算法进行近似,该算法不需要耗时的非线性优化过程。进行了一系列模拟研究,将eMHRM与EM和Metropolis Hastings(MH)算法在参数恢复和执行时间方面进行了比较。本文中的结果表明,eMHRM在计算上比EM和MH高效得多,并且当K较大时,它往往比EM产生更好的估计,这表明eMHRM是一种很有前途的高维DCM参数估计方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient Metropolis-Hastings Robbins-Monro Algorithm for High-Dimensional Diagnostic Classification Models.

The expectation-maximization (EM) algorithm is a commonly used technique for the parameter estimation of the diagnostic classification models (DCMs) with a prespecified Q-matrix; however, it requires O(2 K ) calculations in its expectation-step, which significantly slows down the computation when the number of attributes, K, is large. This study proposes an efficient Metropolis-Hastings Robbins-Monro (eMHRM) algorithm, needing only O(K + 1) calculations in the Monte Carlo expectation step. Furthermore, the item parameters and structural parameters are approximated via the Robbins-Monro algorithm, which does not require time-consuming nonlinear optimization procedures. A series of simulation studies were conducted to compare the eMHRM with the EM and a Metropolis-Hastings (MH) algorithm regarding the parameter recovery and execution time. The outcomes presented in this article reveal that the eMHRM is much more computationally efficient than the EM and MH, and it tends to produce better estimates than the EM when K is large, suggesting that the eMHRM is a promising parameter estimation method for high-dimensional DCMs.

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来源期刊
CiteScore
2.30
自引率
8.30%
发文量
50
期刊介绍: Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.
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