Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis
Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis
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DOI：
10.1007/s11336-018-9646-5
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发表时间：
2019-03-01
期刊：
影响因子：
3
通讯作者：
Zhang, Siliang
中科院分区：
文献类型：
--
作者：
Chen, Yunxiao;Li, Xiaoou;Zhang, Siliang
联合最大似然 (JML) 估计是拟合项目反应理论 (IRT) 模型的最早方法之一。此过程将项目参数和人员参数视为未知但固定的模型参数，并通过解决优化问题来同时估计它们。然而，当样本量趋于无穷大且项目数量保持固定时，JML 估计量对于许多 IRT 模型来说是渐近不一致的。因此，在心理测量学文献中，该估计量不如边际最大似然 (MML) 估计量更受欢迎。在本文中，我们从统计和计算的角度重新研究了用于高维探索性项目因子分析的 JML 估计器。特别是，我们在项目和人员数量都增长到无穷大且许多响应可能丢失的渐近设置下，为受限 JML 估计器建立了统计一致性的概念。为此估计器提出了一种并行计算算法，可以扩展到非常大的数据集。通过模拟研究，我们表明，当维数较高时，所提出的估计器会产生与 MML 估计器相似甚至更好的结果，但可以更有效地计算获得。基于艾森克人格问卷（EPQ-R）的修订版，提供了一个说明性的真实数据示例。
Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck's Personality Questionnaire (EPQ-R).