London School of Economics and Political Science, London, UK.
University of Minnesota, Minneapolis, USA.
Psychometrika. 2019 Mar;84(1):124-146. doi: 10.1007/s11336-018-9646-5. Epub 2018 Nov 19.
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).
联合极大似然（JML）估计是拟合项目反应理论（IRT）模型的最早方法之一。该方法将项目和个体参数都视为未知但固定的模型参数，并通过求解优化问题同时对其进行估计。然而，当样本量趋于无穷大且项目数保持固定时，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，该估计量不如边际极大似然（MML）估计量受欢迎。在本文中，我们从统计和计算两个角度重新研究了高维探索性项目因子分析中的 JML 估计量。具体来说，我们在渐近设置下为受约束的 JML 估计量建立了一种统计一致性的概念，其中项目和人数都趋于无穷大，并且可能存在许多缺失的响应。我们提出了一种用于该估计量的并行计算算法，它可以扩展到非常大的数据集。通过仿真研究，我们表明当维度较高时，所提出的估计量与 MML 估计量的结果相似甚至更好，但在计算上效率更高。基于修订版艾森克人格问卷（EPQ-R）提供了一个实际数据示例。
