L. L. Thurstone Psychometric Laboratory in the Department of Psychology and Neuroscience, University of North Carolina at Chapel Hill, Chapel Hill, USA.
Psychometrika. 2021 Mar;86(1):1-29. doi: 10.1007/s11336-021-09748-3. Epub 2021 Feb 2.
Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called an importance-weighted autoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.
边缘最大似然 (MML) 估计是心理计量学中拟合项目反应理论模型的首选方法，因为 MML 估计器在样本量趋于无穷大时具有一致性、正态性和效率。然而，当样本量和潜在因素数量非常大时，最先进的 MML 估计程序，如 Metropolis-Hastings Robbins-Monro (MH-RM) 算法以及近似 MML 估计程序，如变分推断 (VI)，计算时间都非常长。在这项工作中，我们研究了一种基于深度学习的 VI 算法，用于探索性项目因素分析 (IFA)，即使在具有许多潜在因素的大数据集中，该算法的计算速度也非常快。所提出的方法应用了一种称为重要性加权自动编码器 (IWAE) 的深度人工神经网络模型，用于探索性 IFA。IWAE 使用重要性抽样技术来近似 MML 估计器，其中在拟合过程中增加抽取的重要性加权 (IW) 样本数量可以提高逼近度，但通常会降低计算效率。我们提供了一个真实数据应用程序，该应用程序在随机起始时恢复了与心理理论一致的结果。通过模拟研究，我们表明，随着样本量或 IW 样本数量的增加，IWAE 会产生更准确的估计值（尽管因子相关和截距估计值存在一些偏差），并且在更短的时间内获得与 MH-RM 相似的结果。我们的模拟还表明，该方法的性能与约束联合最大似然估计相似，并且在样本量和项目数量同时趋于无穷大时，该方法具有一致性，并且可能更快。
