We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle constraints on loadings and factor correlations. For GOF assessment, we explore simulation-based tests and indices that extend the classifier two-sample test (C2ST), a method that tests whether a deep neural network can distinguish between observed data and synthetic data sampled from a fitted IFA model. Proposed extensions include a test of approximate fit wherein the user specifies what percentage of observed and synthetic data should be distinguishable as well as a relative fit index (RFI) that is similar in spirit to the RFIs used in structural equation modeling. Via simulation studies, we show that: (1) the confirmatory extension of Urban and Bauer's (2021) algorithm obtains comparable estimates to a state-of-the-art estimation procedure in less time; (2) C2ST-based GOF tests control the empirical type I error rate and detect when the latent dimensionality is misspecified; and (3) the sampling distribution of the C2ST-based RFI depends on the sample size.

翻译：针对包含大量被试、项目及潜在因子的大规模验证性项目因子分析(IFA)，本文探究了新型参数估计与拟合优度(GOF)评估方法。在参数估计方面，我们通过展示如何处理载荷与因子相关性的约束，将Urban与Bauer(2021)提出的探索性IFA深度学习算法扩展至验证性场景。在拟合优度评估方面，我们探索了基于模拟的检验方法与指标，将分类器双样本检验(C2ST)拓展至该领域——C2ST用于检验深度神经网络能否区分观测数据与由拟合IFA模型生成的合成数据。本文提出的拓展方法包括近似拟合检验（允许用户指定观测数据与合成数据中应可区分的百分比）以及相对拟合指数(RFI)——该指数在本质上与结构方程模型中使用的RFI相似。通过模拟研究，我们证实：(1) Urban与Bauer(2021)算法的验证性扩展方案在更短计算时间内可获得与前沿估计方法相当的估计结果；(2)基于C2ST的拟合优度检验能控制经验第一类错误率，并可检测潜在维度设定错误；(3)基于C2ST的RFI的抽样分布取决于样本量。