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：我们研究了适用于包含大量受访者、项目和潜在因子的大规模验证性项目因子分析（IFA）的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和因子相关上的约束，将Urban与Bauer（2021）用于探索性IFA的深度学习算法扩展至验证性场景。在GOF评估方面，我们探索了基于模拟的检验方法与指数，这些方法扩展了分类器双样本检验（C2ST）——一种检验深度神经网络能否区分观测数据与从拟合IFA模型中采样的合成数据的统计方法。所提出的扩展包括近似拟合检验（其中用户指定可区分的观测数据与合成数据百分比）以及相对拟合指数（RFI），其思想与结构方程模型中使用的RFI类似。通过模拟研究，我们证明：（1）Urban与Bauer（2021）算法的验证性扩展能在更短时间内获得可与最先进估计程序相媲美的估计结果；（2）基于C2ST的GOF检验能控制经验第一类错误率并检测潜在维度是否误设；（3）基于C2ST的RFI抽样分布依赖于样本量。