The full information maximum likelihood (FIML) and the two-stage (TS) procedure are two popular likelihood-based approaches to SEM model estimation with missing data. After model estimation, one often needs to choose the best model from a group of candidate models. A popular type of model selection tools is information criteria. Because FIML and TS both give consistent model parameter estimates, it is tempting to assume both FIML-based and TS-based information criteria are appropriate and useful. However, in this paper we show FIML and TS do not both give appropriate information criteria, and model selection results may be different from those under complete data, even in large samples. We first analytically study the implications of missing (completely) at random data for information criteria. Next, we conduct simulations to verify our theoretical proof and understand the empirical performance of information criteria. Our conclusions apply to AIC, BIC, and their variants.

完整信息最大似然（FIML）和两阶段（TS）程序是缺少数据的SEM模型估计的两种流行的基于似然性的方法。在模型估计之后，通常需要从一组候选模型中选择最佳模型。信息选择是一种流行的模型选择工具。由于FIML和TS都提供一致的模型参数估计，因此很容易假设基于FIML和基于TS的信息标准都是适当且有用的。但是，在本文中，我们显示FIML和TS都没有给出适当的信息标准，并且即使在大样本中，模型选择结果也可能与完整数据下的模型选择结果有所不同。我们首先分析研究随机数据缺失（完全）对于信息准则的影响。下一个，我们进行模拟以验证我们的理论证明并了解信息标准的经验表现。我们的结论适用于AIC，BIC及其变体。