Department of Psychology, National Cheng Kung University, No.1, University Road, Tainan City, 701 , Taiwan.
Psychometrika. 2017 Jun;82(2):407-426. doi: 10.1007/s11336-017-9572-y. Epub 2017 Apr 26.
Model selection is a popular strategy in structural equation modeling (SEM). To select an "optimal" model, many selection criteria have been proposed. In this study, we derive the asymptotics of several popular selection procedures in SEM, including AIC, BIC, the RMSEA, and a two-stage rule for the RMSEA (RMSEA-2S). All of the results are derived under weak distributional assumptions and can be applied to a wide class of discrepancy functions. The results show that both AIC and BIC asymptotically select a model with the smallest population minimum discrepancy function (MDF) value regardless of nested or non-nested selection, but only BIC could consistently choose the most parsimonious one under nested model selection. When there are many non-nested models attaining the smallest MDF value, the consistency of BIC for the most parsimonious one fails. On the other hand, the RMSEA asymptotically selects a model that attains the smallest population RMSEA value, and the RESEA-2S chooses the most parsimonious model from all models with the population RMSEA smaller than the pre-specified cutoff. The empirical behavior of the considered criteria is also illustrated via four numerical examples.
模型选择是结构方程建模 (SEM) 中的一种常用策略。为了选择“最优”模型，已经提出了许多选择标准。在本研究中，我们推导出了 SEM 中几种流行选择程序的渐近性质，包括 AIC、BIC、RMSEA 和 RMSEA-2S 的两阶段规则。所有结果都是在弱分布假设下得出的，可以应用于广泛的差异函数类。结果表明，AIC 和 BIC 无论嵌套与否选择，都渐近地选择具有最小总体最小差异函数 (MDF) 值的模型，但只有 BIC 在嵌套模型选择下才能始终选择最简约的模型。当有许多非嵌套模型达到最小 MDF 值时，BIC 对最简约模型的一致性就会失效。另一方面，RMSEA 渐近地选择达到最小总体 RMSEA 值的模型，而 RESEA-2S 则从所有具有小于预定义截止值的总体 RMSEA 的模型中选择最简约的模型。通过四个数值示例说明了所考虑标准的经验行为。
