結構方程模型被廣泛使用於社會、行為科學研究中，常見的運用方式包含檢驗單一模型與根據特定的假設比較巢套模型。巢套模型的運用包含如檢驗模型參數是否等於某一特殊值、不同組別的調節效果相同與否及驗證性因素分析的因素數目等。在比較巢套模型之前，研究者須注意資料是否符合一些假設，如多元常態、大樣本與近乎正確的基模型，但是在實徵研究中，資料不一定總是能符合這些假設，當假設被違反時，型一錯誤率可能會膨脹且統計檢定力可能會下降，統計結果可能進而誤導研究者下決策。為解決這些問題，學者們提出了一些方法如Satorra-Bentler量尺化檢定和Bollen-Stine拔靴法，過去研究也證實這些方法在處理單一模型檢定時的實用性，但於比較巢套模型是否依舊可用則鮮少被評估，因此我們將觀察上述這些方法在比較巢套模型時的表現與假設被違反時的強韌性。研究以蒙地卡羅方式進行，操弄之獨變項為假設 (路徑係數、因素負載量)、檢定統計量 (最大概似法、Satorra-Bentler量尺化檢定和Bollen-Stine拔靴法)、基模型的適配程度、分配與樣本數。結果則看到當假設被違反時，最大概似法由於型一錯誤率不合理的膨脹而變得不適用，Bollen-Stine拔靴法則能將型一錯誤率維持在.05，除非假設被違反的太過嚴重，如基模型RMSEA大於.08、分配呈現重度非常態的情境。當基模型不適配，則三種方法均會使得型一錯誤率膨脹而不適用。總括來說，比較巢套模型時，三種統計量中Satorra-Bentler量尺化檢定於假設被違反時的表現最好，但實際運用時，研究者需注意其較低的統計檢定力。

In social and behavioral sciences, structural equation model remains a popular analytic method. Researchers commonly use SEM analysis for testing a model and comparing nested models, the latter being widely used in testing whether specific paths equal specific values, testing moderation across groups, and testing factor numbers in confirmatory factor analysis by the likelihood ratio test or named chi-square difference test. Researchers should note the existence of several assumptions for comparing nested models, including multivariate normality, a large sample size, and an approximately correctly specified base model. However, the assumptions are not always met in empirical research. If the assumptions are violated, the test statistic of the normal theory maximum likelihood method will be biased, Type I error will be inflated and the statistical decision process might be misled. We propose the previously evaluated the Satorra-Bentler scaled test and Bollen-Stine bootstrapping to deal with the violation of the assumptions of normality and large sample size, adding to the literature by using them to test nested models. To understand the performance of ML estimation, the Satorra-Bentler scaled test and Bollen-Stine bootstrapping in comparing nested models under the violation of assumptions, we conduct a Monte Carlo study and manipulate several independent variables, including different hypotheses (e.g., path coefficient and factor loading), test statistics, base model imperfection, distributions, and sample sizes. Our results show that when assumptions are not met, ML estimation inflates Type I error to unacceptable levels. Bollen-Stine bootstrapping holds the Type I error well until the fit of the base model becomes poor (at RMSEA=.08 or above) and the distribution become severely nonnormal. When the fit of a base model is inadequate, all of methods lead to an inflated Type I error rate, making them unsuitable for analysis. According to this study, we conclude that the Satorra-Bentler scaled test performs best for nested-model analysis, but that researchers should be wary of its attenuated power.

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