Modern Robust Methods for Covariance in Structural Equation Modeling: ADF， SCALED， and Bootstrapping

ML和GLS是結構方程模式分析最常使用的參數估計法，兩種方法是基於常態分配假設來進行估計，然而，真實資料卻時常違反常態性假設。在此情形下，基於這二種估計法所求得的參數是否可靠，值得商榷。本研究旨在比較不同非常態情形下，這二種方法與四種不受常態性假設影響的強韌統計方法第一類錯誤率控制情形。結果發現：ML與GLS在所有非常態模擬資料，即使樣本數高達5，000，二者的第一類錯誤率超過35%。而ADF容易受小樣本影響產生過高的第一類錯誤率。SCALED， bootstrap- o M 和bootstrap-A M 較不易受樣本數影響，且可降低非常態所造成的問題。最後，提出未來研究與實務的建議。

Although the maximum likelihood estimator based on normality theory is default in most available programs in structural equation modeling， the majority of data investigated in behavioral and social sciences violate the assumption of multivariate normality. This study evaluated six covariance structure analysis techniques under various conditions of nonnormality. Results clearly illustrated that the ML and GLS failed to provide a good control of Type I error rates in all conditions of nonnormality even with the sample size of 5000. The ADF was essentially unusable in small to intermediated sample sizes. The SCALED and two bootstrap methods provided promising advantages but they were confined by small sample sizes. Additionally， the minimum requirements of sample sizes and bootstrapped samples for bootstrapping procedures were identified. Finally， a few suggestions were provided in the hope of improving the current practice.