台大心理系

Deviation from normality is commonly observed in empirical data. Incovariance structure analysis (CSA), the structural equation modeling (SEM) based on the asymptotic distribution of covariances, the asymptotically distribution-free (ADF) estimation method proposed by Browne (1984) stands as a landmark contribution for dealing with nonnormal data. Yet ADF requires extremely large samples to yield reliable parameter estimates, associated standard errors, and model test statistics. In correlation structure analysis (RSA), the SEM based on the asymptotic distribution of correlations, Steiger and Hakstian (1982) proposed the two-stage ADF (TADF) estimation method in hope of improving the finite sample behavior of ADF test statistics. TADF first employs a simple estimation method to obtain an estimate of the asymptotic covariance matrix of sample moments (ACOV) based on model-reproduced moments. In the second stage, TADF implements ADF with this structured ACOV estimate.The TADF method has been found to outperform ADF and reweighted least squares with robust corrections (RLS-C) in RSA under restricted conditions (e.g., Bentler & Savalei, 2010; Mels, 2000). In this study, TADF was extended to CSA and the behavior of TADF with nonnormal data under finite samples was systematically investigated in both CSA and RSA. In addition to ADF, the performance of TADF was also compared to other recommended methods for dealing with nonnormal data in SEM. These methods included maximum likelihood with robust corrections (ML-C) and the newly developed distributionally weighted least squares (DLS) method in CSA and RLS-C in RSA. Preliminary results showed that TADF effectively improves the finite sample behavior of ADF in both CSA and RSA in terms of the estimates of parameters and standard errors and the empirical Type I error rates of test statistics. In comparison to other methods, TADF statistics performed better than ML-C and DLS statistics in most conditions, and outperformed RLS-C in nearly all nonnormal cases. Yet TADF tended to underestimate the empirical fluctuation of the parameter estimates when sample sizes was small in both CSA and RSA. The present findings suggest that TADF offers an alternative for handling nonnormal variables with finite sample sizes frequently encountered in SEM applications. The Yuan-Bentler (1997) corrections for standard error estimates could possibly be applied to enhance the overall performance of TADF method. More research is needed. (371)