The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling Under Conditions of Misspecification and Nonnormality

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Abstract
This simulation study demonstrates how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Using a fully crossed design, data were generated for 11 conditions of peakedness, 3 conditions of misspecification, and 5 different sample sizes. Three estimation methods (maximum likelihood [ML], generalized least squares [GLS], and weighted least squares [WLS]) were compared in terms of overall fit and the discrepancy between estimated parameter values and the true parameter values used to generate the data. Consistent with earlier findings, the results show that ML compared to GLS under conditions of misspecification provides more realistic indexes of overall fit and less biased parameter values for paths that overlap with the true model. However, despite recommendations found in the literature that WLS should be used when data are not normally distributed, we find that WLS under no conditions was preferable to the 2 other estimation procedures in terms of parameter bias and fit. In fact, only for large sample sizes (N = 1,000 and 2,000) and mildly misspecified models did WLS provide estimates and fit indexes close to the ones obtained for ML and GLS. For wrongly specified models WLS tended to give unreliable estimates and over-optimistic values of fit.