Comparison of performance of GLS and WLS method in structural equation modeling

ObjectiveTo compare the difference in the performance of generalized least squares(GLS) and weighted least squares(WLS)in structural equation modeling(SEM)for the data with different characteristics.MethodsWe set a true model and a misspecified model including 12 exogenous manifest variables,3 exogenous latent variables,8 endogenous manifest variables,and 2 endogenous latent variables.Using Interactive Matrix Language(IML)module of SAS 9.1 software,we got a simulation of multi-feature data and using Covariance Analysis of Linear Structural Equations(CALIS) procedure we tested the model fit.Then we compared the performance of GLS and WLS methods using the frequency of the two types of error as the indicator.ResultsWhether the distribution of data is multivariate normal,slightly skewed or severely skewed,the relative frequency of the two types of errors shows a downward trend with the increase of the correlation coefficient and the sample size of GLS and WLS when matrix and covariance matrix are used in the analyses.The type I error of GLS method is somewhat great while the type II error is very small;when the sample size reaches 200(10 times of significant variable)the type II error is less than 0.05 and when the sample size reaches 1 000(50 times of significant variable)the typeⅠerror is less than 0.05 for the data with multivariate normal,slightly skewed or severely skewed distribution.The type II error of WLS is nearly 0 and the type I error is somewhat great;the frequency of type I error of the correlation matrix is lower than that of covariance matrix for the data with same characteristics.ConclusionGLS is more stable than WLS for parameter estimation in SEM analysis.