Comparison of GLS and WLS method based on measurement model of structural equation modeling

Objective To investigate the difference in parameter estimation of various datasets between the performances of generalized least squares(GLS) and weighted least squares(WLS)in structural equation modeling(SEM).Methods We set the correlation coefficients between variables and established a true model and misspecified model,which contained 15 variables and 3 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 GLS and WLS methods using the frequency of the two types of error as the indicator.Results Whether the distribution of data is normal,exponential or binomial,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.For the data with same characteristics,the sum relative frequency of the two types of errors of GLS is smaller than that of WLS for the analyses with either correlation or covariance matrix.If r=0.3 and n≥750(50 times of significant variable)or r≥0.5 and n≥300(20 times of significant variable),the relative frequency of the two types of error of GLS is less than 0.05 for the data with normal,exponential or binomial distribution.The results of WLS analyses with covariance matrix are more stable than those with correlation matrix and as long as n≥750 the relative frequency of the two types of error is less than 0.05 whatever correlation coefficient is for the analysis with covariance matrix.Conclusion The parameter estimation with both GLS and WLS method is unbiased and asymptotically efficient and the estimation result will be influenced by different data conditions and matrix,indicating the two methods should be selected correctly according to characteristics of the data in the analysis.