Correlations Among Maximum Likelihood and Weighted/Unweighted Least Squares Estimators in Factor Analysis

The asymptotic correlations among maximum likelihood (ML) and various least squares (LS) estimators in factor analysis are derived. The LS estimators include the unweighted (ULS) and weighted estimators for unstandardized variables and the ULS estimators for standardized variables. The derived formulas cover the cases with restrictions on parameters. Numerical examples with simulations are provided to confirm the accuracy of the formulas and the influence of scales on the asymptotic correlations.