Asymptotic biases of least squares estimators in factor analysis and structural equation modeling under nonnormality and normality
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Formulas of the asymptotic biases of the weighted/unweighted least squares estimators of the parameters in exploratory factor analysis and structural equation modeling are derived with and without the assumption of multivariate normality for observed variables. The weighted least squares estimators include those for unstandardized variables by generalized least squares, simple or scale-free least squares, and least squares with powered diagonals. In addition, a formula for the asymptotic biases of the parameter estimators in correlation structures by unweighted least squares is given. Numerical examples with simulations show large absolute values of the biases by generalized least squares, and relatively small biases by other least square estimators and maximum likelihood.
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