Bias Reduction of Estimated Standard Errors in Factor Analysis

Abstract

Formulas for the asymptotic biases of the estimators of the normal theory standard errors in factor analysis are given with and without the assumption of multivariate normality for observed variables. The biases are derived from the asymptotic variances of standard error estimators and the asymptotic biases of the estimated variances of parameter estimators. The latter biases are derived from the asymptotic vari-ances/covariances and asymptotic biases of the parameter estimators. The formulas cover the cases for unstandardized and standardized variables. Numerical examples using factor analysis models show the accuracy of the formulas. The biases of standard error estimators are theoretically and empirically shown to be of the same order as that of the differences between the asymptotic standard errors neglecting higher-order terms and those considering them.