Asymptotic standard errors of estimated standard errors in structural equation modelling.

Asymptotic standard errors of the estimated asymptotic standard errors for parameter estimates in structural equation modelling are derived using the delta method with the assumption of multivariate normality for observed variables. The derivation covers the cases with and without restrictions on parameters. The result can be used to derive the asymptotic standard error of the z score (a parameter estimate divided by its estimated standard error), which is frequently substantially different from one. The case of standardized observed variables is dealt with as a typical example with restrictions on parameters. For actual covariance (correlation) structure models, the exploratory factor analysis model with factor rotation and the confirmatory factor analysis model are presented with numerical examples. Simulations are performed to assess the accuracy of our method for normally and non-normally distributed variables.