Asymptotic robustness of the asymptotic biases in structural equation modeling

The asymptotic robustness of the normal theory asymptotic biases of the least-squares estimators of the parameters in covariance structures against the violation of normality is shown, which is obtained under the conditions required for the asymptotic robustness for the normal theory standard errors and the usual chi-square statistic. The asymptotic robustness holds not only for the estimators of the parameters whose normal theory asymptotic standard errors are asymptotically robust, but also for the non-robust ones. The Wishart maximum likelihood estimators are also shown to have the asymptotic robustness. A numerical illustration for the factor analysis model shows that the empirical biases of robust estimators under non-normality are close to their corresponding normal theory asymptotic biases.