The small sample performance of estimators of the standard errors of structural equation models

Abstract

In this paper, we compare five asymptotically, under a correctly specified likelihood, equivalent estimators of the standard errors for parameters in structural equation models. The estimators are evaluated under different conditions regarding (i) sample size, varying between N=50 and 3200, (ii) distributional assumption of the latent variables and the disturbance terms, namely normal, and heavy tailed (t), and (iii) the complexity of the model. For the assessment of the five estimators we use overall performance, relative bias, MSE and coverage of confidence intervals. The analysis reveals substantial differences in the performance of the five asymptotically equal estimators. Most diversity was found for t distributed, i.e. heavy tailed, data.

Keywords:

• information matrix
• sandwich estimator Monte Carlo simulation
• estimators of standard errors
• small sample sizes
• structural equation modelling
• SEM

MSC Codes :

• 62F35
• 62H25

Acknowledgements

Comments from an anonymous referee is greatly acknowledged.

Notes

Some preliminary comparisons have been made using the same number of replicates without significantly changing the conclusions.