Sensitivity analysis of structural equation model with non-normal observed variables

Abstract

Structural equation modeling (SEM) relies on normal theory methods – such as maximum likelihood method (ML) and generalized least squares (GLS) when estimating model and testing model goodness of fit. This limits its applicability since most of the observed variables in social sciences are almost never normally distributed. In this paper, we relax this restriction and conduct a simulation experiment with the simplest observed variable SEM model to see the extent and nature of effects of nonnormality on SEM. We incorporate that the distribution of error of the model belongs to g -and- k family of distributions.

Keywords and phrases:

• Structural equation modeling
• implied covariance matrix
• non-normality
• generalized least square method