Consequences of violating assumptions on the estimation of statistics in structural equation models

The goal of this study was to review the studies that examined the effects of non-normality and varying levels of sample size on the resulting statistics in structural equation models. Thirteen studies fit the criteria for inclusion in this research. The resulting statistics used were (a) the parameter estimates of the model's measured variables, covariates, and error variables; and (b) the standard errors of the same. Bias estimates were gleaned for each of the resulting statistics. These estimates were matched with their corresponding levels of skew, kurtosis and sample size, and sorted by method of estimation. Four methods of estimation had enough data upon which to subject response surface methodology: maximum likelihood, generalized least squares, asymptotic distribution free, and elliptical reweighted least squares. Response surface methods were used to integrate the findings of these Monte Carlo studies and assess the accuracy of the hypothesized models for each of the methods of estimation. Results indicated that any of the four methods of estimation were neither inappropriate nor perfect in their optimization; they were generally biased, yet functional. Additionally, this study proposed a model of how varying sample size and non-normality statistics could influence the resulting statistics of SEMs. Across all four methods of estimation, four of the five parameter estimates and standard errors of the covariance estimates were found to be insensitive to the manipulation of sample size and non-normality. Sample size was influential for all of the parameter estimates and standard errors of the measured variables except for those derived from the Elliptical Reweighted Least Squares method of estimation. In the case of ERLS, the parameter estimates and the standard errors of the measured variables were insensitive to changes in sample size or levels of non-normality. Six of the seven results related to the parameter estimates and the standard errors of the error variables were found to be sensitive to the manipulations reviewed in this analysis; three results were sensitive to changes in sample size and three others were sensitive to changes in the levels of non-normality. The remaining standard error of the error variable was found to be insensitive to the manipulations reviewed in this analysis and was obtained through the Elliptical Reweighted Least Squares method of estimation.