title: Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections.
abstract: This simulation study investigates the performance of three test statistics, T1, T2, and T3, used to evaluate structural equation model fit under non normal data conditions. T1 is the well-known mean-adjusted statistic of Satorra and Bentler. T2 is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T3 is a recently proposed version of T2 that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T1 and under-rejected by T2 and T3, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T2 and T3. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.
authors.affiliation: a BI Norwegian Business School.
authors.forename: Njål
authors.initials: N
authors.lastname: Foldnes
authors.affiliation: a BI Norwegian Business School.
authors.forename: Ulf Henning
authors.initials: UH
authors.lastname: Olsson
mesh_terms: D035841:Behavioral Research / Q000379:methods*; D016009:Chi-Square Distribution; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D015203:Reproducibility of Results
keywords: Satorra-Bentler statistics; asymptotic robustness; kurtosis; mean and variance adjusted statistics