Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Evaluating structural equation model (SEM) fit is crucial.
• Non-normal data can compromise standard SEM fit statistics.
• Existing statistics (T1, T2, T3) have varying performance under non-normality.

Purpose of the Study:

• Investigate the performance of three SEM fit statistics (T1, T2, T3) under non-normal data conditions.
• Examine Type I and Type II errors for each statistic.
• Identify factors influencing statistic adequacy.

Main Methods:

• Simulation study comparing T1 (Satorra-Bentler mean-adjusted), T2 (Satterthwaite type mean-and-variance adjusted with df manipulation), and T3 (T2 without df manipulation).
• Data manipulated for varying levels of kurtosis.
• Analysis of Type I and Type II error rates and statistical power.

Main Results:

• All statistics are sensitive to kurtosis, affecting Type I error rates.
• T1 over-rejects true models under excess kurtosis; T2 and T3 under-reject.
• T2 and T3 show similar performance but lose power with increasing kurtosis under misspecification.
• Coefficient of variation of nonzero eigenvalues reliably indicates statistic adequacy.

Conclusions:

• Kurtosis significantly impacts SEM fit statistics performance.
• T2 and T3 offer similar performance, outperforming T1 in certain conditions.
• The coefficient of variation serves as a key diagnostic tool for assessing fit statistic reliability.