Approximations to the distribution of a test statistic in covariance structure analysis: A comprehensive study
2018
In structural equation modelling (SEM), a robust adjustment to the test statistic or to its reference distribution is needed when its null distribution deviates from a χ2 distribution, which usually arises when data do not follow a multivariate normal distribution. Unfortunately, existing studies on this issue typically focus on only a few methods and neglect the majority of alternative methods in statistics. Existing simulation studies typically consider only non-normal distributions of data that either satisfy asymptotic robustness or lead to an asymptotic scaled χ2 distribution. In this work we conduct a comprehensive study that involves both typical methods in SEM and less well-known methods from the statistics literature. We also propose the use of several novel non-normal data distributions that are qualitatively different from the non-normal distributions widely used in existing studies. We found that several under-studied methods give the best performance under specific conditions, but the Satorra–Bentler method remains the most viable method for most situations.
Keywords:
- Statistics
- Mathematics
- Econometrics
- Noncentral chi-squared distribution
- Categorical distribution
- Hotelling's T-squared distribution
- Kolmogorov–Smirnov test
- Normal-gamma distribution
- Inverse-chi-squared distribution
- Asymptotic distribution
- Sampling distribution
- Beta-binomial distribution
- Test statistic
- Anderson–Darling test
- Correction
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