Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses
By Ke-Hai Yuan, K. Hayashi, Peter M. Bentler. 2007
48 citations recorded by the source corpus.
The normal distribution based likelihood ratio (LR) statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and covariance matrix as well as the model and sample size are always fixed. It is hard to justify the validity of the noncentral chi-square distribution for the resulting LR statistic even when data are normally distributed and sample size is large. By extending results in the literature, this paper develops normal distributions to describe the behavior of the LR statistic for mean and covariance structure analysis. A sequence of local alternative hypotheses is not necessary for the proposed distributions to be asymptotically valid. When the effect size is medium and above or when the model is not trivially misspecified, empirical results indicate that a refined normal distribution describes the behavior of the LR statistic better than the commonly used noncentral chi-square distribution, as measured by the Kolmogorov-Smirnov distance. Quantile-quantile plots are also provided to better understand the different distributions.
Subfields: Computer Networks and Communications, Food Science, Management, Monitoring, Policy and Law
View Paper: https://www.semanticscholar.org/paper/b229971a07ab681c21e8a32269e6fd6c138ebd2b
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Citations in the corpus
- The Model Size Effect in SEM: Inflated Goodness-of-Fit Statistics Are Due to the Size of the Covariance Matrix (2012, unknown): “Herzog et al, 2007 ; Yuan, Hayashi, & Bentler, 2007 ).”
- Bootstrapping Confidence Intervals for Fit Indexes in Structural Equation Modeling (2016, methodology): “Because this analytic CI relies on the noncentral chi-square distribution approximation and on the accurate estimation of the noncentrality parameter, the CI might not work as well for severely misspecified models and in small samples (Chun & Shapiro, 2009; Ogasawara, 2005; Yuan, 2008; Yuan et al., ”