The Noncentral Chi-square Distribution in Misspecified Structural Equation Models: Finite Sample Results from a Monte Carlo Simulation

Multivariate Behavioral Research
Patrick J CurranFeinian Chen

Abstract

The noncentral chi-square distribution plays a key role in structural equation modeling (SEM). The likelihood ratio test statistic that accompanies virtually all SEMs asymptotically follows a noncentral chi-square under certain assumptions relating to misspecification and multivariate distribution. Many scholars use the noncentral chi-square distribution in the construction of fit indices, such as Steiger and Lind's (1980) Root Mean Square Error of Approximation (RMSEA) or the family of baseline fit indices (e.g., RNI, CFI), and for the computation of statistical power for model hypothesis testing. Despite this wide use, surprisingly little is known about the extent to which the test statistic follows a noncentral chi-square in applied research. Our study examines several hypotheses about the suitability of the noncentral chi-square distribution for the usual SEM test statistic under conditions commonly encountered in practice. We designed Monte Carlo computer simulation experiments to empirically test these research hypotheses. Our experimental conditions included seven sample sizes ranging from 50 to 1000, and three distinct model types, each with five specifications ranging from a correct model to the severely misspecified u...Continue Reading

References

Apr 1, 1983·Multivariate Behavioral Research·R Cudeck, M W Browne

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Citations

May 11, 2010·Journal of Consumer Psychology : the Official Journal of the Society for Consumer Psychology·Peter M Bentler
Dec 2, 2014·Educational and Psychological Measurement·Georgios SideridisJack Fletcher
Jul 1, 2012·Multivariate Behavioral Research·Luigi Lombardi, Massimiliano Pastore
Jan 1, 2005·Multivariate Behavioral Research·Ke-Hai Yuan

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