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Normal versus Noncentral Chi-square Asymptotics of Misspecified Models

So Yeon Chun () and Alexander Shapiro ()

MPRA Paper from University Library of Munich, Germany

Abstract: The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equations modeling (SEM). Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main goal of this paper is to evaluate the validity of employing these distributions in practice. Monte Carlo simulation results indicate that the noncentral chi-square distribution describes behavior of the LR test statistic well under small, moderate and even severe misspecifications regardless of the sample size (as long as it is sufficiently large), while the normal distribution, with a bias correction, gives a slightly better approximation for extremely severe misspecifications. However, neither the noncentral chi-square distribution nor the theoretical normal distributions give a reasonable approximation of the LR test statistics under extremely severe misspecifications. Of course, extremely misspecified models are not of much practical interest.

Keywords: Model misspecification; covariance structure analysis; maximum likelihood; generalized least squares; discrepancy function; noncentral chi-square distribution; normal distribution; factor analysis (search for similar items in EconPapers)
JEL-codes: C52 C12 C15 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-09
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