Chun, So Yeon and Alexander, Shapiro (2009): Normal versus Noncentral Chisquare Asymptotics of Misspecified Models. Forthcoming in: multivariate behavioral research
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Abstract
The noncentral chisquare 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 chisquare 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 chisquare 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.
Item Type:  MPRA Paper 

Original Title:  Normal versus Noncentral Chisquare Asymptotics of Misspecified Models 
Language:  English 
Keywords:  Model misspecification; covariance structure analysis; maximum likelihood; generalized least squares; discrepancy function; noncentral chisquare distribution; normal distribution; factor analysis 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  17347 
Depositing User:  So Yeon Chun 
Date Deposited:  17. Sep 2009 23:45 
Last Modified:  12. Feb 2013 04:36 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/17347 
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Normal versus Noncentral Chisquare Asymptotics of Misspecified Models. (deposited 16. Sep 2009 18:58)
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