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Psychometrika

, Volume 80, Issue 1, pp 196–199 | Cite as

Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic

Article

Abstract

In a recent article Jennrich and Satorra (Psychometrika 78: 545–552, 2013) showed that a proof by Browne (British Journal of Mathematical and Statistical Psychology 37: 62–83, 1984) of the asymptotic distribution of a goodness of fit test statistic is incomplete because it fails to prove that the orthogonal component function employed is continuous. Jennrich and Satorra (Psychometrika 78: 545–552, 2013) showed how Browne’s proof can be completed satisfactorily but this required the development of an extensive and mathematically sophisticated framework for continuous orthogonal component functions. This short note provides a simple proof of the asymptotic distribution of Browne’s (British Journal of Mathematical and Statistical Psychology 37: 62–83, 1984) test statistic by using an equivalent form of the statistic that does not involve orthogonal component functions and consequently avoids all complicating issues associated with them.

Key words

covariance structures statistical test asymptotics 

References

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  2. Jennrich, R., & Satorra, A. (2013). Continuous orthogonal complement functions and distribution-free goodness of fit tests in moment structure analysis. Psychometrika, 78, 545–552. CrossRefPubMedGoogle Scholar
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Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  1. 1.Department of PsychologyThe Ohio State UniversityColumbusUSA
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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