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

Author

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  • Michael Browne
  • Alexander Shapiro

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Michael Browne & Alexander Shapiro, 2015. "Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 196-199, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:196-199
    DOI: 10.1007/s11336-013-9383-8
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    References listed on IDEAS

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    1. Robert Jennrich & Albert Satorra, 2013. "Erratum to: Continuous orthogonal complement functions and distribution-free goodness of fit tests in moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 553-553, July.
    2. Robert Jennrich & Albert Satorra, 2013. "Continuous Orthogonal Complement Functions and Distribution-Free Goodness of Fit Tests in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 545-552, July.
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    Cited by:

    1. Lifang Deng & Ke-Hai Yuan, 2016. "Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 802-829, September.
    2. So Yeon Chun & Michael W. Browne & Alexander Shapiro, 2018. "Modified Distribution-Free Goodness-of-Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 48-66, March.

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    2. Albert Satorra & Heinz Neudecker, 2015. "A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 938-948, December.
    3. Robert Jennrich & Albert Satorra, 2016. "The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 90-101, March.

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