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The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments

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  • Robert Jennrich
  • Albert Satorra

Abstract

Mean corrected higher order sample moments are asymptotically normally distributed. It is shown that both in the literature and popular software the estimates of their asymptotic covariance matrices are incorrect. An introduction to the infinitesimal jackknife is given and it is shown how to use it to correctly estimate the asymptotic covariance matrices of higher order sample moments. Another advantage in using the infinitesimal jackknife is the ease with which it may be used when stacking or sub-setting estimators. The estimates given are used to test the goodness of fit of a non-linear factor analysis model. A computationally accelerated form for infinitesimal jackknife estimates is given. Copyright The Psychometric Society 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:1:p:90-101
    DOI: 10.1007/s11336-014-9426-9
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    References listed on IDEAS

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    1. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
    2. 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.
    3. 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.
    4. Ab Mooijaart, 1985. "Factor analysis for non-normal variables," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 323-342, September.
    5. Robert Jennrich, 2008. "Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 579-594, December.
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