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The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments

Published online by Cambridge University Press:  01 January 2025

Robert Jennrich  and
Albert Satorra
Robert Jennrich*
Affiliation:
University Of California Los Angeles
Albert Satorra
Affiliation:
Universitat Pompeu Fabra
*
Correspondence should be made to Robert Jennrich, 3400 Purdue Ave., Los Angeles, CA 90066, USA. Email: [email protected]
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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.

Keywords

Kronecker productsAsymptotically normalInfluence functionsPseudo-valuesGoodness of fitAcceleration
Type
Original paper
Information
Psychometrika , Volume 81 , Issue 1 , March 2016 , pp. 90 - 101
Copyright
Copyright © 2014 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:https://doi.org/10.1007/s11336-014-9426-9) contains supplementary material, which is available to authorized users.

References

Bentler, P. M. (2012). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.Google Scholar
Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83.CrossRefGoogle Scholar
Cragg, J. G. (1997). Using higher order moments to estimate the simple errors-in-variables model. The Rand Journal of Economics, S71–S91. Special Issue in honor of Richard E. Quandt.CrossRefGoogle Scholar
Cramer, H. (1946). Mathematical methods of statistics. Princeton, NJ: Princeton University Press.Google Scholar
Efron, B., & Tibshirani, R.J. (1993). An Introduction to the Bootstrap. New York, NY: Chapman & Hall.CrossRefGoogle Scholar
Hausman, J.A., Newey, W.K., Ichimura, H., & Powell, J.L. (1991). Identification and estimation of polynomial errors-in-variables models. Journal of Econometrics, 50, 273–295.CrossRefGoogle Scholar
Jaeckel, L. (1972). The infinitesimal jackknife, Memorandum #MM 72–1215-11. Murray Hill, NJ: Bell Laboratories.Google Scholar
Jennrich, R. I. (2008). Nonparametric estimation of standard errors in covariance structure analysis. Psychometrika, 73, 579–594.CrossRefGoogle Scholar
Jennrich, R.I., & Satorra, A. (2013). Continuous orthogonal complement functions and distribution-free tests in moment structure analysis. Psychometrika, 78, 545–552.CrossRefGoogle ScholarPubMed
Mooijaart, A. (1985). Factor analysis of non-normal variables. Psychometrika, 50, 323–342.CrossRefGoogle Scholar
Mooijaart, A., & Bentler, P.M. (2010). An alternative approach for non-linear latent variable models. Structural Equation Modeling, 17, 357–373.CrossRefGoogle Scholar
Neyman, J. (1937). Remarks on a paper by E. C. Rhodes. Journal of the Royal Statistical Society, 100, 50–57.Google Scholar
Ozaki, K., Toyoda, H., Iwama, N., Kubo, S., & Ando, J. (2011). Using non-normal SEM to resolve the ACDE model in the classical twin design. Behavioral Genetics, 41, 329–339.CrossRefGoogle ScholarPubMed
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