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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: rij@stat.ucla.edu
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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.

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