, Volume 81, Issue 1, pp 90–101 | Cite as

The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments

  • Robert Jennrich
  • Albert Satorra


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.


Kronecker products Asymptotically normal Influence functions Pseudo-values Goodness of fit Acceleration 



The authors would like to thank the review team and in particular reviewer 2 who motivated the inclusion of the offline material. The research of the second author is supported by Grant EC02011-28875 from the Spanish Ministry of Science and Innovation.

Supplementary material

11336_2014_9426_MOESM1_ESM.pdf (62 kb)
Supplementary material 1 (pdf 61 KB)


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Copyright information

© The Psychometric Society 2014

Authors and Affiliations

  1. 1.University Of California Los AngelesLos AngelesUSA
  2. 2.Universitat Pompeu FabraBarcelonaSpain

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