A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing
Albert Satorra (albert.satorra@upf.edu) and
Heinz Neudecker
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Albert Satorra: http://www.econ.upf.edu/~satorra
Psychometrika, 2015, vol. 80, issue 4, 938-948
Abstract:
This paper develops a theorem that facilitates computing the degrees of freedom of Wald-type chi-square tests for moment restrictions when there is rank deficiency of key matrices involved in the definition of the test. An if and only if (iff) condition is developed for a simple rule of difference of ranks to be used when computing the desired degrees of freedom of the test. The theorem is developed exploiting basics tools of matrix algebra. The theorem is shown to play a key role in proving the asymptotic chi-squaredness of a goodness of fit test in moment structure analysis, and in finding the degrees of freedom of this chi-square statistic. Copyright The Psychometric Society 2015
Keywords: matrix algebra; rank deficiency; wald test; chi-square goodness of fit test; augmented moment structures; structural equation modeling (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:80:y:2015:i:4:p:938-948
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DOI: 10.1007/s11336-014-9438-5
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