EconPapers    
Economics at your fingertips  
 

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
Additional contact information
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
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s11336-014-9438-5 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:80:y:2015:i:4:p:938-948

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-014-9438-5

Access Statistics for this article

Psychometrika is currently edited by Irini Moustaki

More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla (sonal.shukla@springer.com) and Springer Nature Abstracting and Indexing (indexing@springernature.com).

 
Page updated 2024-12-29
Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:938-948