caa a22 4500 606242112 CHVBK 20210128101316.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s11336-014-9438-5 doi (NATIONALLICENCE)springer-10.1007/s11336-014-9438-5 A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing [Elektronische Daten] [Albert Satorra, Heinz Neudecker] 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. The Psychometric Society, 2014 matrix algebra nationallicence rank deficiency nationallicence wald test nationallicence chi-square goodness of fit test nationallicence augmented moment structures nationallicence structural equation modeling nationallicence Satorra Albert Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, 08005, Barcelona, Spain aut Neudecker Heinz University of Amsterdam, Amsterdam, The Netherlands aut Psychometrika Springer US; http://www.springer-ny.com 80/4(2015-12-01), 938-948 0033-3123 80:4<938 2015 80 11336 https://doi.org/10.1007/s11336-014-9438-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11336-014-9438-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Satorra Albert Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, 08005, Barcelona, Spain aut NATIONALLICENCE 700 1- Neudecker Heinz University of Amsterdam, Amsterdam, The Netherlands aut NATIONALLICENCE 773 0- Psychometrika Springer US; http://www.springer-ny.com 80/4(2015-12-01), 938-948 0033-3123 80:4<938 2015 80 11336