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On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics

Published online by Cambridge University Press:  01 January 2025

James H. Steiger ,
Alexander Shapiro  and
Michael W. Browne
James H. Steiger*
Affiliation:
University of British Columbia
Alexander Shapiro
Affiliation:
University of South Africa
Michael W. Browne
Affiliation:
University of South Africa
*
Please send requests for reprints to James H. Steiger, Department of Psychology, 2136 West Mall, University of British Columbia, Vancouver, B.C. CANADA V6T IW5.
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Abstract

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.

Keywords

Asymptotic distribution theorysequential Chi-square tests
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 3 , September 1985 , pp. 253 - 263
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

This research was carried out while the first author was Visiting Professor in the Department of Statistics in the University of South Africa, and was supported in part by a research grant (NSERC #67-4640) from the National Sciences and Engineering Council of Canada to the first author. The support of both of these organizations is acknowledged with gratitude.

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