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On a New Property of Partially Balanced Association Schemes useful in Psychometric Structural Analysis

Published online by Cambridge University Press:  01 January 2025

J. N. Srivastava  and
R. L. Maik
J. N. Srivastava
Affiliation:
University of Nebraska
R. L. Maik
Affiliation:
University of Nebraska
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Abstract

In an earlier paper [Psychometrika, 31, 1966, p. 147], Srivastava obtained a test for the Hypothesis H0 : Σ =α0Σ0 + ... +αlΣl, where Σi are known matrices,αi are unknown constants and Σ is the unknown (p × p) covariance matrix of a random variablex (withp components) having ap-variate normal distribution. The test therein was obtained under (p × p) covariance matrix of a random variablex (with p components) the condition that Σ0, Σ1, ..., Σl form a commutative linear associative algebra and a certain vector θ, dependent on these, has non-negative elements. In this paper it is shown that this last condition is always satisfied in the special situation (of importance in structural analysis in psychometrics) where Σ0, Σ1, ..., Σl are the association matrices of a partially balanced association scheme.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 3 , September 1967 , pp. 279 - 289
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

This research was partially supported by the U. S. Air Force under Grant No. AF33(615)-3231, monitored by the Aero Space Research Labs.

†

Now at Colorado State University.

References

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