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Positive Definiteness via Off-diagonal Scaling of a Symmetric Indefinite Matrix

Published online by Cambridge University Press:  01 January 2025

Peter M. Bentler  and
Ke-Hai Yuan
Peter M. Bentler*
Affiliation:
University of California, Los Angeles
Ke-Hai Yuan
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Peter M. Bentler, University of California, Los Angeles, Los Angeles, USA. E-mail: bentler@ucla.edu
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Abstract

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a matrix to achieve positive definiteness. As a contrast to recently developed ridge procedures, the proposed method does not need variables to contain measurement errors. When minimum trace factor analysis is used to implement the theory, only correlations that are associated with Heywood cases are shrunk.

Keywords

indefinite matrixeigenvaluesminimum trace factor analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 1 , January 2011 , pp. 119 - 123
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

This research was supported by grants DA00017 and DA01070 from the National Institute on Drug Abuse. The first author acknowledges a financial interest in EQS and its distributor, Multivariate Software.

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