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

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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.

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Authors and Affiliations

  1. University of California, Los Angeles, Los Angeles, USA

    Peter M. Bentler

  2. University of Notre Dame, Notre Dame, USA

    Ke-Hai Yuan

Authors
  1. Peter M. Bentler
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  2. Ke-Hai Yuan
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Corresponding author

Correspondence to Peter M. Bentler.

Additional information

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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Bentler, P.M., Yuan, KH. Positive Definiteness via Off-diagonal Scaling of a Symmetric Indefinite Matrix. Psychometrika 76, 119–123 (2011). https://doi.org/10.1007/s11336-010-9191-3

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  • DOI: https://doi.org/10.1007/s11336-010-9191-3

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