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Cholesky problems.

Gregory Carey1

  • 1Department of Psychology and Institute for Behavioral Genetics, University of Colorado, Boulder, CO 80309-0345, USA. gregory.carey@colorado.edu

Behavior Genetics
|September 27, 2005
PubMed
Summary
This summary is machine-generated.

Fitting a Cholesky decomposition in behavioral genetics can yield invalid statistical results. Researchers must validate fit statistics and degrees of freedom, especially when dealing with genetic and environmental covariance matrices.

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Area of Science:

  • Behavioral Genetics
  • Quantitative Genetics
  • Statistical Modeling

Background:

  • Behavioral geneticists often use Cholesky decomposition to parameterize covariance matrices.
  • This method involves representing a matrix as a product of a lower triangular matrix and its transpose.
  • The validity of this approach, particularly for genetic and environmental matrices, requires scrutiny.

Purpose of the Study:

  • To investigate the validity of the Cholesky decomposition technique in behavioral genetics.
  • To identify conditions under which the Cholesky parameterization may produce inaccurate statistical inferences.
  • To propose interim solutions for researchers using this method.

Main Methods:

  • Simulations were conducted to test the Cholesky decomposition procedure.

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  • The study examined the distribution of fit statistics and degrees of freedom.
  • Potential issues arising from negative semi-definite matrices were analyzed.

    • Main Results:

    • The Cholesky decomposition does not always yield fit statistics with a chi-squared distribution.
    • Degrees of freedom may not be accurately calculated when comparing models.
    • Sampling error and the derived nature of genetic/environmental matrices can lead to problematic matrices.

    Conclusions:

    • The Cholesky parameterization can constrain numerical search and compromise maximum likelihood theory.
    • Researchers must demonstrate the validity of fit statistics and degrees of freedom when using Cholesky decomposition.
    • An interim remedy involves comparing unconstrained and Cholesky models to assess substantive interpretation differences.