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Derivative-free restricted maximum likelihood estimation in animal models with a sparse matrix solver.

K G Boldman1, L D Van Vleck

  • 1USDA R. L. Hruska US Meat Animal Research Center, University of Nebraska, Lincoln 68583-0908.

Journal of Dairy Science
|December 1, 1991
PubMed
Summary

This study demonstrates that using the SPARSPAK direct sparse matrix solver significantly speeds up variance component estimation in animal models. It requires substantially less computational time and memory compared to traditional Gaussian elimination methods.

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Area of Science:

  • Quantitative genetics
  • Computational biology
  • Statistical genetics

Background:

  • Derivative-free restricted maximum likelihood (REML) for variance component estimation necessitates repeated log-likelihood function evaluations.
  • Gaussian elimination of large mixed model coefficient matrices is computationally intensive for animal models.

Purpose of the Study:

  • To investigate the efficiency of a direct sparse matrix solver, SPARSPAK, for calculating the log-likelihood function in animal models.
  • To compare the computational performance of SPARSPAK with Gaussian elimination for variance component estimation.

Main Methods:

  • Utilized the SPARSPAK package for reordering mixed model equations and Cholesky factorization.
  • Applied SPARSPAK to an animal model with a large coefficient matrix (order 3661) including fixed, maternal permanent environmental, and genetic effects.

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  • Compared computational time and memory usage against Gaussian elimination of the unordered system.

    • Main Results:

    • SPARSPAK reduced central processing unit (CPU) time by 605 times on mainframes and 240 times on personal computers compared to Gaussian elimination.
    • The sparse matrix solver required less memory and successfully provided solutions for all model effects.
    • Demonstrated significant computational gains for derivative-free REML in large animal models.

    Conclusions:

    • Direct sparse matrix solvers like SPARSPAK offer a highly efficient alternative to Gaussian elimination for log-likelihood evaluation in REML.
    • Implementing SPARSPAK can drastically reduce computational burden and memory requirements for complex animal models.
    • This approach enhances the feasibility of derivative-free REML for large-scale genetic analyses.