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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Partial and conditional maximum likelihood for variance-component estimation.

S Xu1, W R Atchley, W M Muir

  • 1Department of Genetics, North Carolina State University, North Carolina Department of Animal Sciences, Purdue University, Indiana, USA.

Journal of Animal Breeding and Genetics = Zeitschrift Fur Tierzuchtung Und Zuchtungsbiologie
|March 15, 2011
PubMed
Summary
This summary is machine-generated.

This study extends error contrasts for variance component estimation, simplifying complex calculations. The new partial and conditional maximum likelihood (PCML) method reduces multidimensional optimization to one-dimensional problems for more efficient analysis.

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • The estimation of variance components is crucial in statistical modeling.
  • Traditional restricted maximum likelihood methods involve complex multidimensional optimization.
  • Patterson and Thompson's 'error contrasts' offered an initial simplification.

Purpose of the Study:

  • To extend the concept of error contrasts for variance component estimation.
  • To develop a more computationally efficient method than traditional restricted maximum likelihood.
  • To introduce a novel approach termed partial and conditional maximum likelihood (PCML).

Main Methods:

  • Extended error contrasts to multiple sets of linear contrasts, isolating specific random effects.
  • Estimated error variance by maximizing a likelihood function derived from error contrasts.
  • Developed conditional likelihood functions for estimating variance and covariance components, treating other effects as fixed.
  • Transformed multidimensional optimization problems into sequential one-dimensional optimizations.

Main Results:

  • Successfully estimated variance components by progressively building likelihood functions.
  • Reduced the computational complexity of variance component estimation.
  • The proposed method is named partial and conditional maximum likelihood (PCML).

Conclusions:

  • PCML offers a computationally efficient alternative for variance component estimation.
  • The method simplifies complex statistical models by breaking down optimization problems.
  • This approach enhances the practical application of variance component estimation in statistical analysis.