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An alternative derivation of Harville's restricted log likelihood function for variance component estimation
1Department of Botany and Plant Sciences, University of California, Riverside, CA, USA.
Biometrical Journal. Biometrische Zeitschrift
|November 3, 2018
Summary
This study simplifies variance component estimation in mixed models. A new method derives the restricted likelihood function, crucial for accurate genetic and environmental variance partitioning in breeding and clinical trials.
Area of Science:
- Statistics
- Quantitative Genetics
- Biometry
Background:
- Variance component estimation is vital for linear mixed models in diverse fields.
- Restricted maximum likelihood (REML) is preferred over maximum likelihood (ML) for accounting for lost degrees of freedom.
- Existing derivations of Harville's restricted likelihood function can be complex.
Purpose of the Study:
- To present a simpler derivation of Harville's restricted likelihood function.
- To offer an alternative method for variance component estimation in mixed models.
- To enhance the accessibility of REML for researchers.
Main Methods:
- Treating fixed effects as random to create a pseudo-random model (PDRM).
- Constructing a likelihood function for the PDRM.
- Taking the limit of the PDRM likelihood as pseudo-random effect variance approaches infinity.
Main Results:
- Successfully derived Harville's restricted likelihood function through a simplified approach.
- Demonstrated the equivalence of the derived function to the established restricted likelihood.
- Provided a novel pathway for understanding REML derivations.
Conclusions:
- The proposed method offers a more straightforward derivation of the restricted likelihood function.
- This simplification can aid in the application and understanding of REML in statistical analysis.
- The technique is applicable to variance component estimation in animal breeding, plant breeding, and clinical trials.