Prediction error variance and restricted maximum likelihood estimation for animal model with relationship grouping.

Area of Science:

• Animal breeding and genetics
• Quantitative genetics
• Statistical genetics

Background:

• Genetic evaluation using animal models with relationship grouping is feasible.
• Existing algorithms for prediction error variance and REML estimation were unavailable.

Purpose of the Study:

• To develop algorithms for prediction error variance and REML estimation in animal models.
• To enhance genetic evaluation accuracy for additive genetic and group effects.

Main Methods:

• Utilized a generalized inverse of the coefficient matrix for a transformed mixed model equation.
• Developed REML algorithms using the transformed equation for computational feasibility.
• Extended algorithms for arbitrary numbers of random factors and covariance components.

Main Results:

• Prediction error variance is a function of the generalized inverse of the coefficient matrix.
• REML algorithms are computationally feasible despite slightly more complex expressions.
• Formulae for prediction error variance are generally applicable.

Conclusions:

• The developed algorithms provide a feasible method for prediction error variance and REML estimation.
• These methods enhance genetic evaluation in animal models, applicable to various random factors and covariance components.