Technical note: computing tests of fixed effects in a restricted class of mixed models

Area of Science:

• Animal Science
• Statistical Modeling
• Quantitative Genetics

Background:

• Inferences about fixed effects in mixed linear models are crucial for animal science research.
• Exact statistical tests are theoretically optimal but computationally challenging with numerous random effects.
• Current practices often rely on less efficient approximate tests due to computational limitations.

Purpose of the Study:

• To describe reduction in error sum of squares (RESS) procedures for exact inference in mixed linear models.
• To enable computation of exact tests and confidence intervals without matrix inversion.
• To address computational challenges in animal models with a high number of random effect levels.

Main Methods:

• Utilized iterative algorithms to solve Henderson's mixed-model equations.
• Employed Reduction in Error Sum of Squares (RESS) procedures.
• Avoided direct inversion of the covariance matrix or computation of a generalized inverse.

Main Results:

• Demonstrated the feasibility of performing exact tests and computing confidence intervals using RESS.
• Successfully applied the method to an animal model with three random effects (two with 1,372 levels, one with 450 levels).
• The iterative approach bypasses computationally intensive matrix operations.

Conclusions:

• The described RESS procedures offer an efficient and exact method for statistical inference in complex mixed linear models.
• This approach overcomes computational bottlenecks, making exact tests practical for large-scale animal science studies.
• Facilitates more accurate and reliable inferences in animal breeding and genetics research.