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Updated: May 6, 2026
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Published on: July 3, 2020
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Variance of prediction error with mixed model equations when relationships are ignored
1Roman L. Hruska Meat Animal Research Center, USDA-ARS, A218 Animal Sciences, University of Nebraska, Lincoln, USA.
Summary
Accurate prediction error variances (PEV) and true-to-predicted correlations (rTI) require correct mixed-model equations (MME). Inbreeding adjustments in the numerator relationship matrix (A) are crucial for precise genetic evaluations.
Area of Science:
- Animal Breeding and Genetics
- Quantitative Genetics
- Statistical Genetics
Background:
- Mixed-model equations (MME) are standard for genetic evaluations.
- Accurate variance-covariance matrices for random effects are essential for reliable predictions.
- Ignoring inbreeding in relationship matrices can lead to biased results.
Purpose of the Study:
- To present formulas for calculating correct prediction error variances (PEV) and true-to-predicted correlations (rTI).
- To illustrate the impact of using incorrect variance-covariance matrices in MME.
- To demonstrate the importance of accounting for inbreeding in genetic evaluations.
Main Methods:
- Formulas for PEV and rTI calculation were derived.
- Mixed-model equations (MME) were used with different approximations of the numerator relationship matrix (A).
- Progeny records from highly related and inbred sires were analyzed.
Main Results:
- PEV were underestimated when inbreeding and relationships were ignored.
- PEV were overestimated when using Henderson's rules for A(-1) without inbreeding.
- Correct PEV were obtained using Quaas' rules for A(-1) that include inbreeding.
- rTI calculations were inaccurate when inbreeding was ignored or approximated incorrectly.
Conclusions:
- Accurate PEV and rTI calculations depend on correctly accounting for relationships and inbreeding in MME.
- Quaas' rules provide the correct A(-1) for accurate genetic predictions.
- Adjusting for inbreeding is necessary for reliable rTI calculations when using the correct A matrix.
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