References

Hayes, J. F., and W. G. Hill. 1981. “Modification of Estimates of Parameters in the Construction of Genetic Selection Indices (’Bending’).” Biometrics 37 (3): 483. https://doi.org/10.2307/2530561.

Hazel, L. N. 1943. “The Genetic Basis for Constructing Selection Indexes.” Genetics 28 (6): 476–90. https://doi.org/10.1093/genetics/28.6.476.

Henderson, C. R. 1975. “Best Linear Unbiased Estimation and Prediction Under a Selection Model.” Biometrics 31 (2): 423–47. https://doi.org/10.2307/2529430.

Henderson, C. R. 1976. “A Simple Method for Computing the Inverse of a Numerator Relationship Matrix Used in Prediction of Breeding Values.” Biometrics 32 (1): 69–83. https://doi.org/10.2307/2529339.

Patterson, H. D., and R. Thompson. 1971. “Recovery of Inter-Block Information When Block Sizes Are Unequal.” Biometrika 58 (3): 545–54. https://doi.org/10.1093/biomet/58.3.545.

Penrose, Roger. 1955. “A Generalized Inverse for Matrices.” Mathematical Proceedings of the Cambridge Philosophical Society 51 (3): 406–13. https://doi.org/10.1017/S0305004100030401.

Rao, C. Radhakrishna. 1962. “A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics.” Journal of the Royal Statistical Society Series B 24 (1): 152–58. https://doi.org/10.1111/j.2517-6161.1962.tb00447.x.

Searle, Shayle R. 1982. Matrix Algebra Useful for Statistics. John Wiley & Sons.

Wells, Martin T. 2009. “A Conversation with Shayle r. Searle.” Statistical Science 24 (2): 244–54. https://doi.org/10.1214/08-STS259.

Additional Resources

Textbooks

Henderson, C. R. (1984). Applications of Linear Models in Animal Breeding. University of Guelph.
Lynch, M., & Walsh, B. (1998). Genetics and Analysis of Quantitative Traits. Sinauer Associates.
Mrode, R. A. (2014). Linear Models for the Prediction of Animal Breeding Values (3rd ed.). CABI.
Falconer, D. S., & Mackay, T. F. C. (1996). Introduction to Quantitative Genetics (4th ed.). Longman.

Key Papers

Mixed Model Theory

Henderson, C. R. (1975). Best linear unbiased estimation and prediction under a selection model. Biometrics, 31(2), 423-447.
Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science, 6(1), 15-32.
Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, 58(3), 545-554.

Non-additive Effects (Ch 16-17)

Henderson, C. R. (1985). Best linear unbiased prediction of nonadditive genetic merits in noninbred populations. Journal of Animal Science, 60(1), 111-117. https://doi.org/10.2527/jas1985.601111x
Hill, W. G., Goddard, M. E., & Visscher, P. M. (2008). Data and theory point to mainly additive genetic variance for complex traits. PLoS Genetics, 4(2), e1000008. https://doi.org/10.1371/journal.pgen.1000008
Hivert, V., Sidorenko, J., Rohart, F., et al. (2021). Estimation of non-additive genetic variance in human complex traits from a large sample of unrelated individuals. The American Journal of Human Genetics, 108(5), 786-798. https://doi.org/10.1016/j.ajhg.2021.02.014

Reference list is incomplete

This page currently holds only references verified against the literature. Chapter-specific references are added as each chapter is drafted; see CHAPTERS.md for the chapters still to be written.

Software and Tools

BLUPF90 Family: http://nce.ads.uga.edu/wiki/doku.php
ASReml: https://vsni.co.uk/software/asreml-r
R Packages:
- sommer: https://cran.r-project.org/package=sommer
- pedigreemm: https://cran.r-project.org/package=pedigreemm
- nadiv: https://cran.r-project.org/package=nadiv
- MCMCglmm: https://cran.r-project.org/package=MCMCglmm

Online Resources

Animal Breeding and Genetics Wiki: http://nce.ads.uga.edu/wiki/
Quarto Documentation: https://quarto.org
R for Data Science: https://r4ds.had.co.nz/
Mixed Models in R: https://m-clark.github.io/mixed-models-with-R/

Datasets and Examples

All datasets used in this book are synthetic and available in the book repository.

Companion Volumes

Genomic selection and large-scale computation are deferred to separate books; see the Scope section on the welcome page.

Citation Style

This book uses the Genetics citation style. For BibTeX entries, see references.bib in the book repository.

# References {.unnumbered} ::: {#refs} ::: ## Additional Resources ### Textbooks - **Henderson, C. R. (1984).** *Applications of Linear Models in Animal Breeding*. University of Guelph. - **Lynch, M., & Walsh, B. (1998).** *Genetics and Analysis of Quantitative Traits*. Sinauer Associates. - **Mrode, R. A. (2014).** *Linear Models for the Prediction of Animal Breeding Values* (3rd ed.). CABI. - **Falconer, D. S., & Mackay, T. F. C. (1996).** *Introduction to Quantitative Genetics* (4th ed.). Longman. ### Key Papers #### Mixed Model Theory - **Henderson, C. R. (1975).** Best linear unbiased estimation and prediction under a selection model. *Biometrics*, 31(2), 423-447. - **Robinson, G. K. (1991).** That BLUP is a good thing: The estimation of random effects. *Statistical Science*, 6(1), 15-32. - **Patterson, H. D., & Thompson, R. (1971).** Recovery of inter-block information when block sizes are unequal. *Biometrika*, 58(3), 545-554. #### Non-additive Effects (Ch 16-17) - **Henderson, C. R. (1985).** Best linear unbiased prediction of nonadditive genetic merits in noninbred populations. *Journal of Animal Science*, 60(1), 111-117. https://doi.org/10.2527/jas1985.601111x - **Hill, W. G., Goddard, M. E., & Visscher, P. M. (2008).** Data and theory point to mainly additive genetic variance for complex traits. *PLoS Genetics*, 4(2), e1000008. https://doi.org/10.1371/journal.pgen.1000008 - **Hivert, V., Sidorenko, J., Rohart, F., et al. (2021).** Estimation of non-additive genetic variance in human complex traits from a large sample of unrelated individuals. *The American Journal of Human Genetics*, 108(5), 786-798. https://doi.org/10.1016/j.ajhg.2021.02.014 ::: {.callout-note} ## Reference list is incomplete This page currently holds only references verified against the literature. Chapter-specific references are added as each chapter is drafted; see `CHAPTERS.md` for the chapters still to be written. ::: ### Software and Tools - **BLUPF90 Family**: http://nce.ads.uga.edu/wiki/doku.php - **ASReml**: https://vsni.co.uk/software/asreml-r - **R Packages**: - sommer: https://cran.r-project.org/package=sommer - pedigreemm: https://cran.r-project.org/package=pedigreemm - nadiv: https://cran.r-project.org/package=nadiv - MCMCglmm: https://cran.r-project.org/package=MCMCglmm ### Online Resources - **Animal Breeding and Genetics Wiki**: http://nce.ads.uga.edu/wiki/ - **Quarto Documentation**: https://quarto.org - **R for Data Science**: https://r4ds.had.co.nz/ - **Mixed Models in R**: https://m-clark.github.io/mixed-models-with-R/ ### Datasets and Examples All datasets used in this book are synthetic and available in the [book repository](https://github.com/austin-putz/linear-models-in-animal-breeding/tree/main/data). ### Companion Volumes Genomic selection and large-scale computation are deferred to separate books; see the Scope section on the [welcome page](index.qmd). ### Citation Style This book uses the Genetics citation style. For BibTeX entries, see `references.bib` in the book repository.