Bayesian Data Analysis for Animal Scientists pp 137-165 | Cite as

# The Linear Model: II. The ‘Mixed’ Model

## Abstract

In a classical context, a ‘mixed model’ consists of a set of fixed effects and covariates plus one or more random effects, plus a random error term. In Chap. 1, Sect. 1.5, we have explained the differences between fixed and random effects in a frequentist context. However, as we said in Chap. 6, in a Bayesian context, all effects are random; thus, there is no distinction between fixed models, random models or mixed models. Nevertheless, we keep the nomenclatures ‘fixed’ and ‘random’ for the effects that are considered so in a frequentist model, because it is widely extended and it facilitates the understanding of the model. Later we will see which type of Bayesian random effects are what we call ‘fixed’ effects in the frequentist school. We will also consider here that the data are normally distributed, although other distributions of the data can be considered, and the procedure would be the same. In this chapter, we examine a common mixed model in animal production, the model with repeated records and the most widely used mixed model in genetic evaluation. We end the chapter with an introduction to multitrait models.

## Preview

Unable to display preview. Download preview PDF.

## References

- Blasco A, Sorensen D, Bidanel JP (1998) A Bayesian analysis of genetic parameters and selection response for litter size components in pigs. Genetics 149:301–306PubMedPubMedCentralGoogle Scholar
- Henderson CR (1973) Sire evaluation and genetic trends. In: Proc. Anim. Breed. and Genet. Symp. in honor of Dr. J. L. Lush. Blacksburg, Virginia, pp 10–41CrossRefGoogle Scholar
- Henderson CR (1976) A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics 32:69CrossRefGoogle Scholar
- Martínez-Álvaro M, Hernández P, Blasco A (2016) Divergent selection on intramuscular fat in rabbits: responses to selection and genetic parameters. J Anim Sci 94:4993–5003CrossRefGoogle Scholar
- Mood AM (1950) Introduction to the theory of statistics. McGraw-Hill, New YorkGoogle Scholar
- Mood AM, Graybill FA (1963) Introduction to the theory of statistics. MacGraw Hill, New YorkGoogle Scholar
- Searle SR (1971) Linear models. Wiley, New YorkGoogle Scholar
- Sorensen DA, Gianola D (2002) Likelihood, Bayesian and MCMC methods in quantitative genetics. Springer, New YorkCrossRefGoogle Scholar