Mixed model analysis for the estimation of components of genetic variation in lamb weaning weight

Abstract

This case study continues the analysis of differences in weaning weight between indigenous genotypes of sheep which was started in Case Study 3. In the previous case study a model containing fixed effects for lamb genotype, year of birth, sex, age at weaning and age of dam was fitted by the method of general least squares. Here we extend the model by introducing random effects for sire and dam and use the method of restricted maximum likelihood (REML) to fit the mixed model. The case study explores the multilevel structure of the data and shows how the different layers can be expressed diagrammatically in the form of a ´mixed model tree´. The outputs produced by REML are described and compared with outputs produced by the method of general least squares. Although the presentations of results are different, analyses of variance and parameter estimates and standard errors are shown to be the same when no random terms are included in the model. Random terms for ram and ewe are then added to the statistical model. The interpretation and significance of their effects are discussed. The use of R for the analysis of these data is illustrated as well as GenStat.