## Normal linear models with genetically structured residual variance heterogeneity: A case study of litter size in pigs

### BibTeX

@MISC{And_normallinear,

author = {Daniel Sorensen And and Daniel Sorensen and Rasmus Waagepetersen},

title = {Normal linear models with genetically structured residual variance heterogeneity: A case study of litter size in pigs},

year = {}

}

### OpenURL

### Abstract

Four normal mixed models with dierent levels of complexity in the residual variance are tted to litter size data in pigs. The model building process is partly guided using posterior predictive model checking based on residuals. Graphical summaries of posterior predictive checks contribute insight about speci c features of the data and suggests extensions of the model in a particular direction. Comparisons based on Bayes factors and related criteria favour models with a genetically structured residual variance heterogeneity. The Monte Carlo estimates of the posterior mean and of the 95% posterior interval of the correlation between additive genetic values affecting litter size and those aecting residual variance are 0:62 and ( 0:79; 0:43), respectively. The models are also compared according to the purposes for which they might be used, such as prediction of \future" data, inference about response to selection, and ranking candidates for selection. It is shown that a simple model may be adequate in a particular context, even though it fails to address features of the data accounted for by the more complex models. A brief overview is given of some implications for selection of the genetically structured residual variance model. 1