Normal mixed models with different levels of heterogeneity in the residual variance are fitted to pig litter size data. Exploratory analysis and model assessment is based on examination of various posterior predictive distributions. Comparisons based on Bayes factors and related criteria favour models with a genetically structured residual variance heterogeneity. There is, moreover, strong evidence of a negative correlation between the additive genetic values affecting litter size and those affecting residual variance. 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. A brief discussion is given of some implications for selection of the genetically structured residual variance model.