Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.In linear mixed models it is often assumed that the residual variance is the same for all observations. However, differences in the residual variance between individuals are quite common and it is important to include the effect of heteroskedastic residuals in models for traditional breeding value evaluation [1]. Such models, having explanatory variables accounting for heteroskedastic residuals, are routinely used by breeding organizations today. The explanatory variables are typically non-genetic [2], but genetic heterogeneity can be present and it is included as random effects in the residual variance part of the model.Modern animal breeding requires animals that are robust to environmental changes. Therefore, we need meth