Comparison of conventional bayesian and approximate bayesian approaches in estimation of variance components using animal models

Animal models are used to model the observations of animal performance that are genetically dependent.These models are considered as generalized linear mixed models and the genetic correlation structure of data is considered through random effects of breeding values. One goal of the mentioned models is to estimate variance components. In this research, an approximate Bayesian approach presented to estimate variance components in animal model and compared with the conventional Bayesian approach. A generated data set for hypothetical animal population with 1084 records was used. The observations are the animal's birth weight and the data includes dam ID, sire ID, sex and birth year. The effect of gender was considered as fixed effect and the effects of dam, animal and year of birth were used as random effect. Four different models were fitted by the conventional Bayesian approach and the appropriate model was selected by deviance information criteria. The approximate Bayesian approach was applied on it. Time consuming with a PC with configuration (Intel Core i7, 4GB, 2.7 GHz) was about 120 second for the conventional Bayesian approach and little than 10 second for the approximate Bayesian approach. Goodness of fit was computed by relative root mean squared error of prediction that was respectively 0.1568 and 0.1499 for conventional Bayesian and the approximate Bayesian approaches. T-test was used to illustrate lack of significant different to fit weight of animals between two approaches. The null hypothesis was accepted with p-value 0.98 that it shows mean of fitted animal weights for two approaches are equal.