Abstract
The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model). The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC) as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months), both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.
Highlights
Genetic evaluations in animal breeding are generally performed using the mixed effects models pioneered by Henderson [9]
The Bayes factor as originally proposed by Verdinelli and Wasserman [25] has been applied to various models used in animal breeding and the genetics research field
The method was initially developed to test for the genetic background of linear traits [5] and the location of quantitative trait loci (QTL) [23], this Bayes factor has been recently modified to discriminate between linked and pleiotropic QTL [24], to test for the genetic background of threshold traits [2,18], and to compare different structures of random genetic groups [3], all with encouraging results
Summary
Genetic evaluations in animal breeding are generally performed using the mixed effects models pioneered by Henderson [9]. These models assume Gaussian distributions for most random effects, including the residuals, and in absence of contradictory evidence, it is practical to assume normality on the basis of both mathematical convenience and biological plausibility. Departures from normality are common in animal breeding, e.g. when more valuable animals receive preferential treatment [14,15] This preferential treatment could be defined as any management practice that increases or decreases production and is applied to one or several animals, but not to their contemporaries [14]. Other potential causes of outliers or abnormal phenotypic records could be measurement errors, sickness, shortterm-changes in herd environment and mismanagement of data [11]
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