what is the definition of "hyper-parameter" in general?
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Inference about genetic covariance matrices using multiple-trait models is often hindered by lack of information. This leads to imprecise estimates of genetic parameters and of breeding values. Patterns in a genetic covariance matrix can be exploited to reduce the number of parameters and to increase quality of inferences. A structural model for genetic covariances was developed and fitted to milk yield data in five regions of the United States. This was compared with a standard multiple-trait analysis using a deviance information criterion, a measure of quality of fit. Data consisted of 3,465,334 Holstein first-lactation records from daughters of 43,755 sires in five regions of the United States (Midwest, Northeast, Northwest, Southeast, Southwest). Parameters of the structural model included an intercept and effects of measures of genetic and of management similarity on genetic covariances. Genetic similarity depended on the number of records contributed by sires that were common to a pair of regions. Management similarity was a function of the quantity of concentrate used to produce 1000 kg of milk in each pair of regions. The structural and the multiple-trait models gave similar estimates of genetic covariances, but the number of parameters was 8 in the former vs. 15 in the latter. Hence, estimates of genetic covariances were more precise with the structural model. A deviance information criterion suggested a slight superiority of the multiple-trait model, although probably within sampling error. For both models, genetic correlations between milk yield in five regions of the United States were larger than 0.93.
Key Words: structural model • covariance component • genotype x environment interaction • Bayesian method
Abbreviation key: DIC = deviance information criterion, GS = genetic similarity, MS = management similarity, MCMC = Markov chain Monte Carlo