Abstract
In this study, a hierarchical threshold mixed model based on a cumulative t-link specification for the analysis of ordinal data or more, specifically, calving ease scores, was developed. The validation of this model and the Markov chain Monte Carlo (MCMC) algorithm was carried out on simulated data from normally and t4 (i.e. a t-distribution with four degrees of freedom) distributed populations using the deviance information criterion (DIC) and a pseudo Bayes factor (PBF) measure to validate recently proposed model choice criteria. The simulation study indicated that although inference on the degrees of freedom parameter is possible, MCMC mixing was problematic. Nevertheless, the DIC and PBF were validated to be satisfactory measures of model fit to data. A sire and maternal grandsire cumulative t-link model was applied to a calving ease dataset from 8847 Italian Piemontese first parity dams. The cumulative t-link model was shown to lead to posterior means of direct and maternal heritabilities (0.40 ± 0.06, 0.11 ± 0.04) and a direct maternal genetic correlation (-0.58 ± 0.15) that were not different from the corresponding posterior means of the heritabilities (0.42 ± 0.07, 0.14 ± 0.04) and the genetic correlation (-0.55 ± 0.14) inferred under the conventional cumulative probit link threshold model. Furthermore, the correlation (> 0.99) between posterior means of sire progeny merit from the two models suggested no meaningful rerankings. Nevertheless, the cumulative t-link model was decisively chosen as the better fitting model for this calving ease data using DIC and PBF.
Highlights
Data quality is an increasingly important issue for the genetic evaluation of livestock, both from a national and international perspective [13]
Given the recent momentum in using heavy-tailed residual specifications for the analysis of production data in animal breeding [36,41,42,47] a hierarchical threshold (CT) mixed model based on a cumulative t-link specification was developed, validated by simulation and applied to a small calving ease dataset from Italian Piemontese cattle
The simulation study indicated that inference on v is possible in a CT model; it appears that either a more suitable Markov chain Monte Carlo (MCMC) strategy is needed or many more samples are required compared to that considered in our study to ensure a more reliable inference on v
Summary
Data quality is an increasingly important issue for the genetic evaluation of livestock, both from a national and international perspective [13]. Breed associations and government agencies typically invoke arbitrary data quality control edits on continuously recorded production characters in order to minimize the impact of recording error, preferential treatment and/or injury/disease on predicted breeding values [5]. These edits are used in the belief that the data residuals should be normally distributed. Based on the work of Lange et al [24] and others, Stranden and Gianola [42] developed the corresponding hierarchical Bayesian models for animal breeding, using Markov chain Monte Carlo (MCMC) methods for inference In their models, residuals are specified as either having independent (univariate) t-distributions or multivariate t-distributions within herd clusters. Outside of possibly longitudinal studies, the multivariate specification is of dubious merit [36,41,42] such that all of our subsequent discussion pertains to the univariate t-error specification only
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