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Cumulative t-link threshold models for the genetic analysis of calving ease scores

  • 1,
  • 2,
  • 3,
  • 2 and
  • 1Email author
Genetics Selection Evolution200335:489

  • Received: 24 June 2002
  • Accepted: 10 March 2003
  • Published:


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.


  • threshold model
  • t-distribution
  • Bayesian inference
  • calving ease

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Authors’ Affiliations

Department of Animal Science, Michigan State University, East Lansing, 48824, USA
Department of Animal Science, University of Padova, Agripolis, 35020 Legnaro, Italy
Associazione Nazionale Allevatori Bovini di Razza Piemontese, Strada Trinità 32a, 12061 Carrù, Italy


© INRA, EDP Sciences 2003