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

Kadir Kizilkaya; Paolo Carnier; Andrea Albera; Giovanni Bittante; Robert J. Tempelman

doi:doi:10.1051/gse:2003036

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Volume 35 / No 5 (September-October 2003)

Genet. Sel. Evol., 35 5 (2003) 489-512

Abstract

Free Access

Issue		Genet. Sel. Evol. Volume 35, Number 5, September-October 2003


Page(s)		489 - 512
DOI		https://doi.org/10.1051/gse:2003036

Genet. Sel. Evol. 35 (2003) 489-512
DOI: 10.1051/gse:2003036

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

Kadir Kizilkaya^a, Paolo Carnier^b, Andrea Albera^c, Giovanni Bittante^b and Robert J. Tempelman^a

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

(Received 24 June 2002; accepted 10 March 2003)

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 ( $0.40 \pm 0.06$ , $0.11 \pm 0.04$ ) and a direct maternal genetic correlation ( $-0.58 \pm 0.15$ ) that were not different from the corresponding posterior means of the heritabilities ( $0.42 \pm 0.07$ , $0.14 \pm 0.04$ ) and the genetic correlation ( $-0.55 \pm 0.14$ ) 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.

Key words: threshold model / t-distribution / Bayesian inference / calving ease

Correspondence and reprints: Robert J. Tempelman
e-mail: tempelma@msu.edu

© INRA, EDP Sciences 2003