Parametric bootstrap for testing model fitting of threshold and grouped data models: an application to the analysis of calving ease of Bruna dels Pirineus beef cattle.

The aim of this study was to compare the goodness of fit of the threshold models with homoscedasticity or heteroscedasticity and the grouped data model for the analysis of calving ease in beef cattle by using a parametric bootstrap procedure. Field data included 8,205 records of the Bruna dels Pirineus beef cattle breed in the Pyrenean mountain areas of Catalonia (Spain). The actual distribution was 81.81% of calvings without assistance, 11.02% slightly assisted by the farmer, 5.12% strongly assisted by the farmer, 0.89% assisted by the veterinarian, and 1.16% cesarean, but these percentages were very different in the different herds. This can be explained partially by the different subjective way of scoring of each farmer. Primiparous cows had a greater (P < 0.001) difficulty calving than cows with 5 or more parities (11.74 vs. 4.49% of calvings strongly assisted by the farmer or the veterinarian and 2.8 vs. 0.65% cesarean). Male calves caused greater (P < 0.001) calving difficulty than females (7.71% of male calvings strongly assisted by the farmer or the veterinarian vs. 4.25% of females and 1.83% cesarean in males vs. 0.47% in females). The month and year of calving also had a strong influence on calving ease. These data were analyzed using 3 different models: the threshold models with homoscedasticity or heteroscedasticity and the grouped data model. The bootstrap comparison among models suggested that the threshold models, even allowing for heteroscedasticity, did not fit the herd effects well. In contrast, fitting deficiencies were not observed for the grouped data model in any factor. The variance of direct effect of the calf was estimated using the 3 models, and the heritability estimate ranged from 0.165 for the grouped data model to 0.185 for the hereroscedastic threshold model. This heritability was moderate, but it would justify the inclusion of direct effects of the calf on calving ease in the breeding objective. Overall, results highlighted the flexibility of the grouped data model for the analysis of discrete traits, like calving ease of beef calves.