| Two different methods for comparing alternative mixed models describing the continuous variable underlying all-none response traits were proposed. The first may be viewed as an extension of the analysis of deviance using posterior density functions associated with alternative models, rather than likelihood functions. The major problem with the statistic generated here (referred hereafter as STAT) resides in calculating the integration constants exactly. To avoid this problem a simpler statistic (referred hereafter as STAT1), based on the joint density of the data and the unknowns, was also proposed. The second method relies on the Bayesian concept of posterior odds ratios. Several alternatives for the specification of prior distributions and the hyperparameters were suggested, and an asymptotic normal approximation of the joint posterior density was presented. Finally, guidelines for the prediction of future observations were also proposed following Bayesian procedures. Three different traits: conception to A.I sires (CAI), fertility I (FI), and conception to pasture sires (CP1) were analyzed as an illustration. These traits represented different aspects of cow fertility measured as a successful conception, i.e., calving a viable calf, to an A.I. sire or to a service sire. Using STAT and STAT1 as criteria, the simplest model explaining CAI may include as fixed factors: days postpartum, hormonal treatment, and the interaction pasture program x age of cow. With respect to FI, influential fixed factors were: type of service sire, days postpartum, age of cow, hormonal treatment, breed of service sire, and the interaction breed of service sire x type of service sire. Fixed factors affecting CP1 were: type of pasture sire, pasture program, the two-way interaction breed of pasture sire x type of pasture sire, and the three-way interaction pasture program x breed of pasture sire x breed of cow. In general, inferences with respect to the models containing interactions were not possible when STAT was used as a criterion because negative values were obtained for this statistic. However, when feasible, it seemed easier to reject null hypotheses when STAT was used. |
