BAYESIAN-ANALYSIS OF TWINNING AND OVULATION RATES USING A MULTIPLE-TRAIT THRESHOLD-MODEL AND GIBBS SAMPLING

The Multiple-Trait Gibbs Sampler for Animal Models programs were exten ded to allow analysis of ordered categorical data using a Bayesian thr eshold model. The algorithm is based on data augmentation, where a val ue on the unobserved underlying normally distributed variable (liabili ty) is generated in each round of iteration for each categorical obser vation. The programs allow analysis of several continuous and ordered categorical traits. Categorical traits can have any number of response levels. Models can be different for each trait. The programs were use d to analyze twinning and ovulation rates from a herd of cattle select ed for twinning rate at the U.S. Meat Animal Research Center. Data inc luded number of calves born at each parturition for the lifetime of a cow and number of eggs ovulated for several estrous cycles before firs t breeding as heifers. A total of 6,411 calvings was recorded for 2,08 7 cows with 83.2% single and 16.8% multiple births. A total of 19,849 ovulations was recorded for 2,332 heifers with 85.2% single and 14.8% multiple ovulations. Mean posterior estimates of heritability and frac tion of variance accounted for by permanent environmental effects (PE) were .128 and .103 for twinning rate and .168 and .079 for ovulation rate. Mean posterior estimate of genetic correlation was .808, and cor relation of PE effects was .517. Use of a threshold model could allow for more rapid genetic improvement of the twinning herd through improv ed identification and selection of genetically superior animals becaus e of higher heritability on the underlying scale.