Bivariate analysis for one continuous and one threshold dichotomous trait with unequal design matrices and an application to birth weight and calving difficulty

A bivariate analysis is described for one continuous and one discrete trait to estimate sire effects in a progeny test. Unequal design matrices, in terms of both missing data as well as different fixed effects are allowed for. Three independent sub data sets are formed, for which the corresponding log-likelihoods are expressed. The parameters are estimated as their maxima a posteriori by maximizing the log-posterior density using a Newton Raphson algorithm; equations are given in a mixed model form. A simulation study is presented showing the benefits of this bivariate analysis for the evaluation of beef bulls for calving difficulty, using birth weight as a correlated trait. Standard errors obtained from the information matrix were close to empirical standard errors, and it was shown that bivariate analysis with unequal design matrices can correct for a bias which may occur when birth weight records are not missing at random.