A method of sire evaluation for dichotomies.

In this paper, the following problems associated with genetic evaluation of categorical traits by linear models are discussed: (1) Scores are arbitrarily assigned to response categories. (2) Mixed model solutions do not incorporate the restriction in the estimation space that the sum of response probabilities must total 1 across categories (3) The variance in the observed scale is not constant and depends on the genotypic value of the candidates for selection. (4) The additive genetic variance in the observed scale depends on the mean incidence of the character in the subpopulations considered in the model. (5) Nonadditive genetic variation is present in the observed scale. (6) Linear relationships fail outside a restricted range of the data. (7) Ranking optimality of best linear predictors is lacking when the conditional expectation of the predictand given the data is not linear. A method of sire evaluation of dichotomies based on a log-linear model is introduced, its properties are discussed and examples are presented.