Best linear unbiased prediction to predict category frequencies of future progeny of a sire for type traits scored in mutually exclusive categories is described. The method accounts for automatic covariances among categories and is comparable to prediction for multiple traits. The method does not require linearity of measurements and also allows nonlinear economic values to be assigned to each category after frequencies are predicted. Evaluations were for 12 descriptive type traits for 712 Brown Swiss bulls having daughters in more than one herd. Problems in obtaining solutions to the mixed-model equations for multiple traits are discussed.

Variances and covariances for herdyear, sire, and residual effects were estimated for 10 standard type traits and milk yield from type records on 12,838 Brown Swiss cows and miIk records on 5,911 of these. A total of 712 sires and 824 herds was involved. The model was a random two-way, cross-classified model (herd-year and sire of cow) with no interaction. Covariances with descriptive type traits scored in categories as present or absent also were estimated as were variance-covariance matrices for descriptive type traits when each category was a separate trait. Genetic correlations of standard type traits with final classification score were large and positive. Genetic correlations of desirable categories of descriptive type traits with final classification also were positive. Standard type traits and final score had positive genetic correlations with milk yield generally ranging from .18 to .29 except for feet and legs .03.