APPROXIMATION OF RELIABILITY FOR MULTIPLE-TRAIT ANIMAL-MODELS WITH MISSING DATA BY CANONICAL TRANSFORMATION

An algorithm for approximation of reliability for multiple traits by m ultiple diagonalization was modified to support missing data by weight ing transformed contributions of records based on the pattern of missi ng data. The accuracy of approximation was assessed with simulated and field data by comparing approximate reliabilities with those from dir ect inversion. Simulated data had several levels of missing data and c ovariances between traits; correlations were close to those for linear type traits of dairy cattle. Field data were 1) dairy records for mil k, fat, and protein yields with 26% of the observations for fat and pr otein removed and 2) beef records for birth weight, weaning weight, an d mean gain after weaning with 43% of observations missing. These file s also contained empty fixed effect classes. The algorithm worked best for simulated data, and, when covariances between traits decreased, p roportion of missing traits decreased and the number of empty fixed cl asses decreased. For dairy data, improvement over single-trait reliabi lity occurred only for traits with missing data; for beef data, little or no improvement occurred. The method is useful with multiple diagon alization if the proportion of missing records or number of empty fixe d effect classes or covariances between traits is moderate.