Approximation of reliability for multiple-trait animal models with missing data by canonical transformation

An algorithm for approximation of reliability for multiple traits by multiple diagonalization was modified to support missing data by weighting transformed contributions of records based on the pattern of missing data. The accuracy of approximation was assessed with simulated and field data by comparing approximate reliabilities with those from direct inversion. Simulated data had several levels of missing data and covariances between traits; correlations were close to those for linear type traits of dairy cattle. Field data were 1) dairy records for milk, fat, and protein yields with 26% of the observations for fat and protein removed and 2) beef records for birth weight, weaning weight, and mean gain after weaning with 43% of observations missing. These files also contained empty fixed effect classes. The algorithm worked best for simulated data, and, when covariances between traits decreased, proportion of missing traits decreased and the number of empty fixed classes decreased. For dairy data, improvement over single-trait reliability occurred only for traits with missing data; for beef data, little or no improvement occurred. The method is useful with multiple diagonalization if the proportion of missing records or number of empty fixed effect classes or covariances between traits is moderate.