Validation of an approximate REML algorithm for parameter estimation in a multitrait, multiple across-country evaluation model: a simulation study

A multitrait, multiple across-country evaluation (MT-MACE) model permitting a variable number of correlated traits per country allows international genetic evaluation models to more closely match national models. Before the MT-MACE evaluation can be applied, genetic (co)variance components within and across country must be estimated. An approximate REML algorithm for parameter estimation was developed and was validated via simulation. This method is based on the expectation maximization REML (EM-REML) algorithm. Because obtaining the inverse of co-efficient matrix is not usually feasible for large amounts of data, an algorithm using the multiple-trait effective daughter contribution (EDC) is proposed to provide approximate diagonal elements of the inverse matrix. The accuracy of the approximate EM-REML was tested with simulated data and compared with an average information REML (AI-REML) from available software. Two simulation studies were performed. First, data of 2 countries were simulated using a single-trait model. Estimates of across-country genetic correlations with the developed algorithm were unbiased and very precise. The precision, however, depended on the percentage of bulls with data in both countries. The results obtained with the approximate EM-REML software were very close to those obtained with the AI-REML software regarding estimated genetic correlations and bulls' estimated breeding values. The second simulation assumed a multiple trait model and the same number of traits, pedigree structure, EDC, and pattern of missing records as for actual observations for milk yield obtained from French and German national Holstein evaluations. As with the single-trait scenarios, the approximate EM-REML gave nearly unbiased and very precise estimates of within- and across-country genetic correlations. The results obtained in both simulation studies confirmed the suitability of the MT-MACE model and approximate EM-REML software in a wide range of situations. Even when the genetic trend was incorrectly estimated by the national evaluations, a joint analysis including a time effect in the MT-MACE model adequately corrected for this bias.