Comparison of two computing algorithms for solving mixed model equations for multiple trait random regression test day models

Two computing algorithms for solving mixed model equations for a multiple l actation, multiple trait random regression test day model were compared. Th e model for each trait (yields of milk, fat, and protein, and somatic cell scores in the first three lactations) included fixed contemporary groups, f ixed regressions within levels of time-region-age-season parity subclasses at calving and two sets of random regressions: animal genetic and permanent environmental effects, giving a total of twelve traits and 36 equations fo r each animal genetic effect and each animal permanent environmental effect . Algorithm A utilized the iteration on data with blocking strategy (with c ontemporary group and animal blocks) in a Gauss-Seidel iteration scheme. Bl ock sizes for animal generic and permanent environmental effects were of or der 36. Algorithm B utilized an alternative blocking strategy for animal ef fects with separate blocks for each lactation of order 12. This allowed for significant reduction in memory requirements, less time per iteration, but slightly slower convergence compared to Algorithm A. The algorithms were c ompared in an application of the test day model to the national Canadian je rsey test day data set. Memory and disk space requirements for the two algo rithms as well as extensions of the model were discussed. (C) 2000 Elsevier Science B.V. All rights reserved.