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 lactation, multiple trait random regression test day model were compared. The model for each trait (yields of milk, fat, and protein, and somatic cell scores in the first three lactations) included fixed contemporary groups, fixed 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 for each animal genetic effect and each animal permanent environmental effect. Algorithm A utilized the iteration on data with blocking strategy (with contemporary group and animal blocks) in a Gauss–Seidel iteration scheme. Block sizes for animal genetic and permanent environmental effects were of order 36. Algorithm B utilized an alternative blocking strategy for animal effects 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 compared in an application of the test day model to the national Canadian Jersey test day data set. Memory and disk space requirements for the two algorithms as well as extensions of the model were discussed.  2000 Elsevier Science B.V. All rights reserved.