Computing options for multiple-trait test-day random regression models while accounting for heat tolerance.

Data included 90,242,799 test day records from first, second and third parities of 5,402,484 Holstein cows and 9,326,754 animals in the pedigree. Additionally, daily temperature humidity indexes (THI) from 202 weather stations were available. The fixed effects included herd test day, age at calving, milking frequency and days in milk classes (DIM). Random effects were additive genetic, permanent environment and herd-year and were fit as random regressions. Covariates included linear splines with four knots at 5, 50, 200 and 305 DIM and a function of THI. Mixed model equations were solved using an iteration on data program with a preconditioned conjugate gradient algorithm. Preconditioners used were diagonal (D), block diagonal due to traits (BT) and block diagonal due to traits and correlated effects (BTCORR). One run included BT with a 'diagonalized' model in which the random effects were reparameterized for diagonal (co)variance matrices among traits (BTDIAG). Memory requirements were 8.7 Gb for D, 10.4 Gb for BT and BTDIAG, and 24.3 Gb for BTCORR. Computing times (rounds) were 14 days (952) for D, 10.7 days (706) for BT, 7.7 days (494) for BTDIAG and 4.6 days (289) for BTCORR. The convergence pattern was strongly influenced by the choice of fixed effects. When sufficient memory is available, the option BTCORR is the fastest and simplest to implement; the next efficient method, BTDIAG, requires additional steps for diagonalization and back-diagonalization.