A GENERALIZED COMPUTING PROCEDURE FOR SETTING UP AND SOLVING MIXED LINEAR-MODELS

A generalized computing procedure applicable to a large set of problems in animal breeding including ordinary least squares, generalized least squares, and mixed model equations is presented. The procedure is implemented using sparse storage of coefficients and iteration on data. It allows any number of fixed and random effects, with any number of levels, any number of covariables, multiple-trait models, heterogeneous variances, missing values, and multiple incidence matrices for different traits. Under the sparse storage scheme, the relationship matrix can be included without sorting. Subroutine interfaces are presented that allow identical treatment of the sparse and full stored coefficient matrices. The system of equations can be solved either by direct procedures or iteratively. Modern computers with adequate memory easily can accommodate 100,000 equations under the sparse storage scheme. The iteration on data version, reading data from memory, can accommodate problems up to 10 times larger. Reading data from disk further increases the scope as might be required in national breeding programs. Pseudo codes for both strategies are given. © 1990, American Dairy Science Association. All rights reserved.