RESTRICTED MAXIMUM-LIKELIHOOD-ESTIMATION OF VARIANCE-COMPONENTS FOR UNIVARIATE ANIMAL-MODELS USING SPARSE-MATRIX TECHNIQUES AND AVERAGE INFORMATION

An algorithm is described to estimate variance components for a univariate animal model using REML. Sparse matrix techniques are employed to calculate those elements of the inverse of the coefficient matrix required for the first derivatives of the likelihood. Residuals and fitted values for random effects can be used to derive additional right-hand sides for which the mixed model equations can be repeatedly solved in turn to yield an average of the observed and expected second derivatives of the likelihood function. This Newton method, using average information, generally converges in <10 iterations. Although the time required per iteration is two to three times greater than that required per likelihood evaluation for derivative-free methods, the total time to convergence is generally much less. An example of a complex model, involving correlated direct and maternal genetic effects, and an additional uncorrelated random effect, indicates that REML, using average information, is about five times faster than a derivative-free algorithm, using the simplex method, which is about three times faster than an expectation-maximization algorithm.