An Expression for Average Information Matrix for a Mixed Linear Multi-Component of Variance Model and REML Iteration Equations

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  • Expression for Average Information Matrix for a Mixed Linear Multi-Component of Variance Model and REML Iteration Equations

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Abstract

For the restricted maximum likelihood (REML) procedure, which is an iterative method and is in common use to estimate variance components in animal breeding researches and applications, there have been proposed the computing algorithms of several kinds. Focussing on the so-called average information (AI) algorithm and assuming a mixed linear, multi-component of variance model, in this study, an expression for the AI matrix in which the vector of predicted residuals is not contained is derived. The resulting elements of the AI matrix are expressed in terms of quadratic and bilinear forms for the vectors of observations and the mixed model solutions. Replacing the Hessian matrix by the current AI matrix, a quasi-Newton type procedure is defined for REML estimation. Although a generalized inverse of the mixed model coefficient matrix and direct solutions to the mixed model equations are required to form the current AI matrix, use of sparse matrix tools makes the proposed numerical technique efficient. As an illustration, some computing performance of the current REML procedure is shown, analyzing a data set on carcass weight in the Japanese Black cattle.

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