Sparse Matrix Inversion for Restricted Maximum Likelihood Estimation of Variance Components by Expectation-Maximization

¹ University of Illinois, Urbana 61801
² University of Wisconsin, Madison 53706

Expectation-maximization algorithms for REML estimation of variance components are regarded as expensive because they involve computation of the inverse of the coefficient matrix of the mixed model equations. The derivative-free algorithms are viewed as a less expensive alternative because they require computation of the determinant of the same matrix but not the inverse. Unfortunately, these algorithms have poorer numerical properties. We show that computing the sparse matrix inverse, used for any round of an expectation-maximization algorithm, is only about three times as expensive as computation of the determinant, used for each step of a derivative-free algorithm. Thus, the total computational costs of the expectation-maximization and derivative-free algorithms are comparable, and the difference in cost will depend mainly on the number of iterations needed to attain convergence.

Key Words: restricted maximum likelihood • sparse matrix • sparse inversion

Submitted on October 20, 1992
Accepted on December 28, 1992

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