A technique for maximum likelihood estimation in mixed models

A computer program is implemented which solves the likelihood equations arising from the general mixed analysis of variance model. A Runge-Kutta procedure is used to solve the system of first order differential equations resulting from the equations of steepest ascent. Because of the frequent evaluation of the right hand sides of these equations required when applying a fifth order Runge-Kutta technique, polynomial approximations to the equations of steepest ascent are used. The Runge-Kutta procedure is then applied to these approximations. Fully documented examples illustrating these techniques are given. Estimates of the variances and covariances of the maximum likelihood estimates are obtained from the inverse of the information matrix. The parameters appearing in the information matrix are replaced by the maximum likelihood estimates and the resulting matrix is inverted giving these estimates. Full documentation for the computer program is given