
Abstract 
An algorithm for the REML estimation of (co) variance components in general multivariate mixed linear models is described. The algorithm is
based on the use of Average Information (AI) as second differentials of the likelihood function. The AI is obtained by averaging the information matrices based on observed and expected information. It is manipulated to a form that is much easier to calculate than either of the two. This involves the setting up of dummy variables as functions of residuals and calculating sums of squares and crossproducts associated with these. Procedures that are based on second differentials can lead to estimates outside the parameter space. By contrast, the EMalgorithm always ensures
that estimates are in the parameter space. An alternative fonnulation of the EMalgorithm allows the possibility of constructing algorithms that are intermediate between AI and EM and can ensure estimates within the parameter space without the problem of slow convergence of the EM algorithm.The new algorithm was compared to derivativefree (DF) and EM algorithms by analysing two sets of field data under several models. The AI algorithm converged in much fewer rounds than the other algorithms
and was in general able to locate a higher maximum of the likelihood function. 