The use of equivalent linear models in mixed model estimation and prediction

Some linear models have a very large number of elements in the vector representing random factors. Consequently, it Is impossible to Invert the resulting mixed model coefficient matrix. This inverse is needed for sampling variances and prediction error variances and for computation of MIVQUE and REML estimates of variances and covariances. An equivalent model with fewer elements in the random vector can be used to solve this problem, Some examples are presented, and algorithms for BLUE, BLUP, MIVQUE, and REML are presented.