 He developed mixed model equations to obtain best linear unbiased predictions of breeding values and, in general, any random effect.He invented three methods for the estimation of variance components in unbalanced settings of mixed models, and invented a method for constructing the inverse of Wright's numerator relationship matrix based on a simple list of pedigree information.He, with his Ph.D. student Shayle R. Searle, greatly extended the use of matrix notation in statistics.