Estimation of Variance and Covariance Components in the Mixed Model

A direct method of computing the coefficient of a variance or covariance component in the expectation of a mean square or mean product when the inverse of the coefficient matrix is available is presented for use with models containing only non-interacting sets of random effects in addition to error. These models may contain any number of sets of fixed effects including interactions and partial regressions for continuous variables. Shortcut computational procedures are presented for the estimation of components of variance and covariance when one set of random effects interacts with one or two sets of fixed main effects and subclass frequencies are unequal. A computational example is given for the two-way classification without interaction and one is available in mimeograph form from the author for the three-way classification with interactions.