Transformation of multitrait to unitrait mixed model analysis of data with multiple random effects.

An algorithm for transforming a multitrait into a unitrait analysis was presented for a mixed model that has equal design matrices for t traits and contains more than one random classification. The class of models was restricted to those in which the covariance matrices for all random effects including the residual can be diagonalized simultaneously. A variation of this assumption was called the common principal component by Flury. As a result of the transformation, setting up and solving the laborious t trait mixed model equations becomes a simple matter of setting up and solving the unitrait mixed model equations separately for each of the t transformed traits. The present procedure would not only simplify computer programming but more importantly it would drastically reduce central processing unit time and computer space requirements. A numerical example was given to illustrate this procedure of indirect multitrait analysis in comparison with direct multitrait analysis.