Balance and orthogonality in designs for mixed classification models

Abstract

A classification model is easiest to analyze when it has a balanced design. Many of the nice features of balanced designs are retained by error-orthogonal designs, which were introduced in a recent paper by the authors. The present paper defines a kind of ‘‘partially balanced’’ design and shows that this partial balance is sufficient to ensure the error-orthogonality of a mixed classification model. Results are provided that make the partial balance condition easy to check. It is shown that, for a maximal-rank error-orthogonal design, the Type I sum of squares for a random effect coincides with the Type II sum of squares.