Abstract
An ANOVA model for estimating three-factor interaction effects in a three-way layout without replication is presented. The model is an application of Tucker's three-mode principal component model to residuals obtained by the elimination of main effects, two-factor interaction effects, and of the general mean. The idea of an interaction element between two levels of a factor is extended to the three-factor interaction effect. It is shown that the co-ordinates of the levels of the factor obtained by applying the principal co-ordinate analysis to the association matrix formed from the three-factor interaction elements correspond to the estimates of the multiplicative terms which represents a three-factor interaction in the ANOVA model. The relationship makes it clear how the multiplicative terms in the model should be interpreted. An numerical example is illustrated.
