Quadratic extension of a joint-regression model
by
Meei Ng
University of Melbourne

Two-way data are traditionally analysed by an additive model or interactive model, using ANOVA techniques. Yates and Cochran (1938) introduced a model that represented a mean response as a linear function of the corresponding column (or row) main effect, called a joint-regression model nowadays. The model was further developed by Finlay & Wilkinson (1963) and Eberhart & Russell (1966). A similar model is a so-called AMMI (additive main effect, multiplicative interaction) model, which expresses the interaction as a sum of terms, each being a product of a row effect and a column effect. We consider an extension of a joint-regression model to include quadratic regression on the column (or row) main effects. This model lies between a joint-regression model and an AMMI model and the parameters are more interpretable.

Date received: August 30, 2001