Nonlinear Treatment‐by‐treatment Interaction Model

Summary

Interaction among factors is of primary importance in the analysis of factorial experiments. But there are experimental situations where interactions can occur among the levels of a single factor. Residual effects from experiments using a latin square design where the treatments are applied in a sequence to the experimental units is an example of that type of interaction.

A class of nonlinear models is proposed to analyze treatment‐by‐treatment interaction in experimental situations where the experimental design does not permit such analysis using linear model techniques. For example, some Latin square designs are such that residual effects cannot be estimated via standard techniques. For that type of design a test of the hypothesis of no treatment‐by‐treatment interaction of a specified type is developed and a procedure for estimating the parameters of the nonlinear model is presented. Two examples where these models can be applied are discussed.