Evaluation and Interpretation of Interactions.

The statistical analysis of two-way tables with interactions arise in different areas of research, among others, in agriculture, plant breeding and genetics, medicine, social science, etc. This is particularly important in agriculture and plant breeding where genotypes or agronomic treatments are evaluated in several environmental conditions and the interaction usually complicates selection decisions. Different models can be used to study and interpret the interaction. Historically in agriculture and plant breeding fixed effects two-way models have been used to study interactions. However, the nature of these models does not allow modeling (co)variance structures for a more realist and accurate parameter estimation. Models combining linear and bilinear terms have been proved to be useful for the analysis of two factor study with interaction especially when the two factors do not have specific structures that might suggest contrasts or response functions. Linear-bilinear mixed models offer a valuable set of (co)variance structure’s that offer the opportunity to researchers to assess the interactions in a more realistic and informative manner. Models that incorporate external covariables related to either of the two-factor interaction are of value for explaining the possible causes of interaction. In this study we will present different data sets applied to agriculture and plant breeding where interaction is important and show different ways to analyze and interpret this interaction under the assumptions of a fixed and mixed model. Simple examples on how to use external covariables that influence the interactions are presented and results are interpreted.