Detecting Interaction Effects
This chapter explores how to search for and identify interactions between predictors that improve models’ predictive performance and focuses on the Ames housing data. Expert knowledge of the system under study is critical for guiding the process of selecting interaction terms. Experimental design employs principles of control, randomization, and replication to construct a framework for gathering evidence to establish causal relationships between independent factors and a dependent response. The interaction hierarchy principle states that the higher degree of the interaction, the less likely the interaction will explain variation in the response. The traditional approach to screening for important interaction terms is to use nested statistical models. The chapter presents a way to search through potential interaction terms when complete enumeration is practically possible. The interaction effect with the largest coefficient crossed the year built and the living area. The practical way to identify interactions use predictor importance information along with principles of hierarchy, sparsity, and heredity.