Adaptive Regression for Modeling Nonlinear Relationships

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This book presents methods for investigating linear versus nonlinear relationships and adaptively fitting appropriate models when nonlinearities are present. Data analysts will learn to incorporate nonlinearity in predictor variables into regression models for various outcome types. Nonlinear relationships, often overlooked in applied research, are common and warrant attention, as standard linear analyses can lead to misleading conclusions. Nonlinear analyses can yield insights not achievable through linear methods. Throughout the book, various examples illustrate the advantages of modeling nonlinear relationships. The techniques discussed involve fractional polynomials based on real-valued power transformations of primary predictor variables, along with model selection using likelihood cross-validation. The book details adaptive fractional polynomial modeling within standard, logistic, and Poisson regression contexts for continuous, discrete, and count outcomes, both univariate and multivariate. It also compares adaptive modeling to generalized additive modeling (GAM) and multiple adaptive regression splines (MARS) for univariate outcomes. Customized SAS macros for conducting adaptive regression modeling are provided, with code available on the first author's website and the book’s Springer page. Detailed instructions on using these macros and interpreting their outputs are included, and the methods can be implemented using o