By George J. Knafl, Kai Ding
This publication offers equipment for investigating even if relationships are linear or nonlinear and for adaptively becoming acceptable versions after they are nonlinear. information analysts will the way to comprise nonlinearity in a single or extra predictor variables into regression types for various sorts of consequence variables. Such nonlinear dependence is usually now not thought of in utilized examine, but nonlinear relationships are universal and so must be addressed. a typical linear research can produce deceptive conclusions, whereas a nonlinear research promises novel insights into information, no longer differently attainable.
A number of examples of the advantages of modeling nonlinear relationships are provided during the ebook. equipment are coated utilizing what are referred to as fractional polynomials in accordance with real-valued strength ameliorations of basic predictor variables mixed with version choice in line with probability cross-validation. The publication covers the right way to formulate and behavior such adaptive fractional polynomial modeling within the regular, logistic, and Poisson regression contexts with non-stop, discrete, and counts results, respectively, both univariate or multivariate. The publication additionally offers a comparability of adaptive modeling to generalized additive modeling (GAM) and a number of adaptive regression splines (MARS) for univariate results.
The authors have created custom-made SAS macros to be used in carrying out adaptive regression modeling. those macros and code for undertaking the analyses mentioned within the e-book can be found throughout the first author's site and on-line through the book’s Springer site. unique descriptions of ways to take advantage of those macros and interpret their output look in the course of the booklet. those equipment should be applied utilizing different courses.
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Additional resources for Adaptive Regression for Modeling Nonlinear Relationships
Nilson, E. , & Walsh, J. L. (1967). The theory of splines and their applications. New York: Academic Press. Burman, P. (1989). A comparative study of ordinary cross-validation, ν-fold cross-validation and the repeated learning-testing methods. Biometrika, 76, 503–514. Cleveland, W. , Devlin, S. , & Gross, E. (1988). Regression by local fitting. Journal of Econometrics, 37, 87–114. , & Everitt, B. S. (2006). Statistical analysis of medical data using SAS. Boca Raton, FL: Chapman & Hall/CRC. Diggle, P.
3 for an example based on a real, non-simulated data set), and so unrestricted real valued powers are considered in the analyses reported in this book. Royston and Sauerbrei (2008) only addressed fractional polynomial modeling of means while fractional polynomials are also used in this book to model variances/dispersions as well as means. They also only considered modeling of univariate outcomes (except for a brief treatment of multi-level models in their Sect. 3) while both univariate and multivariate outcomes are addressed in this book.
Primary predictors generating distinctly inferior LCV scores (as determined by the associated tolerance parameter) at some stage of the expansion are dropped from further consideration. The expansion stops when the next transform to add to the model would reduce the LCV score by more than a tolerable amount (as determined by the expansion stopping tolerance parameter) or when all primary predictors have been dropped from consideration for expanding the model. The expansion can optionally also generate geometric combinations consisting of products of powers of primary predictors generalizing standard interactions (see Sect.
Adaptive Regression for Modeling Nonlinear Relationships by George J. Knafl, Kai Ding