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Adaptive Regression for Modeling Nonlinear RelationshipsIntroduction

Adaptive Regression for Modeling Nonlinear Relationships: Introduction [Nonlinearity in predictor (or explanatory or independent) variables in regression models for different types of outcome (or response or dependent) variables is often not considered in applied research. While relationships can reasonably be treated as linear in some cases, it is not unusual for them to be distinctly nonlinear. A standard linear analysis in the latter cases can produce misleading conclusions while a nonlinear analysis can provide novel insights into data not otherwise possible. Methods are needed for deciding whether relationships are linear or nonlinear and for fitting appropriate models when they are nonlinear. Methods for these purposes are covered in this book using what are called fractional polynomials based on power transformations of primary predictor variables with real valued powers. An adaptive approach is used to construct fractional polynomial models based on heuristic (or rule-based) searches through power transforms of primary predictor variables. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in a variety of contexts including adaptive regression of continuous outcomes, adaptive logistic regression of dichotomous and polytomous outcomes with two or more values, and adaptive Poisson regression of count/rate outcomes. Power transformation of positive valued continuous outcomes is covered as well as modeling of variances/dispersions with fractional polynomials. The book also covers alternative approaches for modeling of nonlinear relationships including standard polynomials, generalized additive models (GAMs) computed using local regression (loess) and spline smoothing approaches (through SAS PROC GAM), and multivariate adaptive regression splines (MARS) models (through SAS PROC ADAPTIVEREG).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Adaptive Regression for Modeling Nonlinear RelationshipsIntroduction

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-33944-3
Pages
1 –8
DOI
10.1007/978-3-319-33946-7_1
Publisher site
See Chapter on Publisher Site

Abstract

[Nonlinearity in predictor (or explanatory or independent) variables in regression models for different types of outcome (or response or dependent) variables is often not considered in applied research. While relationships can reasonably be treated as linear in some cases, it is not unusual for them to be distinctly nonlinear. A standard linear analysis in the latter cases can produce misleading conclusions while a nonlinear analysis can provide novel insights into data not otherwise possible. Methods are needed for deciding whether relationships are linear or nonlinear and for fitting appropriate models when they are nonlinear. Methods for these purposes are covered in this book using what are called fractional polynomials based on power transformations of primary predictor variables with real valued powers. An adaptive approach is used to construct fractional polynomial models based on heuristic (or rule-based) searches through power transforms of primary predictor variables. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in a variety of contexts including adaptive regression of continuous outcomes, adaptive logistic regression of dichotomous and polytomous outcomes with two or more values, and adaptive Poisson regression of count/rate outcomes. Power transformation of positive valued continuous outcomes is covered as well as modeling of variances/dispersions with fractional polynomials. The book also covers alternative approaches for modeling of nonlinear relationships including standard polynomials, generalized additive models (GAMs) computed using local regression (loess) and spline smoothing approaches (through SAS PROC GAM), and multivariate adaptive regression splines (MARS) models (through SAS PROC ADAPTIVEREG).]

Published: Sep 21, 2016

Keywords: Polynomial Model; Multivariate Adaptive Regression Spline; Conditional Model; Adaptive Modeling; Primary Predictor

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