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Adaptive Regression for Modeling Nonlinear RelationshipsMultivariate Adaptive Regression Spline Modeling

Adaptive Regression for Modeling Nonlinear Relationships: Multivariate Adaptive Regression Spline... [This chapter demonstrates multivariate adaptive regression splines (MARS) for modeling of means of continuous outcomes treated as independent and normally distributed with constant variances as in linear regression and of logits (log odds) of means of dichotomous discrete outcomes with unit dispersions as in logistic regression. MARS models provide an alternative to fractional polynomial models for modeling nonlinear relationships between univariate outcomes and predictors, and so MARS models for these two cases are compared to adaptive fractional polynomial models. Poisson regression is not considered for brevity. MARS models can be also adjusted by adaptively power transforming their splines. Example analyses are provided of the univariate continuous outcome death rate per 100,000 in terms of available predictors as also addressed in Chaps. 2, 3, 16 and 17 and the univariate dichotomous outcome a high mercury level in fish over 1.0 ppm versus a lower level in terms of available predictors as also addressed in Chaps. 8, 9, 16 and 17.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Adaptive Regression for Modeling Nonlinear RelationshipsMultivariate Adaptive Regression Spline Modeling

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-33944-3
Pages
329 –338
DOI
10.1007/978-3-319-33946-7_18
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter demonstrates multivariate adaptive regression splines (MARS) for modeling of means of continuous outcomes treated as independent and normally distributed with constant variances as in linear regression and of logits (log odds) of means of dichotomous discrete outcomes with unit dispersions as in logistic regression. MARS models provide an alternative to fractional polynomial models for modeling nonlinear relationships between univariate outcomes and predictors, and so MARS models for these two cases are compared to adaptive fractional polynomial models. Poisson regression is not considered for brevity. MARS models can be also adjusted by adaptively power transforming their splines. Example analyses are provided of the univariate continuous outcome death rate per 100,000 in terms of available predictors as also addressed in Chaps. 2, 3, 16 and 17 and the univariate dichotomous outcome a high mercury level in fish over 1.0 ppm versus a lower level in terms of available predictors as also addressed in Chaps. 8, 9, 16 and 17.]

Published: Sep 21, 2016

Keywords: Mercury Level; Dichotomous Outcome; Multivariate Adaptive Regression Spline Spline; Substantial Benefit; Adaptive Model

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