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Adaptive Regression for Modeling Nonlinear RelationshipsGeneralized Additive Modeling

Adaptive Regression for Modeling Nonlinear Relationships: Generalized Additive Modeling [This chapter formulates and demonstrates generalized additive models (GAMs) for means of continuous outcomes treated as independent and normally distributed with constant variances as in linear regression and for logits (log odds) of means of dichotomous discrete outcomes with unit dispersions as in logistic regression. GAMs provide an alternative to fractional polynomial models for modeling nonlinear relationships between univariate outcomes and predictors, and so GAMs for these two cases are also compared to adaptive fractional polynomial models. Poisson regression is not considered for brevity. Example analyses are provided of the univariate continuous outcome deathrate per 100,000 in terms of available predictors as also addressed in Chaps. 2, 3, 6 and 7 as well as 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 and 9.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Adaptive Regression for Modeling Nonlinear RelationshipsGeneralized Additive Modeling

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References (4)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-33944-3
Pages
299 –314
DOI
10.1007/978-3-319-33946-7_16
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter formulates and demonstrates generalized additive models (GAMs) for means of continuous outcomes treated as independent and normally distributed with constant variances as in linear regression and for logits (log odds) of means of dichotomous discrete outcomes with unit dispersions as in logistic regression. GAMs provide an alternative to fractional polynomial models for modeling nonlinear relationships between univariate outcomes and predictors, and so GAMs for these two cases are also compared to adaptive fractional polynomial models. Poisson regression is not considered for brevity. Example analyses are provided of the univariate continuous outcome deathrate per 100,000 in terms of available predictors as also addressed in Chaps. 2, 3, 6 and 7 as well as 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 and 9.]

Published: Sep 21, 2016

Keywords: Generalize Additive Model; Mercury Level; Dichotomous Outcome; Thin Plate Spline; Adaptive Model

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