Multivariate Adaptive Regression Spline Modeling

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.