A Framework for Comprehensive Model and Variable Selection

Music City Center 

We propose a framework for choosing variables and relationships without assuming additivity or parametric forms. The relationships between the response and each of the continuous predictors are modeled with regression splines and assumed to be smooth and one of the following: increasing, decreasing, convex, concave, or a combination of monotonicity and convexity. The eight shapes include a wide range of popular parametric functions such as linear, quadratic, exponential, etc., and the set of choices is appropriate if the component functions "do not wiggle." An ordinal predictor can have its set of possible orderings, such as increasing, decreasing, tree or umbrella orderings, no ordering, or constant. Interactions between continuous predictors will be modeled as multi-dimensional warped-plane spline surfaces, where the same possibilities for shapes are considered. We propose combining stepwise selection methods with information criteria, LASSO ideas, and model selection using a genetic algorithm.

variable selection

shape and order constraints

nonparametric

nonadditive 

Section on Statistical Computing