Constrained Generalized Additive Model
Extract the Best Fit Returned by the ShapeSelect Routine
Constrained Generalized Additive Model Fitting
Constrained Generalized Additive Mixed-Effects Model Fitting
Specify a Concave Shape-Restriction in a CGAM Formula
Specify a Convex Shape-Restriction in a CGAM Formula
Specify a Decreasing and Concave Shape-Restriction in a CGAM Formula
Specify a Decreasing and Convex Shape-Restriction in a CGAM Formula
Specify a Decreasing Shape-Restriction in a CGAM Formula
To Include a Non-Parametrically Modelled Predictor in a SHAPESELECT Fo...
Specify an Increasing and Concave Shape-Restriction in a CGAM Formula
Specify an Increasing and Convex Shape-Restriction in a CGAM Formula
Specify an Increasing Shape-Restriction in a CGAM Formula
Specify an Ordered Categorical Family in a CGAM Formula
Control Parameters for plotpersp.cgam
Create a 3D Plot for a CGAM Object
Predict Method for CGAM Fits
Specify a Doubly-Concave Shape-Restriction in a CGAM Formula
Specify a Smooth and Concave Shape-Restriction in a CGAM Formula
Specify a Doubly-convex Shape-Restriction in a CGAM Formula
Specify a Smooth and Convex Shape-Restriction in a CGAM Formula
Specify a Smooth, Decreasing and Concave Shape-Restriction in a CGAM F...
Specify a Smooth, Decreasing and Convex Shape-Restriction in a CGAM Fo...
Specify a Doubly-Decreasing Shape-Restriction in a CGAM Formula
Specify a Decreasing-Increasing Shape-Restriction in a CGAM Formula
Specify a Smooth and Decreasing Shape-Restriction in a CGAM Formula
Specify a Smooth, Increasing and Concave Shape-Restriction in a CGAM F...
Specify an Smooth, Increasing and Convex Shape-Restriction in a CGAM F...
Specify an Increasing-Decreasing Shape-Restriction in a CGAM Formula
Specify a Doubly-Increasing Shape-Restriction in a CGAM Formula
Specify a Smooth and Increasing Shape-Restriction in a CGAM Formula
Specify a Smooth Shape-Restriction in a CGAM Formula
To Include a Non-Parametrically Modelled Predictor in a SHAPESELECT Fo...
Variable and Shape Selection via Genetic Algorithm
Parametric Monotone/Quadratic vs Smooth Constrained Test
Specify a Tree-Ordering in a CGAM Formula
Specify an Umbrella-Ordering in a CGAM Formula
A constrained generalized additive model is fitted by the cgam routine. Given a set of predictors, each of which may have a shape or order restrictions, the maximum likelihood estimator for the constrained generalized additive model is found using an iteratively re-weighted cone projection algorithm. The ShapeSelect routine chooses a subset of predictor variables and describes the component relationships with the response. For each predictor, the user needs only specify a set of possible shape or order restrictions. A model selection method chooses the shapes and orderings of the relationships as well as the variables. The cone information criterion (CIC) is used to select the best combination of variables and shapes. A genetic algorithm may be used when the set of possible models is large. In addition, the cgam routine implements a two-dimensional isotonic regression using warped-plane splines without additivity assumptions. It can also fit a convex or concave regression surface with triangle splines without additivity assumptions. See Liao X, Meyer MC (2019)<doi:10.18637/jss.v089.i05> for more details.