cgam: An R Package for the Constrained Generalized Additive Model

Abstract

The cgam package contains routines to fit the generalized additive model where the components may be modeled with shape and smoothness assumptions. The main routine is cgam and nineteen symbolic routines are provided to indicate the relationship between the response and each predictor, which satisfies constraints such as monotonicity, convexity, their combinations, tree, and umbrella orderings. The user may specify constrained splines to fit the individual components for continuous predictors, and various types of orderings for the ordinal predictors. In addition, the user may specify parametrically modeled covariates. Two-way interactions between continuous variables, where the relationship with the response is constrained to be monotone, are modeled with "warpedplane splines." The set over which the likelihood is maximized is a polyhedral convex cone, and a least-squares solution is obtained by projecting the data vector onto the cone. For generalized models, the fit is obtained through iteratively re-weighted cone projections. The cone information criterion (CIC) is provided and may be used to compare fits for combinations of variables and shapes. The graphical routine plotpersp will plot an estimated mean surface for a selected pair of predictors, given an object fitted with cgam. This package is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=cgam.