Methodology for the partial linear generalized additive model is presented, where components for continuous predictors may be modeled with shape-constrained regression splines, and components for ordinal predictors may have partial orderings. The estimated mean function is obtained through a projection (or iteratively reweighted projections) onto a polyhedral convex cone; this is key for formally derived inference procedures. Pointwise confidence bands and hypothesis tests for the individual components, as well as a model selection method, are proposed. These methods are available in the R package cgam.
"A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions." Statist. Sci. 33 (4) 595 - 614, November 2018. https://doi.org/10.1214/18-STS671