mono.con: Monotonicity constraints for a cubic regression spline
In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

mono.con

R Documentation

Monotonicity constraints for a cubic regression spline

Description

Finds linear constraints sufficient for monotonicity (and optionally upper and/or lower boundedness) of a cubic regression spline. The basis representation assumed is that given by the gam, "cr" basis: that is the spline has a set of knots, which have fixed x values, but the y values of which constitute the parameters of the spline.

Usage

mono.con(x,up=TRUE,lower=NA,upper=NA)

Arguments

`x`	The array of knot locations.
`up`	If `TRUE` then the constraints imply increase, if `FALSE` then decrease.
`lower`	This specifies the lower bound on the spline unless it is `NA` in which case no lower bound is imposed.
`upper`	This specifies the upper bound on the spline unless it is `NA` in which case no upper bound is imposed.

Details

Consider the natural cubic spline passing through the points \{x_i,p_i:i=1 \ldots n \} . Then it is possible to find a relatively small set of linear constraints on \mathbf{p} sufficient to ensure monotonicity (and bounds if required): \mathbf{Ap}\ge\mathbf{b}. Details are given in Wood (1994).