sm.decr.conc: Specify a smooth, decreasing and concave shape-restriction in...
In bcgam: Bayesian Constrained Generalised Linear Models

Description Usage Arguments Details Value Author(s) References Examples

A symbolic routine to define that the systematic component η is smooth, decreasing and concave with respect to a predictor in a bcgam formula.

1	sm.decr.conc(x, numknots = 0, knots = 0, space = "Q")

`x`	a numeric predictor of length n.
`numknots`	number of knots used to constrain `x`. It is ignored when the `knots` argument is specified by the user. If neither `numknots` nor `knots` are specified by the user, then `numknots` is floor{4+n^(1/7)}. The default is `0`.
`knots`	knots used to constrain `x`. If they are not specified by the user, then they will be automatically created based on `numknots` and `space`. The default is `0`.
`space`	a character specifying the method to create knots. It is ignored when the `knots` argument is specified by the user. If `space="E"`, then equally spaced knots will be created; if `space="Q"`, then a vector of equal quantiles will be created based on `x` with duplicate elements removed. The default is `"Q"`.

sm.decr.conc returns the vector x and assigns five attributes to it: name, shape (8 for "smooth, decreasing and concave"), numknots, knots and space.

This routine does not create the splines basis vectors by itself.

`x`	The numeric predictor `x`.

Cristian Oliva-Aviles and Mary C. Meyer

Meyer, M. C. (2008) Inference using shape-restricted regression splines. Annals of Applied Statistics 2(3), 1013-1033.

data(duncan)

prestige <- duncan$prestige

# specify knots
sm.decr.conc(prestige, knots=c(3,9,30,57,86,97))

# specify number of knots
prestige.smdecrconc <- sm.decr.conc(prestige, numknots=7)

# check attributes
attributes(prestige.smdecrconc)