bcgam (version 1.0)

sm.conc: Specify a smooth and concave shape-restriction in a bcgam formula

Description

A symbolic routine to define that the systematic component \(\eta\) is smooth and concave with respect to a predictor in a bcgam formula.

Usage

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

Arguments

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".

Value

x

The numeric predictor x.

Details

sm.conc returns the vector x and assigns five attributes to it: name, shape (4 for "smooth and concave"), numknots, knots and space.

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

References

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

Examples

# NOT RUN {
data(duncan)

prestige <- duncan$prestige

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

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

# check attributes
attributes(prestige.smconc)
# }