R: Specify an Increasing and Concave Shape-Restriction in a...
incr.conc
R Documentation
Specify an Increasing and Concave Shape-Restriction in a SHAPEREG Formula
Description
A symbolic routine to define that the mean vector is increasing and concave in a predictor in a formula argument to coneproj.
Usage
incr.conc(x)
Arguments
x
A numeric predictor which has the same length as the response vector.
Details
"incr.conc" returns the vector "x" and imposes on it two attributes: name and shape.
The shape attribute is 7 ("increasing and concave"), and according to the value of the vector itself and this attribute, the cone edges of the cone generated by the constraint matrix, which constrains the relationship between the mean vector and "x" to be increasing and concave, will be made. The cone edges are a set of basis employed in the hinge algorithm.
Note that "incr.conc" does not make the corresponding cone edges itself. It sets things up to a subroutine called makedelta in coneproj.
See references cited in this section for more details.
Value
The vector x with two attributes, i.e., name: the name of x and shape: 7 ("increasing and concave").
Author(s)
Mary C. Meyer and Xiyue Liao
References
Meyer, M. C. (2013b) A simple new algorithm for quadratic programming with applications in statistics. Communications in Statistics 42(5), 1126–1139.
See Also
incr.conv, incr
Examples
data(cubic)
# extract x
x <- - cubic$x
# extract y
y <- - cubic$y
# regress y on x with the shape restriction: "increasing" and "concave"
ans <- shapereg(y ~ incr.conc(x))
# make a plot
par(mar = c(4, 4, 1, 1))
plot(x, y, cex = .7, xlab = "x", ylab = "y")
lines(x, fitted(ans), col = 2)
legend("topleft", bty = "n", "shapereg: increasing and concave fit", col = 2, lty = 1)