cgam (version 1.4)

s.incr: Specify a Smooth and Increasing Shape-Restriction in a CGAM Formula

Description

A symbolic routine to define that the systematic component $\eta$ is smooth and increasing in a predictor in a formula argument to cgam. This is the smooth version.

Usage

s.incr(x, numknots = 0, knots = 0, space = "Q")

Arguments

x

A numeric predictor which has the same length as the response vector.

numknots

The number of knots used to constrain $x$. It will not be used if the user specifies the knots argument. The default is numknots = $0$.

knots

The knots used to constrain $x$. User-defined knots will be used when given. Otherwise, numknots and space will be used to create knots. The default is knots = $0$.

space

A character specifying the method to create knots. It will not be used if the user specifies the knots argument. If space == "E", then equally spaced knots will be created; if space == "Q", then a vector of equal $x$ quantiles will be created bas

Value

• The vector x with five attributes, i.e., name: the name of x; shape: 9("smooth and increasing"); numknots: the numknots argument in "s.incr"; knots: the knots argument in "s.incr"; space: the space argument in "s.incr".

Details

"s.incr" returns the vector "x" and imposes on it five attributes: name, shape, numknots, knots and space. The name attribute is used in the subroutine plotpersp; the numknots, knots and space attributes are the same as the numknots, knots and space arguments in "s.incr"; the shape attribute is 9("smooth and increasing"). According to the value of the vector itself and its shape, numknots, knots and space attributes, the cone edges will be made by I-spline basis functions in Meyer (2008). The cone edges are a set of basis employed in the hinge algorithm.

Note that "s.incr" does not make the corresponding cone edges itself. It sets things up to a subroutine called makedelta in cgam.

See references cited in this section for more details.

References

Meyer, M. C. (2013b) A simple new algorithm for quadratic programming with applications in statistics. Communications in Statistics 42(5), 1126--1139.

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

See Also

incr

Examples

data(cubic)

  # extract x
  x <- cubic$x

  # extract y
  y <- cubic$y

  # regress y on x with the shape restriction: "smooth and increasing"
  ans <- cgam(y ~ s.incr(x))
  knots <- ans$knots[[1]]

  # make a plot
  par(mar = c(4, 4, 1, 1))
  plot(x, y, cex = .7, xlab = "x", ylab = "y")
  lines(x, ans$muhat, col = 2)
  legend("topleft", bty = "n", "smooth and increasing fit", col = 2, lty = 1)
  legend(1.7, 9.2, bty = "o", "knots", pch = "X")
  points(knots, 1:length(knots)*0+min(y), pch = "X")