ShapeChange (version 1.5)

tp: Specify a Unimodal Category in a CHANGEPT Formula

Description

A symbolic routine to define that the underlying mean curve is unimodal, i.e., it has a turn-around point, in the formula argument to changept.

Usage

tp(x, sh = 1)

Value

"tp" returns the vector "x" with three attributes, i.e., nm: the name of x; categ: the category of the change-point, "mode"; sh: the shape constraint on the estimated curve: \(1\) (increasing-decreasing) or \(-1\) (decreasing-increasing).

The nm and categ attributes are used in the plot routine; the sh attribute is used to set up a shape-constrained regression.

Arguments

x

The predictor vector.

sh

If sh is \(1\), then the estimated curve is increasing-decreasing; if sh is \(-1\), it is decreasing-increasing.

Author

Xiyue Liao

See Also

ip, jp

Examples

  # the underlying mean curve is unimodal with a mode at .8 
  n = 100
  x = seq(1/n, 1, length = n)

  # a categorical covariate z with two levels (0 and 1) 
  z = rep(0:1, 50)

  set.seed(123)
  y = 30 * x^4 * (1 - x) + (z == 1) * .5 + rnorm(n, sd = 1)
  ans = changept(y ~ tp(x) + factor(z), family = gaussian())

  plot(ans)
  legend("topleft", "constrained fit for z == 1", bty = "n", col = "skyblue", lty = 2, lwd = 2)