ShapeChange (version 1.5)

ip: Specify an Inflection-Point Category in a CHANGEPT Formula

Description

A symbolic routine to define that the underlying mean curve has an inflection-point in the formula argument to changept.

Usage

ip(x, sh = 1)

Value

The vector "x" with three attributes, i.e., nm: the name of x; categ: the category of the change-point, "inflect"; sh: the shape constraint on the estimated curve: \(1\) (convex-concave) or \(-1\) (concave-convex).

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 convex-concave; if sh is \(-1\), it is concave-convex. Note that when the response is binomial or Poisson, sh is always \(1\). The default is sh = \(1\).

Author

Xiyue Liao

See Also

tp, jp

Examples

  # the underlying mean curve is a non-decreasing growth curve 
  # with an inflection point at .5 and it is convex-concave
  n = 100
  x = seq(1/n, 1, length = n)

  set.seed(123)
  y = 5 * (1 + tanh(10 * (x - .5)))  + rnorm(n, sd = 1)
  ans = changept(y ~ ip(x, sh = 1), fir = TRUE)

  plot(ans)