iso_pen: Penalized Isotonic Regression in one and two dimensions

In isotonic.pen: Penalized Isotonic Regression in one and two dimensions

Description

Given a response vector y and a predictor matrix xmat with (one or two) columns, the isotonic regression estimator is returned, with the usual (complete or partial) ordering.

Usage

iso_pen(y, xmat, wt = 1, pen = TRUE, default = TRUE, lambda = 0, nsim = 0, alpha = 0.05)

Arguments

y	The response vector of length n
xmat	Either a one-dimensional predictor vector or an n by 2 matrix of two-dimensional predictor values.
wt	Optional weights – a positive vector of length n.
pen	If pen=FALSE, no penalty is applied to tame spiking. Default is pen=TRUE.
default	If default=FALSE, the user must specify a penalty value.
lambda	Optional penalty. If pen=0, an unpenalized isotonic regression is performed. If not supplied a default penalty is used.
nsim	The number of simulations used in the computation of approximate point-wise confidence intervals. The default is nsim=0, and no confidence intervals are returned.
alpha	The confidence level of the confidence intervals. Default is alpha=.05 (i.e., 95 percent confidence intervals)

Details

The least-squares isotonic regression is computed using the coneA function of the R package coneproj.

Value

fit	The fitted values; i.e., the estimated expected response
sighat	The estimated model standard deviation
upper	The upper points of the point-wise confidence intervals, returned if nsim>0
lower	The lower points of the point-wise confidence intervals, returned if nsim>0

Author(s)

Mary C Meyer, Professor, Department of Statistics, Colorado State University

References

Meyer, M.C. (2013) A Simple New Algorithm for Quadratic Programming with Applications in Statistics, Communications in Statistics, 42(5), 1126-1139.

Examples

### plot the estimated expected lung volume of children given age and height
data(FEV)
x1=FEV[,1]   ## age
x2=FEV[,3]   ## height
y=FEV[,2]
ans=iso_pen(y,cbind(x1,x2))
persp(ans$xg1,ans$xg2,ans$xgmat,th=-40,tick="detailed",xlab="age",ylab="height",zlab="FEV")

Example output

Loading required package: coneproj
Loading required package: Matrix

isotonic.pen documentation built on May 2, 2019, 6:51 a.m.