iso_pen function

Penalized Isotonic Regression in one and two dimensions

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.

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.

Returns

• 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

References

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

Author(s)

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

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")