Test null hypothesis of constant regression function against a general, high-dimensional alternative

Description

Given a response and 1-3 predictors, the function will test the null hypothesis that the response and predictors are not related (i.e., regression function is constant), against the alternative that the regression function is monotone in each of the predictors. For one predictor, the alternative set is a double cone; for two predictors the alternative set is a quadruple cone, and an octuple cone alternative is used when there are three predictors.

Usage

agconst(y, xmat, nsim = 1000)

Arguments

Details

For one predictor, the set of non-decreasing regression functions can be described by an n-dimensional convex polyhedral cone, and the set of non-increasing regression functions is the "opposite" cone. The one-dimensional null space is the intersection of these cones. For two predictors, the alternative set consists of four cones, defined by combinations of increasing/decreasing assumptions, and for three predictors we have eight cones.

Value

Author(s)

Mary C Meyer and Bodhisattva Sen

References

TBA

See Also

doubconetest,partlintest

Examples

	n=100
	x1=runif(n);x2=runif(n);xmat=cbind(x1,x2)
	mu=1:n;for(i in 1:n){mu[i]=20*max(x1[i]-2/3,x2[i]-2/3,0)^2}
	x1g=1:21/22;x2g=x1g
	par(mar=c(1,1,1,1))
	y=mu+rnorm(n)
	ans=agconst(y,xmat,nsim=0)
	grfit=matrix(nrow=21,ncol=21)
	for(i in 1:21){for(j in 1:21){
			if(sum(x1>=x1g[i]&x2>=x2g[j])>0){
				if(sum(x1<=x1g[i]&x2<=x2g[j])>0){
					f1=min(ans$thetahat[x1>=x1g[i]&x2>=x2g[j]])
					f2=max(ans$thetahat[x1<=x1g[i]&x2<=x2g[j]])
					grfit[i,j]=(f1+f2)/2
				}else{
					grfit[i,j]=min(ans$thetahat)
				}
			}else{grfit[i,j]=max(ans$thetahat)}
	}}
	persp(x1g,x2g,grfit,th=-50,tick="detailed",xlab="x1",ylab="x2",zlab="mu")
##to get p-value for test against constant function:
#	ans=agconst(y,xmat,nsim=1000)
#	ans$pval

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DoubleCone)
Loading required package: coneproj
Loading required package: Matrix
Loading required package: MASS
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DoubleCone/agconst.Rd_%03d_medium.png", width=480, height=480)
> ### Name: agconst
> ### Title: Test null hypothesis of constant regression function against a
> ###   general, high-dimensional alternative
> ### Aliases: agconst
> ### Keywords: multiple isotonic regression model test
> 
> ### ** Examples
> 
> 	n=100
> 	x1=runif(n);x2=runif(n);xmat=cbind(x1,x2)
> 	mu=1:n;for(i in 1:n){mu[i]=20*max(x1[i]-2/3,x2[i]-2/3,0)^2}
> 	x1g=1:21/22;x2g=x1g
> 	par(mar=c(1,1,1,1))
> 	y=mu+rnorm(n)
> 	ans=agconst(y,xmat,nsim=0)
> 	grfit=matrix(nrow=21,ncol=21)
> 	for(i in 1:21){for(j in 1:21){
+ 			if(sum(x1>=x1g[i]&x2>=x2g[j])>0){
+ 				if(sum(x1<=x1g[i]&x2<=x2g[j])>0){
+ 					f1=min(ans$thetahat[x1>=x1g[i]&x2>=x2g[j]])
+ 					f2=max(ans$thetahat[x1<=x1g[i]&x2<=x2g[j]])
+ 					grfit[i,j]=(f1+f2)/2
+ 				}else{
+ 					grfit[i,j]=min(ans$thetahat)
+ 				}
+ 			}else{grfit[i,j]=max(ans$thetahat)}
+ 	}}
> 	persp(x1g,x2g,grfit,th=-50,tick="detailed",xlab="x1",ylab="x2",zlab="mu")
> ##to get p-value for test against constant function:
> #	ans=agconst(y,xmat,nsim=1000)
> #	ans$pval
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>