isotone (version 1.1-1)

mregnn: Regression with Linear Inequality Restrictions on Predicted Values

Description

The package contains three functions for fitting regressions with inequality restrictions: mregnn is the most general one, allowing basically for any partial orders, mregnnM poses a monotone restriction on the fitted values, mregnnP restricts the predicted values to be positive. Monre details can be found below.

Usage

mregnn(x, y, a)
mregnnM(x, y)
mregnnP(x, y)

Value

xb

Predicted values.

lb

Solution of the dual problem.

f

Value of the target function

Arguments

x

Can be a spline basis.

y

Response.

a

Matrix containing order restrictions.

Details

These functions solve the problem $$ f(b) = \frac{1}{2}(y - Xb)'(y - Xb) $$ over all \(b\) for which \(A'Xb \geq 0\). \(A\) can be used require the transformation to be non-negative, or increasing, or satisfying any partial order.

References

de Leeuw, J. (2015). Regression with Linear Inequality Restrictions on Predicted Values. http://rpubs.com/deleeuw/78897.

Examples

## Compute the best fitting quadratic polynomial (in black) 
## and monotone quadratic polynomial (in blue)
set.seed(12345)
x <- outer(1:10,1:3,"^")
x <- apply(x,2,function(x)
x - mean(x))
x <- apply (x,2,function(x)
x / sqrt (sum(x ^ 2)))
y <- rowSums(x) + rnorm(10)
plot(x[,1], y, lwd = 3, col = "RED", xlab = "x", ylab = "P(x)")
o <- mregnnM(x,y)
lines(x[,1], o$xb, col = "BLUE", lwd = 2)
xb <- drop(x %*% qr.solve(x,y))
lines(x[,1],xb,col="BLACK", lwd = 2)

## same monotone model through basic mregnn()
difmat <- function (n) {
  m1 <- ifelse(outer(1:(n - 1),1:n,"-") == -1, 1, 0)
  m2 <- ifelse(outer(1:(n - 1),1:n,"-") == 0,-1, 0)
  return (m1 + m2)
}
a <- difmat(nrow(x))      ## order restriction
o2 <- mregnn(x, y, a)