nnreg {lazy.stat}

R Documentation

Non-negative or Ordered Regression

Description

This function fits the regression model y = X %*% beta + eps with the constraints:
1) beta[j] > 0, j=omit+1, omit+2, ...., ncol(X)
or
2) beta[1] < beta[2] < ... beta[ncol(X)]

Usage

nnreg(
  y,
  X,
  beta = NULL,
  ms = 0,
  omit = 0,
  init = 1,
  maxiter = 50,
  maxiters = 10,
  eps = 1e-06,
  epsg = 1e-06,
  ymin = NA,
  ymax = NA,
  print = 1
)

Arguments

y	Vector of criterion variable
X	Matrix of regressor variables
beta	The initial value of beta
ms	= 1 to enforce the order constraints on beta This should be used in conjunction with monotone spline.
omit	Constraints will not be enforced on beta[1:omit]
init	= 0 to use random initial when beta=NULL otherwize, a rational initial will be used.
maxiter	# of iterations
maxiters	# of step size halving for GN
eps	Criterion of convergence for the relative improvement of rss
epsg	Criterion for the maximum absolute value of the gradient
ymin	Not yet available
ymax	Not yet available
print	= 1 to print the result

Details

Non-negative beta constraints 1:
beta[(omit+1):nq] > 0
can be enfoeced by reparametrizing
beta[(omit+1):nq] = exp(c)
where c is not restricted.

Increasing beta constraints 2:
beta[j] <= beta[j+1]
can be enfoeced as follows:
Let
beta = G %*% b
where G is the lower triangular design matrix consisting of ones
and
b[2:nq] > 0
That is,
beta = G %*% b = G %*% c(b1,exp(c))
or
y = X %*% G %*% b + error, with b[2:nq] > 0
The problem is now translated to the non-negative constraint.

Value

A list of:
beta Regression coefficient vector satisfying the constraint.
g Final gradient value.
rss Residual Sum of Squares minimized.
maxag Maximum of the absolute values of gradient.
bc vector of c( beta[1:omit], c[(omit+1):length(beta)]
omit conv = 1 to indicate convergence.
rssimpr Relative improvement of rss.
iter # of iterations required for convergence.

Note that, when ms=1, beta can be calculated as
b[1] <- bc[1]; b[2:nq] <- exp(bc[2:nq]); beta <- G %*% b
where G is the lower-half triangular matrix consisting of 1s.

Examples

set.seed(1701)
n=50; nq=9
X=cbind(1,matrix(rnorm(n*(nq-1)),n))
beta=(1:nq-1.8); beta=beta/max(beta)
y=X%*%beta + 0.7*rnorm(n)
# Simple non-negative regression
res=nnreg( y, X, print=1 )
# Enforce order restrictions on beta coef.
res=nnreg( y, X, ms=1, print=1 )

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