On Oct 31, 2010, at 12:54 PM, Spencer Graves wrote:
Have you tried the 'sos' package?
I have, and I am taking this opportunity to load it with my .Rprofile
to make it more accessible. It works very well. Very clean display. I
also have constructed a variant of RSiteSearch that I find more useful
than the current defaults.
rhelpSearch <- function(string,
restrict = c("Rhelp10", "Rhelp08", "Rhelp02",
"functions" ),
matchesPerPage = 100, ...) {
RSiteSearch(string=string,
restrict = restrict,
matchesPerPage = matchesPerPage, ...)}
install.packages('sos') # if not already installed
library(sos)
cr <- ???'constrained regression' # found 149 matches
summary(cr) # in 69 packages
cr # opens a table in a browser listing all 169 matches with links
to the help pages
However, I agree with Ravi Varadhan: I'd want to understand
the physical mechanism generating the data. If each is, for
example, a proportion, then I'd want to use logistic regression,
possible after some approximate logistic transformation of X1 and X2
that prevents logit(X) from going to +/-Inf. This is a different
model, but it achieves the need to avoid predictions of Y going
outside the range (0, 1).
No argument. I defer to both of your greater experiences in such
problems and your interest in educating us less knowledgeable users. I
also need to amend my suggested strategy in situations where a linear
model _might_ be appropriate, since I think the inclusion of the
surrogate variable in the solve.QP setup is very probably creating
confusion. After reconsideration I think one should keep the two
approaches separate. These are two approaches to the non-intercept
versions of the model that yield the same estimate (but only because
the constraints do not get invoked ):
> lm(medv~I(age-lstat) +offset(lstat) -1, data=Boston)
Call:
lm(formula = medv ~ I(age - lstat) + offset(lstat) - 1, data = Boston)
Coefficients:
I(age - lstat)
0.1163
> library(MASS) ## to access the Boston data
> designmat <- model.matrix(medv~age+lstat-1, data=Boston)
> Dmat <-crossprod(designmat, designmat); dvec <- crossprod(designmat,
+ Boston$medv)
> Amat <- cbind(1, diag(NROW(Dmat))); bvec <-
c(1,rep(0,NROW(Dmat))); meq <- 1
> library(quadprog);
> res <- solve.QP(Dmat, dvec, Amat, bvec, meq)
> zapsmall(res$solution) # zapsmall not really needed in this instance
[1] 0.1163065 0.8836935
--
David.
Spencer
On 10/31/2010 9:01 AM, David Winsemius wrote:
On Oct 31, 2010, at 2:44 AM, Jim Silverton wrote:
Hello everyone,
I have 3 variables Y, X1 and X2. Each variables lies between 0 and
1. I want
to do a constrained regression such that a>0 and (1-a) >0
for the model:
Y = a*X1 + (1-a)*X2
It would not accomplish the constraint that a > 0 but you could
accomplish the other constraint within an lm fit:
X3 <- X1-X2
lm(Y ~ X3 + offset(X2) )
Since beta1 is for the model Y ~ 1 + beta1(X1- X2) + 1*X2)
Y ~ intercept + beta1*X1 + (1 -beta1)*X2
... so beta1 is a.
In the case beta < 0 then I suppose a would be assigned 0. This
might be accomplished within an iterative calculation framework by
a large penalization for negative values. In a reply (1) to a
question by Carlos Alzola in 2008 on rhalp, Berwin Turlach offered
a solution to a similar problem ( sum(coef) == 1 AND coef non-
negative). Modifying his code to incorporate the above strategy
(and choosing two variables for which parameter values might be
inside the constraint boundaries) we get:
library(MASS) ## to access the Boston data
designmat <- model.matrix(medv~I(age-lstat) +offset(lstat),
data=Boston)
Dmat <-crossprod(designmat, designmat); dvec <- crossprod(designmat,
Boston$medv)
Amat <- cbind(1, diag(NROW(Dmat)))
bvec <- c(1,rep(0,NROW(Dmat)))
meq <- 1
library(quadprog)
res <- solve.QP(Dmat, dvec, Amat, bvec, meq)
> zapsmall(res$solution)
[1] 0.686547 0.313453
Turlach specifically advised against any interpretation of this
particular result which was only contructed to demonstrate the
mathematical mechanics.
I tried the help on the constrained regression in R but I concede
that it
was not helpful.
I must not have that package installed because I got nothing that
appeared to be useful with ??"constrained regression" .
David Winsemius, MD
West Hartford, CT
1) http://finzi.psych.upenn.edu/Rhelp10/2008-March/155990.html
______________________________________________
David Winsemius, MD
West Hartford, CT
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