R help - Mar 2004 - regression problem

i need to know how to estimate a linear regression whose coefficients sum
to zero

Assuming that you want to estimate via least squares, you can
do something like this:

reg.coefsum <- function(x, y, start=coef(lm.fit(x, y)), coefsum=0, 
penalty=1000) {
        subfun.objective <- function(coef){
                sum((y - x %*% coef)^2) + abs(sum(coef)) * penalty
        }
        opt <- optim(start, subfun.objective, method='BFGS')
        ans <- list(coefficients=opt$par)
        ans
}

You can enhance the return value and make other improvements,
like check that the coefficient sum is accurate enough for you.

Patrick Burns

Burns Statistics
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

pnick at virgilio.it wrote:
>i need to know how to estimate a linear regression whose coefficients sum
>to zero
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
>
>  
>

Consider a regression equation say:-

Y=a+b1*X1+b2*X2+b3*X3 

if all the regression coefficients have to sum to 0 
then 

a+b1+b2+b3=0

i.e. 

b3=-a-b1-b2

Substituting this back into the regression equation we get 


Y=a(1-X3)+b1(X1-X3)+b2(X2-X3)

All you need to do then is to create the new input variables say 

Z1=1-X3, Z2=X1-X3, Z3=X2-X3

so that 

Y=a*Z1+b1*Z2+b*Z3

You can parameterise a,b1 and b2 directly by fitting a linear model with no
intercept term 

you can then calculate b3 from b3=-a-b1-b2 

This example will generalize to an arbitrary number of parameters..


Regards

Wayne

-----Original Message-----
From: Patrick Burns [mailto:pburns@pburns.seanet.com]
Sent: 26 March 2004 16:23
To: pnick@virgilio.it; 'r-help@stat.math.ethz.ch'
Subject: Re: [R] regression problem


Assuming that you want to estimate via least squares, you can
do something like this:

reg.coefsum <- function(x, y, start=coef(lm.fit(x, y)), coefsum=0, 
penalty=1000) {
        subfun.objective <- function(coef){
                sum((y - x %*% coef)^2) + abs(sum(coef)) * penalty
        }
        opt <- optim(start, subfun.objective, method='BFGS')
        ans <- list(coefficients=opt$par)
        ans
}

You can enhance the return value and make other improvements,
like check that the coefficient sum is accurate enough for you.

Patrick Burns

Burns Statistics
patrick@burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

pnick@virgilio.it wrote:
>i need to know how to estimate a linear regression whose coefficients sum
>to zero
>
>______________________________________________
>R-help@stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
>
>  
>
______________________________________________
R-help@stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html


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<pnick <at> virgilio.it> writes:
> 
> i need to know how to estimate a linear regression whose coefficients sum
> to zero
> 

Transform the model:

y = Xb + error

to

y = XPb + error 

where P is the projection onto the orthogonal complement of the vector 1.
Solve this regression for b and then Pb will be your desired coefficients.
In R this would be:

n <- ncol(X)
P <- diag(n)-matrix(1,n,n)/n
z <- lm(y ~.-1, data=(X%*%P))
b <- coef(z)
b[is.na(b)] <- 0
P %*% b