[R] why does lm() not allow for negative weights?

[Jens Hainmueller]

Thanks Duncan Murdoch,

> > Why do commonly used estimator functions (such as lm(), 
> > glm(), etc.) 
> > not allow negative case weights?
 
> Residual sums of squares (or deviances) could be negative 
> with negative case weights.  This doesn't seem like a good 
> thing:  would you really want the fit to be far from those points?

Yes, this is actually what I want for this particular estimator. But I can
see now why this generally doesn't seem like a a good idea.

Best,
Jens



> -----Ursprüngliche Nachricht-----
> Von: Duncan Murdoch [mailto:murdoch at stats.uwo.ca] 
> Gesendet: Friday, August 04, 2006 7:36 PM
> An: Jens Hainmueller
> Cc: r-help at stat.math.ethz.ch
> Betreff: Re: [R] why does lm() not allow for negative weights?
> 
> On 8/4/2006 1:26 PM, Jens Hainmueller wrote:
> > Dear List,
> > 

> 

> 
>  > I suspect that there is a good reason for this.
> > Yet, I can see reasonable cases when one wants to use 
> negative case weights.
> > 
> > Take lm() for example:
> > 
> > ###
> > 
> > n <- 20
> > Y <- rnorm(n)
> > X <- cbind(rep(1,n),runif(n),rnorm(n)) Weights <- rnorm(n) 
> # Includes 
> > Pos and Neg Weights Weights
> > 
> > # Now do Weighted LS and get beta coeffs:
> > b <- solve(t(X)%*%diag(Weights)%*%X) %*% t(X) %*% diag(Weights)%*%Y
> 
> That formula does not necessarily give least squares 
> estimates in the case where weights might be negative.  For 
> example, with a single observation y, a single parameter mu, 
> design matrix X = 1, and weight -1, that formula becomes
> 
> b <- y,
> 
> but that is the worst possible estimator in a least squares 
> sense.  The residual sum of squares can be made arbitrarily 
> large and negative by setting b to a large value.
> 
> Duncan Murdoch
> 
> 
> > b
> > 
> > # This seems like a valid model, but when I try lm(Y ~ 
> > X[,2:3],weights=Weights)
> > 
> > # I get: "missing or negative weights not allowed"
> > 
> > ###
> > 
> > What is the rationale for not allowing negative weights? I 
> ask this, 
> > because I am currently trying to implement a (two stage) estimator 
> > into R that involves negative case weights. Weights are 
> generated in 
> > the first stage, so it would be nice if I could use canned 
> functions 
> > such as
> > lm(,weights=Weights) in the second stage.
> > 
> > Thank you for your help.
> > 
> > Best,
> > Jens
> > 
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