[R] Multivariate Regression with Weights

[Arne Henningsen]

> -----Original Message-----
> From: markleeds at verizon.net [mailto:markleeds at verizon.net]
> Sent: Monday, August 04, 2008 5:15 PM
> To: Zhang Yanwei - Princeton-MRAm
> Subject: RE: [R] Multivariate Regression with Weights
>
>   the systemfit package can do that and the documentation is quite nice
> also.

The systemfit() function of the systemfit package can use different weights 
for the different *equations* but NOT different weights for different 
*observations* (if argument "method" is "SUR", "WLS", "3SLS" or "W2SLS").
I guess that you can divide the first equation by x_1 and the second equation 
by x_2 to obtain
   y_1^* = 1 + x_2^* + e_1^*
   y_2^* = 1 + x_1^* + e_2^*
with 
   y_1^* = y_1 / x_1
   x_2^* = x_2 / x_1
   e_1^* = e_1 / x_1
   y_2^* = y_2 / x_2
   x_1^* = x_1 / x_2
   e_2^* = e_2 / x_2

In this case, you should have homoscedastic error terms. Hence, you can use 
systemfit to estimate the system of the modified equations.

> On Mon, Aug 4, 2008 at  4:39 PM, Zhang Yanwei - Princeton-MRAm wrote:
> > Hi all,
> >   I'd like to fit a multivariate regression with the variance of the
> > error term porportional to the predictors, like the WLS in the
> > univariate case.
> >   y_1~x_1+x_2
> >   y_2~x_1+x_2
> >   var(y_1)=x_1*sigma_1^2

I guess that you mean var(e_1). Right?

> >   var(y_2)=x_2*sigma_2^2
> >   cov(y_1,y_2)=sqrt(x_1*x_2)*sigma_12^2
> >
> >  How can I specify this in R? Is there a corresponding function to the
> > univariate specification lm(y~x,weights=x)?? Thanks.

Unfortunately, systemfit has not (yet) a "weights" argument. (If you add this 
feature, I would be happy if you send me the code that I can include this 
feature in the official version.)

Best wishes,
Arne

-- 
Arne Henningsen
arne.henningsen at googlemail.com
http://www.arne-henningsen.name
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