[R] Multivariate regression with constraints

[Zhang Yanwei - Princeton-MRAm]

Thanks.
If I set the coefficient of p1 equal to zero, then I only have three parameters left in the model. Suppose e is the residual matrix for this regression, 2 by 2 here. Is the covariance matrix for the residuals, 2 by 2, still estimated by t(e)%*%e/(n-3), where n is the number of observations?

Also, I want to specify different weights for each of the two equations. For example, the first regression weighted by p1, and the second by R1. How can I do that using systemfit? The systemfit("SUR") seems to deal with this problem, but it does not allow one to set the weights explicitely. I wonder if you would help me out on that.

Thanks a lot. Really appreiciate.


Sincerely,
Yanwei Zhang
Department of Actuarial Research and Modeling
Munich Re America
Tel: 609-275-2176
Email: yzhang at munichreamerica.com

-----Original Message-----
From: Patrizio Frederic [mailto:frederic.patrizio at gmail.com]
Sent: Friday, August 08, 2008 12:57 PM
To: Zhang Yanwei - Princeton-MRAm
Cc: r-help at r-project.org
Subject: Re: [R] Multivariate regression with constraints

Hi Zhang ,
take a look to sur package

http://www.systemfit.org/

regards,

Patrizio Frederic

+-------------------------------------------------
| Patrizio Frederic
| Research associate in Statistics,
| Department of Economics,
| University of Modena and Reggio Emilia, Via Berengario 51, 41100
| Modena, Italy
|
| tel:  +39 059 205 6727
| fax:  +39 059 205 6947
| mail: patrizio.frederic at unimore.it
+-------------------------------------------------


2008/8/8 Zhang Yanwei - Princeton-MRAm <YZhang at munichreamerica.com>:
> Hi all,
>   I am running a bivariate regression with the following:
>
> p1=c(184,155,676,67,922,22,76,24,39)
> p2=c(1845,1483,2287,367,1693,488,435,1782,745)
> I1=c(1530,1505,2505,204,2285,269,1271,298,2023)
> I2=c(8238,6247,6150,2748,4361,5549,2657,3533,5415)
> R1=I1-p1
> R2=I2-p2
>
> x1=cbind(p1,R1)
> y1=cbind(p2,R2)
>
> fit1=lm(y1~-1+x1)
> summary(fit1)
>
> Response 2:
> Coefficients:
>     Estimate Std. Error t value Pr(>|t|)
> x1p1  -1.4969     2.7004  -0.554  0.59662
> x1R1   3.0937     0.8366   3.698  0.00767 **
>
>
> One can see that in the second regression, i.e. R2~-1+p1+R1,  the coefficient for p1 is not significant. I wonder if I can run this bivariate regression again with the constraint that the coefficient for p1 in the second regression equation  is zero? Thanks a lot.
>
> Sincerely,
> Yanwei Zhang
> Department of Actuarial Research and Modeling Munich Re America
> Tel: 609-275-2176
> Email: yzhang at munichreamerica.com<mailto:yzhang at munichreamerica.com>
>
>
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>
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