[R] Multivariate regression with constraints

[Zhang Yanwei - Princeton-MRAm]

I should have stated this better.
I want to fit this bivariate regressions with weights as well as contemporaneous correlation. One should use the systemfit(method="SUR") to have the model include the comtemporaneous correlation. But how can I specify the weights in addition? Just divide all the terms in the first equation by sqrt(p1) and those in the second by sqrt(R1) and then fit the bivariate regression? Thanks.


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

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Zhang Yanwei - Princeton-MRAm
Sent: Friday, August 08, 2008 1:26 PM
To: Patrizio Frederic
Cc: r-help at r-project.org
Subject: Re: [R] Multivariate regression with constraints

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>
>
>
>        [[alternative HTML version deleted]]
>
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