Constrained coefficients in lm (correction)

[Jorge Ivan Velez]

Dear list,

In my previous email, the model I'd like to estimate is
rea=a*st+b*mod+error, where a+b=1 and a,b>0. My apologies for the
misunderstanding.

Thanks for all your help,

Jorge


On Wed, Jul 23, 2008 at 3:35 PM, Jorge Ivan Velez <jorgeivanvelez@...>
wrote:

>
> Dear list,
>
> I have a data set which looks like myDF (see below) and I'd like to
> estimate the linear model rea=a*rea+b*mod+error, where a+b=1 and a,b>0. I
> tried
>
> mymodel=lm(rea~ st + mod-1, data=myDF)
> summary(mymodel)
>
> but I couldn't get what I'm looking for.  Also, I tried
> RSiteSearch("constrained coefficients in lm") which produces 20 hints, but
> they're not what I need.
>
> Any help would be appreciated.
>
> Thanks in advance,
>
>
> Jorge
>
>
> # Data set to estimate the model
> myDF=read.table(textConnection("rea     st      mod
>  14482734 14305907 14761000
>  14427969 14502228 14848024
>  14698723 14408264 14259492
>  15741064 14797138 14565303
>  15914249 16162714 14348592
>  16475594 15977623 15592229
>  17124613 16688456 14988151
>  17575281 17383822 15647240
>  17721548 17757635 15624907
>  18178273 17779858 15598802
>  18005810 18364233 16363321
>  18032618 17938963 16536844
>  17737470 18043063 17096089
>  17652014 17624039 17056355"),header=TRUE,sep="")
> closeAllConnections()
>
>
>

        [[alternative HTML version deleted]]

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[Horace Tso]

Take a look at the systemfit package. A constraint on a parameter, like the one you described, could be implemented using R*beta0 = q, where R is R.restr and q is q.restr in the function call. I haven't tried it but it's easy to test with some data.

Horace



-----Original Message-----
From: r-help-bounces@... [mailto:r-help-bounces@...] On Behalf Of Jorge Ivan Velez
Sent: Wednesday, July 23, 2008 12:39 PM
To: R mailing list
Subject: [R] Constrained coefficients in lm (correction)

Dear list,

In my previous email, the model I'd like to estimate is
rea=a*st+b*mod+error, where a+b=1 and a,b>0. My apologies for the
misunderstanding.

Thanks for all your help,

Jorge


On Wed, Jul 23, 2008 at 3:35 PM, Jorge Ivan Velez <jorgeivanvelez@...>
wrote:

>
> Dear list,
>
> I have a data set which looks like myDF (see below) and I'd like to
> estimate the linear model rea=a*rea+b*mod+error, where a+b=1 and a,b>0. I
> tried
>
> mymodel=lm(rea~ st + mod-1, data=myDF)
> summary(mymodel)
>
> but I couldn't get what I'm looking for.  Also, I tried
> RSiteSearch("constrained coefficients in lm") which produces 20 hints, but
> they're not what I need.
>
> Any help would be appreciated.
>
> Thanks in advance,
>
>
> Jorge
>
>
> # Data set to estimate the model
> myDF=read.table(textConnection("rea     st      mod
>  14482734 14305907 14761000
>  14427969 14502228 14848024
>  14698723 14408264 14259492
>  15741064 14797138 14565303
>  15914249 16162714 14348592
>  16475594 15977623 15592229
>  17124613 16688456 14988151
>  17575281 17383822 15647240
>  17721548 17757635 15624907
>  18178273 17779858 15598802
>  18005810 18364233 16363321
>  18032618 17938963 16536844
>  17737470 18043063 17096089
>  17652014 17624039 17056355"),header=TRUE,sep="")
> closeAllConnections()
>
>
>

        [[alternative HTML version deleted]]

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Moshe Olshansky-2]

This problem can be easily solved analytically:

we want to minimize sum(res(i) -a*st(i) -b*mod(i))^2 subject to a+b=1,a,b>=0, so we want to minimize

f(a) = sum((res(i)-mod(i)) - a*(st(i)-mod(i)))^2 for 0<=a<=1

Define Xi = res(i) - mod(i),  Yi = st(i) - mod(i), then

f(a) = sum(Xi - a*Yi)^2

f(0) = sum(Xi^2), f(1) = sum(Xi-Yi)^2, f'(a) = -2*sum(Yi*(Xi-aYi)), so

f'(a) = 0 for a* = sum(Xi*Yi)/sum(Yi^2)

So if 0 <= a* <= 1 then a* is the solution, otherwise take a=0 or a=1 depending on whether f(0) < f(1) or not.






--- On Thu, 24/7/08, Jorge Ivan Velez <jorgeivanvelez@...> wrote:

> From: Jorge Ivan Velez <jorgeivanvelez@...>
> Subject: [R] Constrained coefficients in lm (correction)
> To: "R mailing list" <r-help@...>
> Received: Thursday, 24 July, 2008, 5:39 AM
> Dear list,
>
> In my previous email, the model I'd like to estimate is
> rea=a*st+b*mod+error, where a+b=1 and a,b>0. My
> apologies for the
> misunderstanding.
>
> Thanks for all your help,
>
> Jorge
>
>
> On Wed, Jul 23, 2008 at 3:35 PM, Jorge Ivan Velez
> <jorgeivanvelez@...>
> wrote:
>
> >
> > Dear list,
> >
> > I have a data set which looks like myDF (see below)
> and I'd like to
> > estimate the linear model rea=a*rea+b*mod+error, where
> a+b=1 and a,b>0. I
> > tried
> >
> > mymodel=lm(rea~ st + mod-1, data=myDF)
> > summary(mymodel)
> >
> > but I couldn't get what I'm looking for.
> Also, I tried
> > RSiteSearch("constrained coefficients in
> lm") which produces 20 hints, but
> > they're not what I need.
> >
> > Any help would be appreciated.
> >
> > Thanks in advance,
> >
> >
> > Jorge
> >
> >
> > # Data set to estimate the model
> > myDF=read.table(textConnection("rea     st    
> mod
> >  14482734 14305907 14761000
> >  14427969 14502228 14848024
> >  14698723 14408264 14259492
> >  15741064 14797138 14565303
> >  15914249 16162714 14348592
> >  16475594 15977623 15592229
> >  17124613 16688456 14988151
> >  17575281 17383822 15647240
> >  17721548 17757635 15624907
> >  18178273 17779858 15598802
> >  18005810 18364233 16363321
> >  18032618 17938963 16536844
> >  17737470 18043063 17096089
> >  17652014 17624039
> 17056355"),header=TRUE,sep="")
> > closeAllConnections()
> >
> >
> >
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@... mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.

______________________________________________
R-help@... mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.