You can accommodate the constraints by, e.g., putting
c2 = pnorm(theta2)
c3 = pnorm(theta3)
x1 has a known coefficient (unity) so it becomes an offset. Essentially your
problem can be written
y1 = y-x1 = c1 + pnorm(theta2)*x2 - pnorm(theta3)*x3 + error
This is then a (pretty simple) non-linear regression which could be fitted
using, e.g. nls
If you could not rule out the possibility that the solution is on the boundary,
you could put c2 = (cos(theta2))^2, and the fitting procedure could take you
there. The solution is not unique, but the original coefficients, c2,c3, would
be unique, of course.
With just 6 observations and 4 parameters to estimate, you will need the model
to be an exceptionally close fitting one for the fit to have any credibility at
all.
Bill Venables.
________________________________________
From: r-help-boun...@r-project.org [r-help-boun...@r-project.org] On Behalf Of
Emmanuel Charpentier [charp...@bacbuc.dyndns.org]
Sent: 27 May 2009 17:05
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] Linear Regression with Constraints
Le mardi 26 mai 2009 à 14:11 -0400, Stu @ AGS a écrit :
> Hi!
> I am a bit new to R.
> I am looking for the right function to use for a multiple regression problem
> of the form:
>
> y = c1 + x1 + (c2 * x2) - (c3 * x3)
>
> Where c1, c2, and c3 are the desired regression coefficients that are
> subject to the following constraints:
>
> 0.0 < c2 < 1.0, and
> 0.0 < c3 < 1.0
Sounds rather like an in-the-closet Bayesian problem (with a very
strange prior...). Did you consider to submit it to WinBUGS (or JAGS) ?
If you still want a direct optimization, you could have started :
RSiteSearch("optimization constraint")
Which would have quickly led you to ask :
? constrOptim
> y, x1, x2, and x3 are observed data.
> I have a total of 6 rows of data in a data set.
??? I that's real-life data, I wonder what kind of situation forces you
to estimate 3+1 parameters (c1, c2, c3 and the residual, which is not
really a parameter) with 6 data points ? Your problem can be written as
a system of 6 linear equations with 3 unknowns (c1, c2, c3), leaving you
room to search in (a small piece of) R^3 (the residual is another way to
express your objective function, not an independent parameter).
Of course, if it's homework, get lost !
Emmanuel Charpentier
> Is "optim" in the stats package the right function to use?
> Also, I can't quite figure out how to specify the constraints.
> Thank you!
>
> -Stu
>
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