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Re: st: Fitting a linear regression where coefficients are bounded proportions


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Fitting a linear regression where coefficients are bounded proportions
Date   Thu, 12 Dec 2013 10:43:58 +0000

This is, I know, not what you are asking but

y as a linear function of nine predictors

each coefficient being in the same interval

the coefficients summing to 1

sounds rather close to

y is the average of the predictors

as your coefficients must average 1/9 by your own rules.

This is all apart from some intercept (which you can always subtract
out, at least approximately). So, if I were reviewing/hearing about
your work I would ask for a graph of

y vs average of predictors

as giving an easy but possibly informative idea of your data. It might
also be a supplementary graph to throw light on your fitted
hyperplane, especially if the eventual fit is puzzling or problematic
in any detail.
Nick
njcoxstata@gmail.com


On 12 December 2013 09:49, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Wed, Dec 11, 2013 at 8:00 PM, Martin Trombetta wrote:
>> Thanks Maarten, I had read this post before and, even though it was
>> useful at first, I think the methods suggested there do not quite help
>> with my particular problem. Please notice that I wish to include both
>> an equality constraint and several inequality constraints in the same
>> problem, I do not see how to use the methods from this post.
>
> Example 6 of <http://www.stata.com/support/faqs/statistics/linear-regression-with-interval-constraints/>
> does exactly what you want: it incorporates both the inequality
> constraint that all proportions must be between 0 and 1 _and_ the
> constraint that they must add up to 1.
>
> -- Maarten
>
> ---------------------------------
> Maarten L. Buis
> WZB
> Reichpietschufer 50
> 10785 Berlin
> Germany
>
> http://www.maartenbuis.nl
> ---------------------------------
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