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


From   Martin Trombetta <martintrombetta@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fitting a linear regression where coefficients are bounded proportions
Date   Thu, 12 Dec 2013 11:49:47 -0200

other software, but since I regularly work in Stata, I would be happy
to find a way to do it there

Maarten: I do not just want them to be bounded to the (0,1) interval,
I want them to be bounded to the (a,b) interval, where 0<a<b<1 and I
can choose a and b arbitrarily

Nick: sounds interesting, maybe I will plot a few things like that and
send them later.

Thanks everybody for your attention so far

2013/12/12 Nick Cox <njcoxstata@gmail.com>:
> 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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-- 
Martin Trombetta
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