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


From   Nick Cox <[email protected]>
To   "[email protected]" <[email protected]>
Subject   Re: st: Fitting a linear regression where coefficients are bounded proportions
Date   Thu, 12 Dec 2013 14:53:54 +0000

Your interval [a,b] still calls for a reparameterisation using logit
ideas, just in a generalized form, ln((x - a)/(b - x)) at a quick
guess. I am assuming that b and a are specified in advance and the
same for each predictor.
Nick
[email protected]


On 12 December 2013 13:49, Martin Trombetta <[email protected]> wrote:
> 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 <[email protected]>:
>> 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
>> [email protected]
>>
>>
>> On 12 December 2013 09:49, Maarten Buis <[email protected]> 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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