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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 14:54:15 +0000

<>

Should be (a,b).
Nick
njcoxstata@gmail.com


On 12 December 2013 14:53, Nick Cox <njcoxstata@gmail.com> wrote:
> 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
> njcoxstata@gmail.com
>
>
> On 12 December 2013 13:49, Martin Trombetta <martintrombetta@gmail.com> 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 <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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