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| From | Martin Trombetta <martintrombetta@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: Fitting a linear regression where coefficients are bounded proportions |
| Date | Wed, 11 Dec 2013 17:27:14 -0200 |
Yes, it can be done, Nick. The problem is quite straightforward from a mathematical point of view. The objective function is quadratic and the constraints are linear. Besides, think about it this way: imagine we only have two regressors. Since parameters must be proportions, we might as well call them b and 1-b. All my inequality constraints say is that not all combinations of b and 1-b are acceptable, only those that belong to a specific subset. In that specific subset, there must be one combination that minimizes the sum of square residuals and that is the one I want. The problem is that I have 9 regressors instead of 2. I have considered the possibility of using the multinomial logit approach, but then I cannot guarantee that the inequality constraints will be satisfied. Alternatively, I could use (appropriately defined) individual logits for each coefficient, but then they would not sum to one. I need an approach that guarantees both things. 2013/12/11 Nick Cox <njcoxstata@gmail.com>: > Interval constraints are handled by reparameterisation; the logit is > your friend. > > Constraints on parameter totals by one being total - sum of others. > > Your regression sounds so constrained that I wonder whether > > 1. You need data at all. > > 2. You have a real chance of getting it to fit. > > Nick > njcoxstata@gmail.com > > > On 11 December 2013 19:00, Martin Trombetta <martintrombetta@gmail.com> 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. >> >> 2013/12/11 Maarten Buis <maartenlbuis@gmail.com>: >>> On Tue, Dec 10, 2013 at 7:50 PM, Martin Trombetta wrote: >>>> I need to fit a linear regression where coefficients are to be >>>> interpreted as proportions (that is, they must sum to 1), but at the >>>> same time I wish to impose inequality constraints on each of them: >>>> they all should belong to a specific interval (a,b) inside the unit >>>> interval. >>> >>> There is a discussion of how to do that here: >>> http://www.stata.com/support/faqs/statistics/linear-regression-with-interval-constraints/ >>> >>> Hope this helps, >>> Maarten >>> >>> --------------------------------- >>> Maarten L. Buis >>> WZB >>> Reichpietschufer 50 >>> 10785 Berlin >>> Germany >>> >>> http://www.maartenbuis.nl >>> --------------------------------- >>> * >>> * For searches and help try: >>> * http://www.stata.com/help.cgi?search >>> * http://www.stata.com/support/faqs/resources/statalist-faq/ >>> * http://www.ats.ucla.edu/stat/stata/ >> >> >> >> -- >> Martin Trombetta >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/faqs/resources/statalist-faq/ >> * http://www.ats.ucla.edu/stat/stata/ > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ -- Martin Trombetta * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/