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| 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 14:53:54 +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 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 >>> --------------------------------- >>> * >>> * 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/ * * 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/