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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 |
Wed, 11 Dec 2013 19:35:39 +0000 |

I am thinking from a statistical point of view, with first axiom that data are messy. My #2 really meant "getting it to fit in a way that satisfies you". I don't understand your difficulty in coding this as the principles are laid out in a FAQ, but at the same time I am not volunteering code. Nick njcoxstata@gmail.com On 11 December 2013 19:27, Martin Trombetta <martintrombetta@gmail.com> wrote: > 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/ * * 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/

**Follow-Ups**:**RE: st: Fitting a linear regression where coefficients are bounded proportions***From:*Timothy Mak <tshmak@hku.hk>

**References**:**st: Fitting a linear regression where coefficients are bounded proportions***From:*Martin Trombetta <martintrombetta@gmail.com>

**Re: st: Fitting a linear regression where coefficients are bounded proportions***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: Fitting a linear regression where coefficients are bounded proportions***From:*Martin Trombetta <martintrombetta@gmail.com>

**Re: st: Fitting a linear regression where coefficients are bounded proportions***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: Fitting a linear regression where coefficients are bounded proportions***From:*Martin Trombetta <martintrombetta@gmail.com>

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