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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: Bounded Inequality Constraints |

Date |
Tue, 6 Dec 2011 11:30:24 -0500 |

In the event that these are useful: van de Schoot, R., Hoijtink, H. & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443-463. http://www.statmodel.com/download/vandeschoot.pdf Kelderman, H. (1987). LISREL models for inequality constraints in factor and regression analysis. In P. Cuttance & R. Ecob (Eds.), Structural modeling by example: applications in educational, behavioral, and social research (pp. 121-135). New York: Cambridge University Press. Shapiro, A (1988). Towards a Unified Theory in Inequality-Constrained Testing in Multivariate Analysis. International Statistical Review, 56, 49-62. Berger, R.L. (1989). Uniformly More Powerful Tests for Hypotheses Concerning Linear Inequalities and Normal Means. Journal of the American Statistical Association, 84, 192-199. Liu, H., & Berger, R.L. (1995). Uniformly More Powerful One-Sided Tests for Hypotheses About Linear Inequalities. The Annals of Statistics, 23, 55-72.http://www.west.asu.edu/rlberge1/papers/aos95.pdf Gromping, U. (2010). Inference with Linear Equality and Inequality Constraints Using R: The Package ic.infer. Journal of Statistical Software, 33(10).http://www.jstatsoft.org/v33/i10/paper Gromping, U. (November 30, 2011). Inequality constrained inference in linear normal situations: Package ‘ic.infer’, Version 1.1-3.http://cran.r-project.org/web/packages/ic.infer/ic.infer.pdfhttp://cran.r-project.org/web/packages/ic.infer/index.html Cam ---------------------------------------- > From: n.j.cox@durham.ac.uk > To: statalist@hsphsun2.harvard.edu > Date: Tue, 6 Dec 2011 14:54:57 +0000 > Subject: RE: st: RE: Bounded Inequality Constraints > > Generically, Alan's equation implies that (c - 2) / 3 is between 0 and 1, so c - 2 is between 0 and 3 and c is between 2 and 5. > > You stated in your first posting that you want c to be between 2.5 and 5, so also if that is so you would want (c - 2.5) / 2.5. But as you stated in your second posting that 2 is the lowest allowable value, that presumably is what Alan was working from. > > 3.5 is just an initial value at the midpoint of the range. > > Nick > n.j.cox@durham.ac.uk > > Dmitriy Glumov > > Thank you very much for showing the tranformation, this is very > helpful. However, I have some trouble understanding the values you > chose in the transformation (I apologize for using a bad example), so > would it be possible for you to briefly go over them. In particular > would this transformation account for the upper bound of 5, if the > coefficients were to go that far? Again, thank you for the help and > consideration. > > > On Mon, Dec 5, 2011 at 12:09 PM, Feiveson, Alan H. (JSC-SK311) > <alan.h.feiveson@nasa.gov> wrote: > > Dmitriy - The example from the auto data doesn't work very well, but if you want to crank it out by brute force, you could use nonlinear least squares with a logit transformation: > > > > nl (price = {A} + logit( ( {c1=3.5}-2)/3) * weight + logit( ( {c2=3.5}-2)/3) * mpg + logit( ( {c3=3.5}-2)/3) * length ) > > > > > > > > Source | SS df MS > > -------------+------------------------------ Number of obs = 74 > > Model | -2.6420e+09 3 -880670066 R-squared = -4.1602 > > Residual | 3.2771e+09 70 46815365.6 Adj R-squared = -4.3814 > > -------------+------------------------------ Root MSE = 6842.176 > > Total | 635065396 73 8699525.97 Res. dev. = 1512.858 > > > > ------------------------------------------------------------------------------ > > price | Coef. Std. Err. t P>|t| [95% Conf. Interval] > > -------------+---------------------------------------------------------------- > > /A | 1677.936 5890.632 0.28 0.777 -10070.56 13426.43 > > /c1 | 3.870228 .822251 4.71 0.000 2.2303 5.510156 > > /c2 | 2.000028 .0023649 845.71 0.000 1.995311 2.004744 > > /c3 | 2.000001 .0000529 37836.18 0.000 1.999896 2.000106 > > ------------------------------------------------------------------------------ > > Parameter A taken as constant term in model & ANOVA table > > > > > > > > The coefficients c2 and c2 are estimated at their lowest allowable value (2.0) because they are negative in the unrestricted model. In this example, I didn't try to restrict the constant term ("A"). > > > > Al Feiveson > > > > > > > > > > > > -----Original Message----- > > From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Dmitriy Glumov > > Sent: Monday, December 05, 2011 8:21 AM > > To: statalist@hsphsun2.harvard.edu > > Subject: st: Bounded Inequality Constraints > > > > Dear Statalist Users, > > > > I need to include inequality constraints into the regression I am > > working on. In particular, I would like the coefficients of all the > > independent variables to be between 2.5 and 5. To provide you with an > > example, suppose I was using an Auto dataset and running the following > > simple regression: > > > > regress price mpg weight length > > > > This regression needs to be constrained in such a way so that the > > coefficients for mpg, weight, and length all stay bounded between 2.5 > > and 5 (and disregarded if they are outside this range). I know there > > has been a fair amount of discussion in regards to this topic and > > Maarten has posted this solution > > (http://www.stata.com/support/faqs/stat/intconst.html), but I wasn't > > sure if there's potentially an another, perhaps more appropriate way, > > to solve the problem I am dealing with - one that requires bounding > > (rather than a one-sided inequality). Moreover, I could not figure out > > how to transform the solution that Maarten posted into the one where > > both bounds are accounted for. Hence, any help with this would be > > greatly appreciated. Thank you for your consideration. > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/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/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Bounded Inequality Constraints***From:*Dmitriy Glumov <glumovdm@gmail.com>

**st: RE: Bounded Inequality Constraints***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**Re: st: RE: Bounded Inequality Constraints***From:*Dmitriy Glumov <glumovdm@gmail.com>

**RE: st: RE: Bounded Inequality Constraints***From:*Nick Cox <n.j.cox@durham.ac.uk>

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