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RE: st: RE: Bounded Inequality Constraints
From
Cameron McIntosh <[email protected]>
To
STATA LIST <[email protected]>
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: [email protected]
> To: [email protected]
> 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
> [email protected]
>
> 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)
> <[email protected]> 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: [email protected] [mailto:[email protected]] On Behalf Of Dmitriy Glumov
> > Sent: Monday, December 05, 2011 8:21 AM
> > To: [email protected]
> > 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.
> >
>
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