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RE: st: RE: Bounded Inequality Constraints


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.
> >
>
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