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st: RE: Bounded Inequality Constraints


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Bounded Inequality Constraints
Date   Mon, 5 Dec 2011 11:09:32 -0600

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.

Regards,
Dmitriy
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