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RE: st: RE: Bounded Inequality Constraints


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Bounded Inequality Constraints
Date   Tue, 6 Dec 2011 14:54:57 +0000

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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