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Re: FW: st: cnsreg with singular


From   Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: FW: st: cnsreg with singular
Date   Wed, 7 Sep 2011 08:05:10 -0700

If you have difficulty downloading the file from that location, here
is a more convenient link:
http://dl.dropbox.com/u/35775690/statalist.pdf

T

On Wed, Sep 7, 2011 at 8:01 AM, Tirthankar Chakravarty
<tirthankar.chakravarty@gmail.com> wrote:
> Demetris,
>
> The answer to your question involves considerable algebra as well as
> knowing what Stata does with the constraints you supply to it. I have
> done the algebra for you in a document I have uploaded here:
> http://pdfcast.org/download/statalist-query.pdf
>
> Basically, I have shown you the algebraic (closed-form)
> quasi-equivalence between the two solutions and a Stata example to
> illustrate this. No iterative optimization algorithms are required or
> are used by Stata.
>
> You will also need to look at the manual entry in [P] for -makecns- to
> see further algebraic manipulations - if I have time, I will add these
> also to the document also.
>
> T
>
> PS> Note the typo in the last line of eqn. 11; a 1/3 is missing.
>
> On Wed, Sep 7, 2011 at 6:44 AM, Cameron McIntosh <cnm100@hotmail.com> wrote:
>> No problem, hope you find the references helpful... but sorry, I don't know what cnsreg does behind the scenes in such a case. So the various manual treatments of the problem may or may not be better, I'm not sure. :)
>> Cam
>>
>>> Subject: Re: st: cnsreg with singular
>>> From: Demetris.Christodoulou@sydney.edu.au
>>> Date: Wed, 7 Sep 2011 21:24:27 +1000
>>> To: statalist@hsphsun2.harvard.edu
>>>
>>> Thanks for the very useful references Cam, these will keep e busy for a while!
>>>
>>> Still, can someone please describe the current mechanics of cnsreg in the case of a singular design matrix?
>>>
>>> many thanks, Demetris
>>>
>>> On 07/09/2011, at 10:57 AM, Cameron McIntosh wrote:
>>>
>>> > Hi Demetris,
>>> >
>>> > I wonder if it would also be worthwhile to try some corrective procedures on the design matrix, and see how these compare to the built-in methods in cnsreg?
>>> > Yuan, K.-H., & Chan, W. (2008). Structural equation modeling with near singular covariance matrices. Computational Statistics & Data Analysis, 52(10), 4842-4858.
>>> >
>>> > Yuan, K.H., Wu, R., & Bentler, P.M. (2010). Ridge structural equation modelling with correlation matrices for ordinal and continuous data. British Journal of Mathematical and Statistical Psychology, 64(1), 107–133.
>>> >
>>> > Bentler, P.M., & Yuan, K.-H. (2010). Positive Definiteness via Offdiagonal Scaling of a Symmetric Indefinite Matrix. Psychometrika, 76(1), 119-123. http://www.springerlink.com/content/k5154122171551l2/fulltext.pdf
>>> >
>>> > Highham, N.J. (2002). Computing the nearest correlation matrix - a problem from finance. IMA Journal of Numerical Analysis, 22(3), 329–343.
>>> >
>>> > Knol, D.L., & ten Berge, J.M.F. (1989). Least-squares approximation of an improper correlation matrix by a proper one. Psychometrika, 54, 53–61.
>>> >
>>> > Are you using the model option "col" (keep collinear variables)? Sorry if I am off base given the substantive and methodological nature of your analysis (which I don't know).
>>> >
>>> > Best,
>>> >
>>> > Cam
>>> >
>>> >> From: demetris.christodoulou@sydney.edu.au
>>> >> To: statalist@hsphsun2.harvard.edu
>>> >> Date: Wed, 7 Sep 2011 09:50:35 +1000
>>> >> Subject: st: cnsreg with singular
>>> >>
>>> >> My question is how does cnsreg deals with a singular matrix?
>>> >>
>>> >> Consider the following example:
>>> >>
>>> >> . sysuse auto
>>> >> . generate mpgrep78 = mpg + rep78
>>> >> . regress price mpg rep78 mpgrep78
>>> >>
>>> >> Due to perfect collinearity (i.e. a singular design matrix), linear OLS drops one of the explanatory variables.
>>> >> But I can force 'estimation' by:
>>> >>
>>> >> . constraint 1 mpgrep78 = mpg + rep78
>>> >> . cnsreg price mpg rep78 mpgrep78, cons(1)
>>> >>
>>> >> This produces estimates for all three explanatory variables.
>>> >> I noticed that the estimates of cnsreg are exactly the same, as taking the estimates of regress and apply the linear relationship to calculate the third parameter.
>>> >>
>>> >> This is what Greene (2010, p.274) suggests as well but in a more elaborate context using multiple regressions. That is, estimate the M-1 parameters and then use the linear relationship to calculate the M parameter.
>>> >> Can someone please confirm whether this is what Stata does too?
>>> >>
>>> >> Or does it use some more complex iterative numerical optimisation procedure, perhaps even involving a singular value decomposition?
>>> >>
>>> >> I am using Stata/MP2 version 11.2 on Mac.
>>> >>
>>> >> many thanks in advance,
>>> >> Demetris
>>> >> *
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>>> >
>>> > *
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>>>
>>>
>>> *
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>>
>> *
>> *   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/
>>
>
>
>
> --
> Tirthankar Chakravarty
> tchakravarty@ucsd.edu
> tirthankar.chakravarty@gmail.com
>



-- 
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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