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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 >>> >> * >>> >> * 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/ >>> > >>> > * >>> > * 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/ >>> >>> >>> * >>> * 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/ >> >> * >> * 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 * * 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/

**References**:**st: Testing for serial correlation in small panel samples***From:*christina sakali <christina.sakali@googlemail.com>

**Re: st: Testing for serial correlation in small panel samples***From:*Scott Merryman <scott.merryman@gmail.com>

**st: cnsreg with singular***From:*Demetris Christodoulou <demetris.christodoulou@sydney.edu.au>

**RE: st: cnsreg with singular***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: cnsreg with singular***From:*Demetris Christodoulou <Demetris.Christodoulou@sydney.edu.au>

**FW: st: cnsreg with singular***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: FW: st: cnsreg with singular***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

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