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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 08:01:27 -0700 |

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 * * 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/

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

**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>

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