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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

Subject |
FW: st: cnsreg with singular |

Date |
Wed, 7 Sep 2011 09:44:29 -0400 |

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/

**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>

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