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

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

Subject |
RE: st: cnsreg with singular |

Date |
Tue, 6 Sep 2011 20:57:25 -0400 |

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/

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

**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>

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