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FW: st: cnsreg with singular


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
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