Re: st: cnsreg with singular

[Demetris Christodoulou <Demetris.Christodoulou@sydney.edu.au>]

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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