RE: st: cnsreg with singular

[Cameron McIntosh <cnm100@hotmail.com>]

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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