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| From | Demetris Christodoulou <Demetris.Christodoulou@sydney.edu.au> |
| To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
| Subject | Re: st: cnsreg with singular |
| Date | Wed, 7 Sep 2011 21:24:27 +1000 |
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/