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From |
Rodolphe Desbordes <rodolphe.desbordes@strath.ac.uk> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: Interpretation of quadratic terms |

Date |
Wed, 10 Mar 2010 17:09:20 +0000 |

Dear Richard, My hunch is that high multicollinearity will be detected in any case by very low eigenvalues. However, these diagnostic tests may be very misleading since "better values" may fool a researcher into thinking that his model after rescaling now performs better, e.g. . collin mpg mpg2 Collinearity Diagnostics SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- mpg 34.69 5.89 0.0288 0.9712 mpg2 34.69 5.89 0.0288 0.9712 ---------------------------------------------------- Mean VIF 34.69 Cond Eigenval Index --------------------------------- 1 2.8654 1.0000 2 0.1334 4.6350 3 0.0013 47.4208 --------------------------------- Condition Number 47.4208 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.0288 . gen double mpgm=mpg-`m' . gen double mpgm2=mpgm^2 . collin mpgm mpgm2 Collinearity Diagnostics SQRT R- Variable VIF VIF Tolerance Squared ---------------------------------------------------- mpgm 1.43 1.20 0.6975 0.3025 mpgm2 1.43 1.20 0.6975 0.3025 ---------------------------------------------------- Mean VIF 1.43 Cond Eigenval Index --------------------------------- 1 1.6914 1.0000 2 1.0000 1.3005 3 0.3086 2.3410 --------------------------------- Condition Number 2.3410 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept) Det(correlation matrix) 0.6975 Rodolphe ________________________________________ From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Williams [Richard.A.Williams.5@ND.edu] Sent: 10 March 2010 13:40 To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu Subject: RE: st: RE: Interpretation of quadratic terms At 07:34 AM 3/10/2010, Rodolphe Desbordes wrote: >Dear Rosie, Nick and Roger, > >To conclude this thread and summarise the main arguments put forward >by Nick, Roger and myself: > >A) There can be some good reasons for "pre-emptive centering": a) to >avoid computational issues, which are unlikely to arise with modern >econometric softwares such as Stata; b) to provide substantive interpretation. I agree with that, and I may add a sentence like that to my notes in the future! One other thought that I have had though: Suppose you are doing tests for collinearity and you have other variables in the model, so I use something like the -collin- command. Is there an advantage to minimizing the collinearity involving the variables that have the squared term? That is, would doing so make me better able to detect where the collinearity is among other variables? Or would it make no difference? For example, suppose x1 is highly collinear with other variables. If I have x1^squared in the model, I am thinking I might miss the collinearity because x1 and x1^squared are so highly correlated (unless I have centered x1 first). This is just idle speculation on my part, I haven't fiddled around with it to see. ------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW: http://www.nd.edu/~rwilliam * * 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/

**References**:**Re: st: RE: Interpretation of quadratic terms***From:*Rosie Chen <jiarongchen2002@yahoo.com>

**RE: st: RE: Interpretation of quadratic terms***From:*Rodolphe Desbordes <rodolphe.desbordes@strath.ac.uk>

**RE: st: RE: Interpretation of quadratic terms***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**Re: st: RE: Interpretation of quadratic terms***From:*Roger Newson <r.newson@imperial.ac.uk>

**RE: st: RE: Interpretation of quadratic terms***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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