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From |
Roger Newson <r.newson@imperial.ac.uk> |

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

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

Date |
Wed, 10 Mar 2010 10:44:43 +0000 |

Roger On 09/03/2010 21:02, Nick Cox wrote:

I think you're both right. In olden days, pre-emptive centring, as we say in English, was a good idea in order to avoid numerical problems with mediocre programs that did not handle near multicollinearity well. Nowadays, decent programs including Stata take care that you get bitten as little as possible by such problems. If course, if you really do have multicollinearity, nothing much can help, except that Stata drops predictors and flags the issue. Nick n.j.cox@durham.ac.uk Rodolphe Desbordes My point is that centering does not reduce multicollinearity. As you can see in my example, the standard errors of the estimated marginal effects at the mean of `mpg' are the same using uncentered or centered values of `mpg'. Rosie Chen Thanks, Rodolphe, for this helpful demonstration. Agree that the major purpose of centering seems to be that we make the interpretation of X meaningful. I guess reducing multicollinearity is a bi-product of the benefit. Rodolphe Desbordes<rodolphe.desbordes@strath.ac.uk> Centering will not affect your estimates and their uncertainty. However, centering allows you to directly obtain the estimated effect of X on Y for a meaningful value of X, i.e. the mean of X. . sysuse auto.dta,clear (1978 Automobile Data) . gen double mpg2=mpg^2 . reg price mpg mpg2 Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 2, 71) = 18.28 Model | 215835615 2 107917807 Prob> F = 0.0000 Residual | 419229781 71 5904644.81 R-squared = 0.3399 -------------+------------------------------ Adj R-squared = 0.3213 Total | 635065396 73 8699525.97 Root MSE = 2429.9 ------------------------------------------------------------------------ ------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------- ------ mpg | -1265.194 289.5443 -4.37 0.000 -1842.529 -687.8593 mpg2 | 21.36069 5.938885 3.60 0.001 9.518891 33.20249 _cons | 22716.48 3366.577 6.75 0.000 16003.71 29429.24 ------------------------------------------------------------------------ ------ . sum mpg Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 74 21.2973 5.785503 12 41 . local m=r(mean) . lincom _b[mpg]+2*_b[mpg2]*`m' ( 1) mpg + 42.59459 mpg2 = 0 ------------------------------------------------------------------------ ------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------- ------ (1) | -355.3442 58.86205 -6.04 0.000 -472.7118 -237.9766 ------------------------------------------------------------------------ ------ . gen double mpgm=mpg-`m' . gen double mpgm2=mpgm^2 . reg price mpgm mpgm2 Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 2, 71) = 18.28 Model | 215835615 2 107917807 Prob> F = 0.0000 Residual | 419229781 71 5904644.81 R-squared = 0.3399 -------------+------------------------------ Adj R-squared = 0.3213 Total | 635065396 73 8699525.97 Root MSE = 2429.9 ------------------------------------------------------------------------ ------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------- ------ mpgm | -355.3442 58.86205 -6.04 0.000 -472.7118 -237.9766 mpgm2 | 21.36069 5.938885 3.60 0.001 9.518891 33.20249 _cons | 5459.933 343.8718 15.88 0.000 4774.272 6145.594 ------------------------------------------------------------------------ ------ * * 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/

-- Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: http://www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ Opinions expressed are those of the author, not of the institution. * * 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/

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

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

**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>

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