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From |
"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu> |

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

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

Date |
Mon, 8 Mar 2010 14:06:46 -0800 |

When you think about it, the residual will be 1-predicted or 0-predicted. Thus, they will plot as two parallel straight lines. Nick and I (mostly Nick) wrote a possible solution to this by using binned plots. I've been meaning to write it up for the SSC (and maybe even SJ). It's based on work by Andrew Gelman reported in his book with Jennifer Hill. Tony Peter A. Lachenbruch Department of Public Health Oregon State University Corvallis, OR 97330 Phone: 541-737-3832 FAX: 541-737-4001 -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Rosie Chen Sent: Monday, March 08, 2010 1:27 PM To: statalist@hsphsun2.harvard.edu Subject: Re: st: RE: Interpretation of quadratic terms Nick, thank you for the guidance. The model I am estimating is a logistic regression. What I did to check the plot was to save the residual of the model, and then plotted the standardized residual against the predictor. I didn't really found a curve-linear relationship. Is there anything wrong with the way I plot the residual? If not, then why the inclusion of a quadratic term actually improves the model fitting when I made a model comparison using the -2log-likelihood? In addition, the nonsignificant predictor in the original form turned to be significant after using the quadratic term? Your further advice would be appreciated. Rosie ----- Original Message ---- From: Nick Cox <n.j.cox@durham.ac.uk> To: statalist@hsphsun2.harvard.edu Sent: Mon, March 8, 2010 1:43:29 PM Subject: st: RE: Interpretation of quadratic terms I don't know what kind of guidance you need, but the first step is surely to plot this curve and think about its substantive interpretation within the entire range of the data. That should include bringing in whatever science is behind this analysis. Nick n.j.cox@durham.ac.uk Rosie Chen I have a question regarding how to interpret quadratic terms in regression, and would appreciate your help very much. Because the non-linear nature of the relationship between X and Y; I need to include quadratic terms in the model. To avoid multicollinearity problem with the original variable and its quadratic term, I centered the variable first (X) and then created the square term (Xsq). The model with the quadratic term (Xsq) was proved to be significantly better. Suppose the output is like the following (both coefficients are significant), how to interpret the results? The two signs are opposite. Could anyone provide some insight? Thank you very much in advance! --Rosie y= a + 1.3*X - 0.2*Xsq + e * * 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/

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

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

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

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

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