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From |
Richard Williams <richardwilliams.ndu@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Why -margins- does not present marginal effects for interaction terms |

Date |
Mon, 07 Jan 2013 16:12:44 -0500 |

http://www.nd.edu/~rwilliam/stats/Margins01.pdf http://www.statajournal.com/article.html?article=st0260

From: Stata Technical Support <tech-support@stata.com> To: Richard Williams <Richard.A.Williams.5@nd.edu> Date: Mon, 7 Jan 2013 14:15:13 -0500 Subject: Re: Marginal effects of interaction terms Dear Richard,From our experience, when users ask for "interaction effects", theyare mostlyinterested in some way to explain or visualize the interaction. As you pointed out, the philosophy behind -margins-, is that you enter actual variables in your model, and you compute the effects of those actual variables on the prediction. If your model includes x1, x2, and x1*x2, the variables in your model are x1 and x2. -margins-, with the option -dydx()-, answers questions like the following: If I increment x1 on one unit, how much will my prediction be affected? We can't change x1*x2 without also making changes to x1 and x2, so it is impossible to try to explain the effect of x1*x2 in isolation of x1 and x2. Usually, when a researcher wants to see how two variables interact, the most natural way to do that is to use -margins- with a range of values specified in the -at()- option, then follow it up with a call to -marginsplot-. For example, the following shows how sex and age affect the marginal predicted probability of a positive outcome: . webuse nhanes2, clear . logit heartatk age i.sex i.sex#c.age age c.age#c.age bmi . margins sex, at(age = (20(5)75)) . marginsplot Besides the documentation in -[R] margins- and -[R] marginsplot-, there is also a nice article about this in the last issue of the Stata News, available at: http://www.stata.com/stata-news/statanews.27.4.pdf We are aware that there are other takes to the construction of marginal effects, and some authors report a second derivative as the marginal effect due to the interaction between two continuous variables. We find nothing wrong with this practice, except that a single number rarely tells the whole story in this case. It was for this reason and our belief that most researchers are interested in other things that we decided to only implement effects based on first order derivatives in -margins-. With the addition of -contrast- and contrast operators in -margins- in Stata 12, it is possible to compute all the discrete interaction effects. The contrast operators can be combined with continuous variables in the -dydx()- option to compute effects of interactions that also contain a single continuous variable. Sincerely, Isabel Isabel Canette, Ph.D. Senior Statistician StataCorp LP

------------------------------------------- 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/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

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