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From |
Alan Acock <acock@mac.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: probit with interaction dummies (significance and marginaleffects) |

Date |
Sat, 26 Jul 2008 19:54:10 -0700 |

I've not followed all of this discussion, but with continuous variables, what Tony says makes centering extremely important. Centering education at 12 years in the U.S. Makes the 0 value meaningful. Changing where you center a variable can dramatically change interactions so the centering should be conceptually justified. Uncentered continuous variables for which a zero value is extremely rare, e.g., years of education, age, etc., can produce bizarre results. Alan Acock On 7/25/08 8:19 AM, "Tony Lachenbruch" <Peter.Lachenbruch@oregonstate.edu> wrote:Tony Lachenbruch > With logistic regression, interaction is usually interpreted as effect > modification: the effect of predictor A is different at different levels of > predictor B. With probit regression it is likely to be similar although not > identical. > > It is often useful to write the predicted probabilities: > For logistic regression you have > (1) ln(p/(1-p))=B0 when A=B=0 > (2) ln(p/(1-p))=B0+B1 when A=1, B=0 > (3) ln(p/(1-p))=B0+ B2 when A=0, B=1 > (4) ln(p/(1-p))=B0+B1+B2+B3 when A=1, B=1 > > The differences (2)-(1)=B1 is the ln(OR) for A at B=0 > (3)-(1)=B2 is the ln(OR) for B at A=0 > If B2=0 the interpretation of the above is how the ln(OR)s behave. If B2 is > not 0, then > (4)-(2)=B2+B3 is how the ln(OR) for A is modified when B=1 > (4)-(3)=B1+B3 is how the ln(OR) for B is modified when A=1 > > 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 Erasmo Giambona > Sent: Friday, July 25, 2008 3:05 AM > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: probit with interaction dummies (significance and marginal > effects) > > Dear Statalisters, > > I have found this thread particulalrly interesting. I have found the > questions asked by Andrea and especially the answer of Marteen very > useful. However, despite having read a lot about it over the last > several days, it is still hard for me to have a good intuition on how > to intepret interaction terms in logit regressions. I have also found > that papers in finance (my field) usually miss to provide a clear > interpretation of interaction terms in logit regressions. > > I truly hope some other people might join the thread to provide more insights. > > Here is my major source of confusion. Consider the case of interaction > of two continuos variables (e.g., profit and number of employees) in a > logit model. The dependent variable is 1 if the firm's ceo is fired > and zero otherwise. The coefficient estimate on the interaction from > the logit output is positive (for example, +0.25) and statistically > significant. I interpret this to mean that the odds that the ceo is > fired are higher when both profit and number of employees are large > (small) in absolute term (rather than changes). However, Ali et al. > (2004) show that the marginal effect for the interaction of two > continuos variables can be negative even if its coefficient estimate > is positive. Assuming that the marginal effect is negative (e.g., > -0.2) in my example, I would interpret this to mean that the > likelihood of firing the ceo decreases by 20% on average as the > interaction term increases by 1%. > > Assuming that my way of interpreting coefficient and marginal effect > of the interaction term in a logit is correct, I would still find it > hard to reconcile the "seemingly contradictory" evidence of the above > example. > > I hope this can stimulate further discussion on the issue. > > Best regards, > Erasmo > > Reference > Norton, Wang, & Ai. 2004. Computing interaction effects in logit and > probit models. The Stata Journal 4(2):103116. > > > > > On Fri, Jul 18, 2008 at 5:00 AM, Andrea Bennett <mac.stata@gmail.com> wrote: >> Thank you so much! >> >> May I sum up for clarification: When I am using e.g. a probit model with a >> dependent variable Y and include an interaction term -female*wage- and I am >> primarily interested in the interaction effect of a woman with wage then it >> is save to use the standard regression output to interpret the direction >> (AND the significance?) from the regression table. E.g. if the >> beta-estimators are -female- ==0.5, -wage- == 0.34 and -female*wage- == >> -0.03 and all being significant then I can say that the wage effect is >> significantly smaller when being a woman? Does this also hold when one is >> formulating models like -female*low_education-, -female*mid_education-, >> -female-high_education-? Or did I misinterpret you line "as long as you >> interpret the effects in terms of the effect on the latent variable you are >> ok in simply using the output from -probit-"? >> >> When I want to know if (and for which range) the interaction of female and >> wage has a significant effect on Y I should use -inteff-. When I want to do >> the same for the interaction of female with the education levels, then there >> is not yet consensus on how it shall be done. Norton et al. 2004 mention >> -predictnl- but urge to use it with extra care. Another source would be Rich >> Williams webpage. >> >> Did I completely mess it up (I fear so!) or is it like I described? >> >> Andrea >> >> >> On Jul 17, 2008, at 6:13 PM, Maarten buis wrote: >> >>> Regarding problem 1, this is just a matter of interpretation, as long >>> as you interpret the effects in terms of the effect on the latent >>> variable you are ok in simply using the output from -probit-, if you >>> want to interpret the results in terms of the probability you should >>> use -inteff-. >>> >>> Problem 2 is much harder to solve. Any solution would in one way or >>> another try to controll for things that haven't been observed. It >>> should not come as a surprise that that is hard (read: impossible). So, >>> the fact that "the solution" hasn't been implemented yet in Stata is >>> not so much a problem with Stata but with the state of the statistical >>> science: we know the problem, but we just don't know the answer. Though >>> Rich Williams discusses one solution on his website. >>> >>> -- Maarten >>> >>> --- Andrea Bennett <mac.stata@gmail.com> wrote: >>>> >>>> Thanks for the link! Still, I wonder if there's really no Stata >>>> command I could use to "simply" test if the interaction is >>>> significant and what influence (direction) it has on the dependent >>>> variable. I'd be just rather surprised if this does not exist >>>> because it seems to me this is a very common issue in any regression >>>> design (interaction effects). >>> >>> --- Maarten buis wrote: >>>>> >>>>> There are two distinct issues when interpreting interaction effects >>>>> in a probit: >>>>> >>>>> 1) a significant positive (negative) interaction in terms of the >>>>> latent >>>>> variable does not mean a significant positive (negative) >>>>> interaction effect in terms of the probability that y = 1. >>>>> >>>>> 2) The scale of the latent variable is identified by setting the >>>>> residual variance at 1. If the residual variance differs between >>>>> the groups than that means that the scale of the latent variable >>>>> differs between the groups and when comparing differences in >>>>> effects across the groups you are basically comparing apples and >>>>> oranges. >>> >>> >>> ----------------------------------------- >>> Maarten L. Buis >>> Department of Social Research Methodology >>> Vrije Universiteit Amsterdam >>> Boelelaan 1081 >>> 1081 HV Amsterdam >>> The Netherlands >>> >>> visiting address: >>> Buitenveldertselaan 3 (Metropolitan), room Z434 >>> >>> +31 20 5986715 >>> >>> http://home.fsw.vu.nl/m.buis/ >>> ----------------------------------------- >>> >>> >>> __________________________________________________________ >>> Not happy with your email address?. >>> Get the one you really want - millions of new email addresses available >>> now at Yahoo! http://uk.docs.yahoo.com/ymail/new.html >>> * >>> * 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/ > > * > * 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: probit with interaction dummies (significance and marginal effects)***From:*"Erasmo Giambona" <e.giambona@gmail.com>

**References**:**RE: st: probit with interaction dummies (significance and marginal effects)***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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