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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: interaction effect with logit |

Date |
Wed, 5 Sep 2012 16:54:09 +0200 |

On Wed, Sep 5, 2012 at 2:34 PM, Luca Fumarco wrote: > In Maarten L. Buis, "Stata tip 87: Interpretation of interactions in non-linear models", The Stata Journal (2010) Vol. 10 No. 2, pp. 305-308, and from discussion with fellow researchers I understand that the logit model is better. > However, in Edward C. Norton, Hua Wang, Chunrong Ai, "Computing interaction eﬀects and standard errors in logit and probit models", The Stata Journal (2004) 4, Number 2, pp. 154–167, they illustrate how what we would tend to interpret as an odd ratio is instead something different....the ratio of odds ratios (i.e.,odds ratio for X1|X2=1/odds ratio for X1|X2=0) !? > > I do not see in which way the computational issue illustrate in Norton et al. is solved using the logit, since also this model is affected by the issue (see paragraph 2.6 Odds ratio in Norton et al.) I don't disagree with Norton et al. on what an interaction effect in a logit model is: it is a ratio of odds ratios. This is exactly the point of my Stata tip. We disagree on the point of interpretability: he claims that he they cannot understand that, I claim I do and that you can too. The logic is to take it step by step: start with the baseline odds to refresh the audience's memory about what an odds is, move on to one of the main effect to refresh the audience's memory about that we are comparing groups with ratios rather than differences, and than go to the interaction effect. We also disagree on the usefulness of marginal effects. In essence I see marginal effects as attempts to get an interpretation like a linear probability model without admitting that in essence you estimated a linear probability model in disguise. As a consequence you get the worst of two models. So if you really believe that you want effects in terms of constant differences (and differences in differences for the interaction effects), be honest and estimate a linear probability model with all the associated advantages and disadvantages. Otherwise use a logit and interpret the results in its natural metric: odds, and odds ratios (and ratios of odds ratios for interaction terms). Hope this clarifies things, Maarten --------------------------------- Maarten L. Buis WZB Reichpietschufer 50 10785 Berlin Germany http://www.maartenbuis.nl --------------------------------- * * 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**:**st: interaction effect with logit***From:*Luca Fumarco <luca.fumarco@lnu.se>

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