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From |
Maarten Buis <[email protected]> |

To |
[email protected] |

Subject |
st: Re: Stata tip 87: Interpretation of interactions in non-linear models |

Date |
Wed, 18 May 2011 17:55:02 +0200 |

On Wed, May 18, 2011 at 4:48 PM, andre ebner wrote: > Regarding your concern to interpret differences between APE please allow > me one more consideration: > > When comparing differences you write: > >> In your case (with a panel model) this would be a mixture of average > partial effects while fixing the unobserved group constants at the > average. This is not very pretty, especially be-cause the variability of > the individual partial effects for interaction effects is so high that > it really matters. > > If I understood you correctly, your worry is that this approach does not > take into account that mean and variance of RE are likely to be different > across groups (by interacting two discrete variables I get four groups) > but instead fixes the unobserved group constants at the average. No I worry about the fact that there is variance, regardless of whether that variance is the same or different across groups. Think of the random effects as group specific constants. The value of a marginal or partial effect depends on that constant. To get _average_ partial effects we need to compute the partial effect for every individual and than average those individual partial effects. What you are doing is you first fix the group specific constants at their average, than compute partial effects and than you average those (over the distribution of the observed variables). The two are not the same, as there is a non-linear transformation involved. As long as everything is nice and (approximately) linear all this does not matter (much). Unfortunately that is not the case when dealing with interaction effects in non-linear models. It is not uncommon for estimated marginal effects for interaction terms to vary from significantly positive to non-significant to significantly negative depending on the values of the other covariates. In essence you are computing an uncomfortable mix between average partial effects and marginal effects at average values of the covariates. Anyhow, my main point is that you should _not_ average the individual partial effects and certainly not compute the marginal effects at the average. Instead you should take Norton et al.'s point seriously and accept that when you want to present your results as marginal effects, the marginal effects of interaction terms will vary widely from individual to individual, even though the underlying ratio of odds ratios is constant. This variation tends to be so extreme that trying to summarize it with one number just does not make sense. The problem is that you'll end up with a conclusion like "the interaction term is significantly positive, significantly negative, and not significant, depending on the values of the covariates", which is not much of a conclusion, especially if you consider that the underlying ratio of odds ratios leads to a single unambiguous conclusion... Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen 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/

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