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

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Tue, 17 May 2011 11:02:00 +0200 |

On Mon, May 16, 2011 at 3:52 PM, andre ebner wrote: > The only doubt I still have for the moment concerns the > "marginal effect as the difference between the expected > odds of women with and without a college degree, rather than as the > derivative of the expected odds with respect to collgrad." > > as explained in your STATA tip 87. > > With my data the difference changes depending at which values I fix the > other covariates. Is this due to the fact that we estimate marginal > effects at certain values and marginal effects depend on these values? For > calculating the impact of collgrade on black and white women would it then > make sense to calculate the difference between average partial effects > using > > margins , over(black collgrad) expression(exp(xb())) post > > also (or especially) if the regression includes additional covariates? > > Using my data, the differences are: > > * fixing covariates at certain value > inc_shock no inc_shock difference > loan_const 0.21 0.02 0.19 > no loan_const 0.00 0.02 -0.02 > > > * fixing covariates at slightly different values > inc_shock no inc_shock difference > loan_const 0.24 0.03 0.21 > no loan_const 0.00 0.02 -0.02 > > * using margins, over(inc_shock loan_const)expression(exp(xb())) /// post > inc_shock no inc_shock difference > loan_const 0.71 0.11 0.59 > no loan_const 0.02 0.08 -0.06 > > > You mention that without fixing the covariates one gets the odds averaged > over the other control variables, while the logistic regression model is > based on odds before averaging. Is it however possible to interprete the > last table as kind of average partial effects (APE) over the odds of > individuals showing the respective combination of inc_shock (=income > shock) and loan_const (loan constrained). Would you agree to look at the > last table if one is interested in differences between APEs? 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 because the variability of the individual partial effects for interaction effects is so high that it really matters. The problem with partial effects or marginal effects for interaction effects is that they are very unstable. They tend to depend strongly on the values of all explanatory variables, and it is perfectly normal that for some observations you find a significant negative interaction effect and for other observations you find a significant positive effect. The computation of average partial or marginal effects only makes sense if that average is a reasonable summary. My feeling is that the variation is typically so large that the only way to faithfully represent marginal or partial effects of interaction effects is to compute them for each observation and just graph them, just as Edward Norton, Hua Wang, and Chunrong Ai (2004) did. This is where my suggestion (Buis 2010) for interpreting them as ratios of odds ratios has an edge, the interaction effect is than really one number. Hope this helps, Maarten Maarten L. Buis (2010) "Stata tip 87: Interpretation of interactions in non-linear models", The Stata Journal, 10(2): 305-308. Edward Norton, Hua Wang, and Chunrong Ai (2004) "Computing interaction effects and standard errors in logit and probit models" The Stata Journal, 4(2):154--167. -------------------------- 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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