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RE: st: Interpreting interactions


From   "Fogel, Ariel" <AFogel@urban.org>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Interpreting interactions
Date   Wed, 17 Oct 2012 21:20:06 +0000

Thanks Maarten and sorry all for a superfluous post.
I did not see this response earlier.

Ariel Fogel


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis
Sent: Wednesday, October 17, 2012 3:44 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Interpreting interactions

On Tue, Oct 16, 2012 at 10:44 PM, Amal Khanolkar wrote:
> I ran the following set of logistic regression models:
>
> 1. Crude:
>
> xi: logit vent6h i.mom_race2 sexx if age_mom!=. & parity!=. & 
> gestcalc!=. & cigs_befx!=. & gestdb!=. & gesthy!=. & MBMI!=. & 
> ht_cm!=. & plural==1 & edu_mom!=. & marriedx!=., or
>
> 2.  Adjusted for confounders:
>
> xi: logit vent6h i.mom_race2 i.edu_mom i.marriedx age_mom sexx age_mom 
> i.parity gestcalc i.cigs_befx i.gestdb i.gesthy i.MBMI ht_cm if 
> plural==1., or
>
> 3. With interactions:
>
> xi: logit vent6h i.mom_race2*i.edu_mom i.mom_race2*i.marriedx sexx 
> age_mom i.parity gestcalc i.cigs_befx i.gestdb i.gesthy i.MBMI ht_cm 
> if plural==1., or
>
>
> I see that the Odds ratios (for racial groups) do not really change between models 1 and 2 - i.e. additional adjustment for potential confounders do not seen to affect the odds of a particular ethnic group of being diagnosed with my outcome of interest.

>
> However, I see that the OR for ethnic group 2 go from 1.23 (95% CI 1.00 to 1.48) in model 1 to 1.13 (0.92 to 1.37) in model 2 to 2.33 (1.46 to 3.72) in model 3.

Unfortunately, such comparison of models with different numbers of covariates is not appropriate for non-linear models like logistic regression. Think of it this way: A probability captures a measure of uncertainty. That uncertainty comes from somewhere and could in principle be captured in covariates, but we decided (for substantive or pragmatic reasons) that these events/shocks/peculiarities are "just random". This is not a bad thing, it is exactly what we want to measure, but it also means that our dependent variable, a probability, is only defined within the context of our model, that is, by our decision which variables are "just random" and which variables are not. This is different from say a variable length or weight, which can exist outside the context of a model. The problem with comparing models models with different numbers of covariates is that this also changes the dependent variable, making the comparison meaningless.
This is different when we had a variable like length or weight as our dependent variable, as in that case the dependent variables is not affected by the changes in the model. For several different solutions for this problem that have been implemented in Stata see: (Sinning et al. 2008, Buis 2010a, Kohler et al. 2011, Hicks and Tingley 2011).

> Model 3 only has the interactions in it, otherwise it is the same as model 2. How does one interpret the OR's for i.mom_race2 in model 3? I get the usual set of OR's for mom_race2 in the beginning of the output, and the the interactions towards the bottom of the model.
>
> I assumed that the OR's in model 3 should be same as those in model 2 as I'm not additionally adjusting for anything new (ie it is the same as model 2 except for the interaction term).

Model 2 allows the effects of mother's education and mother's marital status to be different for mothers with different racial backgrounds.
However, this argument is symmetric (var1*var2 = var2*var1), so one can also interpret model 3 as allowing the effect of mother's racial background to differ between mother with different education and marital status. If you want to interpret the main effects you need to keep in mind that it is the effect of mother's race for mothers in the reference category in education and marital status. For more on how to interpret interaction terms in non-linear models see: (Buis 2010b)

Hope this helps,
Maarten

Buis, M. L. (2010a). Direct and indirect effects in a logit model. The Stata Journal 10(1), 11-29.

M.L. Buis (2010b) "Stata tip 87: Interpretation of interactions in non-linear models", The Stata Journal, 10(2), pp. 305-308.

Hicks, R. and D. Tingley (2011). Causal mediation analysis. The Stata Journal 11(4), 605-619.

Kohler, U., K. B. Karlson, and A. Holm (2011). Comparing coefficients of nested nonlinear probability models. The Stata Journal 11(3), 420-438.

Sinning, M., M. Hahn, and T. K. Bauer (2008). The Blinder-Oaxaca decomposition for nonlinear regression models. The Stata Journal 8(4), 480-492.

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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