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I ran a logistic regression with categorical variables. The estimates and odds ratios are: Marital_Status- Estimate: .6605 Odds Ratio: 3.747 Professional Suffix: .5342 Odds Ratio: 2.911

I understand that the odds ratio says : "The odds of the dependent variable happening is 3.747 times higher if someone is married than if someone is single"
and "The odds of the dependent variable happening is 2.911 times higher if someone has a professional suffix than if they don't"

Question: Is there a way to say "If someone is married AND they have a professional suffix then they odds of the dependent variable happening will be ___? Would it be Y(1)= intercept + .6605O + .5342? Or is that unnecessary to do? Should results only be looked at with holding all other independent variables constant?

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  • $\begingroup$ Odds ratio means one's odds vs another's odds. In your example, the ratio of odds of married vs not married is 3.747. In your question, one person is married and has a professional suffix. Which one is another person? $\endgroup$
    – user158565
    Jun 1 '17 at 16:38
  • $\begingroup$ I'm not sure I understand your question but for example i guess I'd wonder what is the odds of married and has a professional suffix vs not married with no professional suffix. $\endgroup$
    – Mike
    Jun 1 '17 at 17:05
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    $\begingroup$ Yes, your answer is clear. Your another person is not married with no professional suffix. Could you post more information on your model fitting? Given the estimate of the that coefficient being 0.6605, the odds ratio should be $\exp(0.6605) = 1.9358$. where that 3.747 comes from? Same question for 2.911. Any interaction and/or other variables in the model? $\endgroup$
    – user158565
    Jun 1 '17 at 17:49
  • $\begingroup$ There are a total of 14 variables in the model. I ran a correlation matrix to see if there were any correlations between variables and there didn't seem to be any $\endgroup$
    – Mike
    Jun 5 '17 at 13:20
  • $\begingroup$ To help with the understanding here is the cross tab for both variables. Marital Status 0 - Donor 0 - 29264 Marital Status 0 - Donor 1 - 9137 Marital Status 1 - Donor 0 - 9631 Marital Status 1 - Donor 0 - 13325 Prof Suffix 0 - Donor 0 - 38382 Prof Suffix 0 - Donor 1 - 21143 Prof Suffix 1 - Donor 0 - 513 Prof Suffix 1 - Donor 0 - 1319 Doing the odds ratio calculations by had I observed: Marital Status - 4.43 and Prof Suffix - 4.67 $\endgroup$
    – Mike
    Jun 5 '17 at 14:01
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The interpretation you suggest is in fact the one that is expected. Interaction effects and the effects of the constituent predictors need to be interpreted jointly, and one computes marginal effects for this.

See e.g. Buis M. 2010. "Stata tip 87: Interpretation of interactions in nonlinear models" The Stata Journal, 10(2) or the equivalent in R.

You might also want to read: Brambor, T., Clark, W. R., and Golder, M. (2006). Understanding interaction models: Improving empirical analyses. Political Analysis, 14(1):63–82.

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If you created a derived binary variable to flag that condition vs the other, you could retrain the model after removing the original variables and get your answer. I do not think you can arrive at the answer you want without doing so.

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