Understanding Interactions in R

Question

I would like to interpret interactions and their confidence intervals in a logit model.

My model looks like:

model.3 <- glm(NRSsuff ~ Gender + NRS0 + Meds + Gender:Meds, family=binomial(link="logit"), data=dataset.model)

The output:

                        Estimate Std. Error z value Pr(>|z|)    
(Intercept)            0.742068   1.036340   0.716 0.473962    
Gender                -0.168875   0.439052  -0.385 0.700508    
NRS05                   0.158400   0.289230   0.548 0.583924    
NRS06                   0.551517   0.322361   1.711 0.087105 .  
NRS07                  -0.694288   0.340947  -2.036 0.041715 *    
Meds                    0.863118   0.376975   2.290 0.022045 *     
Gender:Meds             0.946943   0.465266   2.035 0.041823 *  

The response (ref level: NRS=0), Gender (ref level: Gender=F), and Meds (ref level: Meds=0) are all binary.

The OR for a patient when Gender=F and Meds=0 is then exp(coeff.intercept).

The OR for a patient when Gender=M and Meds=0 includes the intercept. The OR for Gender=M,Meds=0 is then exp(coeff.intercept + coeff.Gender).

But what about for the interaction? I would like the OR for patients treated by males and given meds compared with when patients are treated by females and given meds. I've then:

exp(coeff.Gender + coeff.interaction)

Is this correct? Why is the intercept coefficient not included?

Some information in a previous post seems to be conflicting (Interpreting interaction terms in logit regression with categorical variables) The top answer refers changes in the baseline, while a link out to "COMMUNICATING COMPLEX INFORMATION: THE INTERPRETATION OF STATISTICAL INTERACTION IN MULTIPLE LOGISTIC REGRESSION ANALYSIS" J. J. Chen, 2003 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1447969/) does not talk about the intercept at all.

Thanks!

Answer 1

You need to distinguish between odds and odds ratios. Using your notation exp(coeff.intercept) gives you the odds for having whatever NRSsuff is for untreated women not the odds ratio. The exp(coeff.Gender) gives you the odds ratio for men compared to women and exp(coeff.intercept + coeff.Gender) gives you the odds for untreated men. The interaction term gives you the extra effect of treatment for men over and above the effect of treatment for women.