# Understanding Interactions in R

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!