I ran a logistic regression (in R using the glm function) and didn't find significance for a variable I expected to be significant (numerous articles have found significance). When I examined my data carefully, using interaction.plot(), I noticed a huge interaction effect between a co-variate (ethnicity) and this IV. When I included the interaction effect between ethnicity and this IV I do get a significant result. This is great but I want a scientifically sound/reproducible way of explaining why I chose to include this interaction effect in my logistic regression and not others (there is no established theory that would support having this interaction effect, though it is not surprising in hindsight). I ran glmulti() to see if it would tell me what interaction effects I should include. The following is my logistic test:
glm(DV ~ CV1+CV2+IV2+IV3+CV3*IV1, data=LR, family="binomial")
CV1 is sex (factor with two levels), CV2 is age (integer), CV3 is ethnicity (factor with 7 levels), IV1 (integer) is the variable of interest, IV2 and IV3 (factor with two levels). When I ran the following I get "DV ~ 1 + CV3 + IV1" which isn't showing an interaction effect.
gm <- glmulti("Depr", c("CV1","CV2","CV3","IV1","IV2","IV3"), data = LR, family="binomial", marginality=TRUE, exclude=c("CV1:CV2","CV1:CV3","CV2:CV3")) print(gm)
1) what is an objective (scientifically/methodologically sound) way of determining which interaction effects to include in my logistic regression?
2) how do I do this in R? I suspect glmulti() may be wildly inappropriate for this as it is intended to model/predict.
3) related question: I have another independent variable but it is highly correlated with IV1 so I am not sure whether I should exclude it from the logistic regression. Removing it slightly increases the p-values of significant variables but not enough to make much of a difference.
Note: I saw a question related to mine (How to know which interaction terms to include in a regression model?) but I hope my question is more detailed and the only answer to that question recommended pre-existing theory in that area to determine interaction effects (which I don't have).