# With multiple imputed data, how do you probe a categorical-by-categorical interaction in logistic regression?

I am working with 10 multiple imputed datasets in SAS. I used the command PROC SURVEYLOGISTIC to fit a multivariate model with 6 predictors (3 dichotomous and 3 categorical) and their interaction terms, controlling for a numbers of relevant covariates.

The predictor variables are as follow:

• CVD (0 = No; 1 =Yes)
• HCA (0 = Low; 1= High)
• EDU (1=High School Dropout; 2=Graduated High School; 3=Some College; 4=Graduated College)
• POV (1=Low; 2=Medium; 3=High)
• LAN (1=Spanish; 2=English)
• STA (0=Old, 1=New, 2=None)

My outcome variable is diabetes medication use and is coded as 0 = no use and 1 = current use I found the following:

1. One of the levels of the interaction of EDU*STA is marginally significant.
2. Only one of the levels of the interaction of POV*STA is marginally significant.

My questions are:

1. When working with multiple imputed data, how do you probe a categorical-by-categorical interaction in logistic regression?
2. What would be the appropriate approach to graphically represent the interaction?

For example, the EDU*STA interaction provides 6 separate coefficients. Examine whether the whole set of those coefficients is different from 0. That's sometimes called a "chunk test." Analyzing a set of interaction coefficients all together gets around the problems arising from which particular levels were specified as references. That can be done with a Wald test; I think you can do that with the CONTRAST statement in SAS, specifying all of a set of interaction coefficients = 0 as a combined null hypothesis (although I don't use SAS and might be mistaken). You also could do a likelihood-ratio test between the full model and the model without that particular set of interactions.
If you do find that an overall test on a set of interactions significantly rules out the null hypothesis, then you can proceed to evaluate particular circumstances. For illustration you should display model predictions for particular scenarios involving the interaction terms of interest, as the interaction terms alone can be hard to interpret without the rest of the model. For example, if you find a particular EDU*STA interaction to be interesting, fix all the other covariate/predictor values at reasonable levels and show how particular combinations of EDU and STA values lead to different outcomes than you would have expected based on each individually.