Reporting of an interaction in a binary logistic regression

Question

I've found some interesting results that I'm trying to write up appropriately, but I'm having a hard time finding any guidance into how to write up an interaction in a binary logistic regression (outcome is 0,1). The interaction was predicted, and this is not an issue. The issue is that I have two categorical predictors. One has 2 levels Var1(1 and 2) the other Var2 has 3 levels (creatively 1,2,3 in the coding). We have a significant Var1*Var2 interaction. Our output lists the beta, SE, Wald,df, Sig, and Exp(B) for Var 1, but due to the 3 levels of Var2, we get only the Wald, df and Sig columns for Var2 (overall, I assume this is a type of omnibus-like test) and the full set of results for Var1 at levels 1 and 2. A similar situation happens with the interaction term. On the overall interaction we have wald, df and sig, and then Var1 (level1) x Var 2 (level1) and Var1(level1) x Var2(level2) interactions with all 5 results.
Our premise is that we expect the interaction, and then do the appropriate follow up contrast test. This we can handle (I think).

Our hangup is basically just how to report the interaction and the model results. The only examples I can find are either only 2x2 interactions (which don't have this complication) or no interaction binary regression write ups. Is there any reference for how to write up these findings that someone could point me towards?

I guess secondly too, is there any good source for explanation of the difference between model fit statistics that SAS spews out? Likelihood Ratio, Score and Wald all seem to test whether the model as a whole with variables, is better than the intercept only model. From what I can see the LR is the preferred method (and the only one that SPSS reports by default), but is there any reference that could tell me why SAS lists the other two, or better when they would be preferrable measures? THanks, Ned

Answer 1

You can report the odds ratios and predicted probabilities and so on for each independent variable at different levels of the other variable. Since you are using SAS see the slice statement in PROC LOGISTIC.

Answer 2

In reply to the second part of your question " I guess secondly too, is there any good source for explanation of the difference between model fit statistics that SAS spews out..." let me suggest Hosmer and Lemeshow's book "Applied Logistic Regression." In the 2000 edition, pp. 14 -16 discuss pros and cons of the likelihood ratio, Wald statistic, and Score test.

I hope this helps!

Answer 3

I only use the LR for determining the signficance of including or excluding a particular variable or block of variables.

I do not have an explicit example, but there are some other ways to assess mode fit. The Hosmer-Lemshow Goodness of Fit test, classification tables, and ROC curves are others that come to mind. Specify the LACKFIT option in the MODEL statement in SAS to request the Hosmer-Lemshow Goodness of Fit test. It also helps to examine the classification table to see how well the model is predicting status. You can request that table with the CTABLE option in the MODEL statement. Finally, you might consider ROC curves as well. There are several options for ROC curves, so it might be wise to go to SAS support documentation for more details.