I have cross classified data in a 2 x 2 x 6 table. Let's call the dimensions
B. I fit a logistic regression to the data with the model
response ~ A * B. An analysis of deviance of that model says that both terms and their interaction are significant.
However, looking at the proportions of the data, it looks like only 2 or so levels of
B are responsible for these significant effects. I would like to test to see which levels are the culprits. Right now, my approach is to perform 6 chi-squared tests on 2 x 2 tables of
response ~ A, and then to adjust the p-values from those tests for multiple comparisons (using the Holm adjustment).
My question is whether there is a better approach to this problem. Is there a more principled modeling approach, or multiple chi-squared test comparison approach?