Multiple Chi-Squared Tests I have cross classified data in a 2 x 2 x 6 table. Let's call the dimensions response, A and 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?
 A: You should look into "partitioning chi-squared".  This is similar in logic to performing post-hoc tests in ANOVA.  It will allow you to determine whether your significant overall test is primarily attributable to differences in particular categories or groups of categories.
A quick google turned up this presentation, which at the end discusses methods for partitioning chi-squared.
http://www.ed.uiuc.edu/courses/EdPsy490AT/lectures/2way_chi-ha-online.pdf
A: The unprincipled approach is to discard the disproportionate data, refit the model and see if logit/conditional odds ratios for response and A are very different (controlling for B).  This might tell you if there's cause for concern.  Pooling the levels of B is another approach.  On more principled lines, If you're worried about relative proportions inducing Simpson's paradox, then you can look into the conditional and marginal odds ratios for response/A and see if they reverse.
For avoiding multiple comparisons in particular, the only thing that occurs to me is to use a hierarchical model which accounts for random effects across levels.
A: Post Hoc test may fit to your problem.
chisqPostHoc() function in R tests for significant differences among all pairs of populations in a chi-square test. Even though, I haven't use it but this link may be useful.
https://www.rforge.net/doc/packages/NCStats/chisqPostHoc.html
Another alternative may be chisq.desc() function from EnQuireR package. 
