How to do post-hoc tests with logistic regression? I looked at whether participants recycled after being subjected to a given message. There were three groups: a Control group, group A, and group B.
Since my dependent measure was dichotomous (recycling vs. using the waste bin), I performed a logistic regression in SPSS. However, SPSS only let me compare individual groups to the Control group. I found that group A recycled more than controls, but group B did not.
What I am curious about now is whether group A recycled significantly more than group B.
Is it possible to do such a post-hoc test? If so, how?
 A: Unfortunately, I don't know SPSS. That said, if you want to carry out a Wald test where the null is $H_0: \beta_{groupA} - \beta_{groupB} = 0$ you could  ask SPSS the variance/covariance matrix of your parameter estimates and construct the Wald test by hand.
Under $H_0$ your test statistics $\chi^2_{obs}$ is distributed as a $\chi^2$ r.v. with 1 degree of freedom
$$
\chi^2_{obs} = \frac{(\hat{\beta}_{groupA} - \hat{\beta}_{groupB})^2}{{\rm var}[\hat{\beta}_{groupA}]+{\rm var}[\hat{\beta}_{groupB}]-2*{\rm cov}[\hat{\beta}_{groupA},\hat{\beta}_{groupB}]}
$$ 
Now you can calculate your p-value.
But I am sure that SPSS has a command to perform specific tests on the estimated parameters.
A: 
SPSS only let me compare individual groups to the Control group.

Actually SPSS Logistic Regression has about 6 built-in types of contrasts.  One of them (Indicator) compares each group to a control group, which you can specify using the group's number.  I.e., among groups numbered 1 through 4 and labeled as North, South, East, and West, "indicator(3)" will set East as the control group.  Another type (Deviation) shows how each group's logit deviates from the (unweighted) average group's logit.  It's useful to go into either the general Help files or the Command Syntax Reference, also found in Help, to find the definitions for each type.  Personally, I find that Deviation and Indicator are all I ever seem to need.  Maybe that makes me a minor-leaguer :-)
A: In R you can do general multiplicity-adjusted contrasts for logistic regression.  See for example the rms package's contrast.rms function, which uses the R multcomp package. 
