Choosing the best type of analysis for my variables and objectives I am struggling to identify the best analysis for my design. My two independent variables are binary (dichotomous) and my dependent variable is also binary (dichotomous). The goal is to find whether there are differences between the IVs in affecting the DV, and whether there is an interaction between my variables. I need what ANOVA does but I cannot use ANOVA as my DV is dichotomous. I'm not sure if a binary logistic regression is a good fit for my aim? I also worry that I may have to use a loglinear model (logit) analysis (I have seen a paper using it for this type of design) as I am struggling to find tutorials of how to conduct the logit type of loglinear analysis in spss.
 A: This answer is likely from a completely different world than the one you live in, but I would recommend to consider partial information decomposition (PID). It is a rather new development, I have recently written a publication detailing its application to experimental data.
The idea is that PID splits the information shared by two IVs and one DV into 4 parts: information uniquely shared by each IV, information redundantly shared by both IVs, and information synergistically shared by both IVs. The procedure is rather stable for discrete variables (not yet the case for continuous variables), and should be straightforward to apply to your case. For example, consider the IDTxl library in Python.
In simple terms, your IVs can have independent predictive power over the DV (called unique in PID), shared or redundant predictive power over the DV, and can also interact synergistically, such that predictive power of both IVs taken together is greater than that of individual IVs. A great example of such synergistic interaction is the XOR function. It is easy to observe that for XOR both IVs are completely uncorrelated to the DV, but taken together they completely determine the DV.
A: Binary logistic regression should be fine (basically, ANOVA is linear regression on categorical dummy variables, and what you have is a logistic regression of this kind, at least if model assumptions are OK).
There is no specific distinction between IV and DV in loglinear models, although I think this could probably also be applied here. It would require some thought about what exactly to test, so "out of the box" I'd prefer the logistic regression.
