I want to determine the interaction between two of my continuous (scale) independent variables on the one dependent variable, which is dichotomous (cases are coded as 0 and 1). I was going to use a two-way ANOVA, but you need categorical or continuous independent variables as well as a continuous dependent. Is there any similar test that would work for my variable types?
I was also going to do a logistic regression to determine how my independent variables predict my dependent. However, upon performing the Box-Tidwell test in SPSS, I learned that two of my independent variables do not have a linear relationship with the logit transformation of the dependent. This violates an assumption of performing logistic regression. My options are to either take out the offending variables (I'd prefer not to) or not do the regressions. What is recommended when a logistic regression cannot work?