Which test to run ... probit or logistic? IV's: categorical School, categorical Grade Level, categorical Living Arrangement, categorical Race, categorical Illness, continuous Time.
DV: withdrawn status (withdrawn or not withdrawn)
I want to determine how much of each variable influences the likelihood a student will withdrawal.  I was looking at probit and logit models, but I am unsure if that's the best way to explain my data.  I am using R as my software.  Any help or feedback would be greatly appreciated.
 A: Probit and logit are both equally appropriate for when your dependent variable is binary, which seems to be the case for you. There isn't any mathematical or theoretical reason to prefer one over the other. The two models make slightly different assumptions about something you can never verify in practice anyways (namely: the distribution of the errors in a OLS model of the latent "propensity to withdraw" - the logit model assumes these errors are logistically distributed and the probit model assumes they are normally distributed, but since you can't ever see the latent variable yourself, you can't ever know what the errors "really" look like). Either logit or probit will give you substantively the same "answer" (and almost identical p values) even though the coefficients that they produce will look very different: this is because the coefficients produced by these models have no intuitive interpretation. You need to do some extra work (like calculating marginal effects) to see how "big" the effect sizes are. This is a whole other issue, so you might want to research "interpreting results from logit models" here or somewhere else.
I'll also note that the sorts of independent variables in your model don't really matter when you are trying to decide what "flavor" of regression to use (OLS, logit, probit, tobit etc.). In general all of these forms of regression all accept the same sorts of independent variables - which can be any combination of continuous or categorical (just make sure you transform your categorical variables into a set of dummy variables before you put them in your model).
