I need to perform logistic regression for my study. Pretty new to it but have read up on it and have tried it on SPSS. I would like to seek the advice from all of you regarding it.

A brief description on my study: I want to see which factors (categorical and continuous) are significant in influencing the likelihood of occurrence of an event - bird colliding into buildings when they fly. As I'm not sure which are the more important factors, I've used Stepwise Logistic Regression to pinpoint the more significant factors. The two outcomes are collision or no collision.

1) Some of my factors are correlated to one another. But because I did stepwise, it happens that all the correlated ones are eliminated from the final model. Is it still legit to keep the model? Or do I have to check for multicollinearity before I perform Stepwise Logistic Regression and remove the correlated ones before even putting them to the test? (From what I gather, it seems like I could check the remaining factors after but just want to confirm it.)

2) I was expecting that I need to write a final equation like y = b0 +b1x1 +b2x2 +.... but I've been finding papers and I don't see anyone doing it. They merely report the statistically significant factors and the associated odd ratio etc. So we don't have to explicitly write out the model? If we do, can someone advise me how is it written? (Sorry, I think this is quite a noob qn!)

3) From the SPSS output I have, I could calculate sensitivity, specificity, positive predictive values and negative predictive values. I would like your opinion on which of these are more important in telling us how good a model is, and the pros and cons if we use one of them more than others.

(I know I could use AICc but that I think in SPSS, I could only use that in multinomial log regression?)

Thanks for all of your help!!