I am attempting to conduct a binary logistic regression but I have come to a roadblock relating to multicollinearity. I originally conducted a latent class analysis which resulted in the identification of two classes however now I am interested in investigating whether or not my variables (all categorical) can predict the class that an individual is categorised into? However because variables were able to produce classes does that not mean they are correlated and consequently does that not mean I can't do the logistic regression? I have seen papers use logistic regression following on after latent class analysis so is this ok? Some of them seem to run series of logistic regression analyses is this a way to combat multicollinearity?
I think it is important to realize what a binary logistic regression really does.
Say your input is a continuous variable X, and you regress it on binary Y using binary logistic regression and then forecast fitted values you can have any value in between of 0 and 1. A value of 0.40 is a possible outcome as well, which you can interpret as it being a 0. Outcomes larger than 0.5 are to be considered a 1 in case you want to predict something!