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I have been working my way through some data to build a logistic model. I screened variables (most of them categorical) through an unconditional analysis, letting variables with a p-value of <0.2 pass into a full model. With this full model I built a final model using a backward stepwise elimination based on significant LRT (I'd run a summary on the model, remove the variable with a dummy with the highest p value and run an LRT). I've also done some exploratory stuff with the model building, first using AIC [stepAIC(model,trace=FALSE)] and then using [drop1(model, test = "LRT")] all three resulting in slightly different final models. I was planning on just picking the final model with lowest AIC but not sure if that is appropriate. I also thought I should check on the collinearity, final models were good but when I look at the model without the elimination, if I had removed variables with high GVIF first I would have ended with a different model entirely. Is there a correct process to this? should I have in fact started with VIF and from there done a stepwise elimination?

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