I understand that for experienced statisticians it seems as though this question has been solved elsewhere but for me, none of those threads have explained, in language which I can understand, the difference between odds ratios between a binary categorical, and continuous independent variable. Which makes it immensely frustrating to have the thread marked as duplicate by someone

Sorry to open this up again @AchimZeileis ...would you know how to computer AIC/BIC resulting from the encompassing tests?

Thanks all. @robin.datadrivers I'm using R and have edited my post to include code. When I say very large, its the British Election study so a couple of thousand perhaps. What is imputation and how can I use it? Thanks