I am running a probit regression which aims to determine which variables influence whether a graduate feels 'mismatched' (e.g. not using the qualification they've learned) in their job.
We are using a dataset which contains a lot of variables regarding demographics, previous study, current work, and perceptions of 'mismatch'. There is plenty of multicollinearity in different variables and I presumably have to exercise judgement about what is included in the model.
One big problem I have encountered regards multicollinearity: By a large margin, the best explanatory variable for one type of mismatch, is another type of mismatch (e.g. the biggest influence of whether you feel your qualification is mismatched to your job is whether you feel your field of study is mismatched to your job). However, including this variable in the model reduces the p-values of every other potentially interesting variable which are relevant to my underlying theoretical model. It also doesn't feel like p-values should guide my variable selection.
My question - can I leave out these variables, and opt for a less predictive model which considers a broader set of variables (demographics, study and work)? My concern would be that this model would then be naive to the effects of this variable, but I'm genuinely confused.