So I am using LASSO in order to reduce the amount of independent variables (~150) I have for my logistic model (n=1200). However, when doing so, the end result (i.e. number of predictors) it chooses varies depending on the seed I provide. 2-3 predictors are consistent, but then sometimes others are added. I guess this is due to the cross-validation for the best lambda parameter often used for LASSO. However, it just seem so inconsistent.
I mean I am using bootstrap in order to validate my results. So in the end I end up with meaningful standard errors, frequency of predictors, corrected statistics etc., but that doesn't change the fact, that the main model, defined on the original data, is kind of random depending on the seed.
How does one "solve" this ? Run the "main model" (i.e. original data) with 100-1000 different seeds to see which predictors are most frequently chosen, and then chose the model that actually has these predictors, or is there anything else that could be recommended ?