I am trying to select features for a data set that contains what food people have eaten with a result of BMI. However, since I want to see what foods impact BMI most I am trying to use various forms of feature selection for that. When I use LASSO, all coefficients are set to zero which seems to mean that none of them are significant in the model. I then moved on toe recursive feature elimination and that will rank my features but will not tell me if it is important that the person eats more of less of the food. I was wondering if there were other feature selection methods that would work for this and how I could go about selecting features in this data set.
Maybe LASSO is right and none of the variables are good predictors of your outcome (not about significance). If you want a less stringent form of LASSO you can use the ELASTIC NET.
RFE is not a good approach for feature selection. You should compare different models with predictions from a test set, to check whether they truly learned anything.