Preface: I am aware of this post: Why is lambda "within one standard error from the minimum" is a recommended value for lambda in an elastic net regression?
(It is generally recommended to use lambda.min or preferably lambda.1se).
However, if I pick lambda.min, all predictors remain in my model; if I pick lambda.1se, all predictors are dropped from model.
When I go for a linear model with all variables (lambda.min variant), several predictors seem to be uninformative (no significant relevance for model).
Edit: Conducting a OLS-regression seems to be a no-go in this case - I understand the rationale. However, I wonder, how I can assess model quality apart from predictive power in LASSO-setting?
Since lambda.1se seems to be a convention, I wondered whether it is possible to pick something in between, like lambda.0.5se (lambda.1se/2). I tried it out and it seems to be more informative within variable selection (some predictors remain in model, some predictors are dropped). Is this a reasonable approach?
Edit: I added a graph with lambda/MSE for more information (thanks for hint, @StupidWolf). I guess that it tells me that there is no suitable lambda for a really low CV error, right?
Data set contains around 250 rows, 9 predictor variables, 1 continuous outcome variable. Any advice for me?