The attached paper shows what I believe that we should do for predictive models. Best wishes David Booth

Thank you David Eugene Booth . I am wary because we reported on and reviewers expect CIs and p-values (because we plotted the coefficient estimates that incl. these values) thus, your statement in the discussion may throw a stone in the bush we cannot afford at this stage, considering we're on our 2nd revision: "...there is no known way to get confidence intervals and p-values for lasso estimates...". Also, I cannot employ a different statistical method at this stage (we literally do not have time). However, I did notice that you suggest the use of BIC and AIC which relate directly to my question. Lastly, I will keep this paper for future reference and possible use in ecology (my field). Thanks again for sharing and the advances you and your co-authors have made in this regard.

@Rion if you want to compare prediction models you don't use P-VALUEs. See Ewout Steyerberg's book on subject reference in our paper. Good luck, David

Agree however, as per the attached, we can see that the p-values (as asterisks) are valuable to show degrees of significance re. independent variables. I was thus assuming that the lasso method cannot provide these values as per your paper's mention on the pitfalls of using lasso.

Whether lasso can or can't doesn't matter. The point is that tests on regression coefficients don't help you compare prediction ability of your models By the way I believe we said that at the time the paper was under review the omnibus test was the only one available. I believe that Ryan Tibshirani has now extended that. However those tests don't answer the question about comparing different prediction models. See Steyerberg's book. David Booth