# Using variables selected from lasso regression in standard regression

I was wondering about the ethics of using lasso regression for variable selection and then simply entering the selected variables into a standard regression.

Is it kosher to do this?

• probably not because Lasso has an additional L1 constraint compared to the "standard" regression. Both will produce different estimates – user3119750 Oct 19 '17 at 19:30
• Yes I suspected as much but was interested in why. I just wondered whether the shrinkage towards 0 in a lasso, in its own way, produces another form of bias. I guess I'm interested in which estimates are more 'accurate' (acknowledging the difficulty with notions like accuracy in statistics) – llewmills Oct 19 '17 at 19:42
• What's your goal with the analysis? Why do the LASSO estimates not meet this goal? – Matthew Drury Oct 19 '17 at 20:07
• @Matthew Drury my goal is to select the model, from a list of 17 predictors, that best predicts the outcome variable. My boss chose the variables, from a much larger number, that were the most theoretically sound; however 17 seems like too large a number to appear like anything other than fishing. if I am going to fish, I want to do it ethically (i.e. no stepwise regression). But my boss wants p-values and the glmnet package in R doesn't seem to supply any. I wondered if it was ok to use glmnet to supply me with variables, then lm() to run the analysis. I guessed not but wanted to check. – llewmills Oct 19 '17 at 21:39
• Do you know what your boss intends to do with the p-values? If your goal is predictive power, p-values have nothing to say on that issue, so your boss's request is not inline with the business problem. Here are some simple examples to make that point: stats.stackexchange.com/questions/291210/… – Matthew Drury Oct 19 '17 at 23:52

The reason this is frowned upon is because you are performing model selection (that's the second S in LASSO), and in model selection you are reusing your data to figure out the best model. I'm hoping someone else can give you a better explanation mathematically, because I don't think I can. You are simply messing with the conditionality that got you to $\hat\beta^{LASSO}$.