LASSO vs. Standard Variable Selection via p-value How can I reason about compare/contrast variable selection between

*

*LASSO

*running a standard multi-variate regression and setting betas to zero if the p-value is > 0.05

?

The answer is this: you should not, under any circumstances, do the second one.
Statisticians have been crying and screaming at scientists for decades. This is not an appropriate use of p-values. A nonsignificant p-value does not mean there is no effect. All it means is that you have not rejected the null hypothesis.
Moreover, stepwise regression invalidates your p-values and creates inconsistent confidence intervals, unless the model-building process is taken into account.
LASSO is different. LASSO will automatically try to identify useless coefficients and set those to 0, when it is appropriate. Use LASSO and not stepwise regression (the thing where you set coefficients to 0 if they’re not significant). You can also use ridge regression, or a Bayesian model.
