Thank you for your detailed explanation and useful references. However I am not sure this is a good example? I just run regular linear regression (i.e. using "regress") with no2_class and all the control variables. The result for no2_class is: coef=2.412, t=4.29. The results are similar to what was shown in the post and there is little benefit of lasso. I don't think one needs to do variable selection at all for this case. Austin and Steyerberg (2015, http://dx.doi.org/10.1016/j... ) shows that for linear regression two observations per variable (there is more than 4 for this example) is quite sufficient.
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