I've run a LASSO to build a model out of ~60 potential predictors. I'm wondering what the next step is? If there were OLS regression I would find model fit statistics like R2 or AIC. I would also find some statistic like squared semi-partial correlation for each of the predictors.

I'm wondering if there is anything one can do for a LASSO model that tells you about its prediction accuracy, and the relative importance of the coefficients it has generated?

  • $\begingroup$ Is this linear regression or logistic? $\endgroup$ – Christopher John Oct 26 '19 at 10:48
  • $\begingroup$ What is your preferred programming language or statistics software? $\endgroup$ – James Phillips Oct 26 '19 at 11:07
  • $\begingroup$ @ChristopherJohn Linear $\endgroup$ – Dave Oct 28 '19 at 21:14
  • $\begingroup$ @JanesPhillips R $\endgroup$ – Dave Oct 28 '19 at 21:14

You can do repeated cross validation and if it is logistic get the ROC-AUC or perhaps the Brier score. If it is linear regression you can use R^2.

For variable importance you can use the coefficient size.

  • $\begingroup$ Variable importance can only be assessed by coefficient size if the design matrix was scaled columnwise to mean 0 and unit variance. I'd rather use stability selection for variable importance with LASSO, though. $\endgroup$ – Edgar Oct 28 '19 at 16:43
  • $\begingroup$ @Edgar Can you elaborate on both of these ideas? $\endgroup$ – Dave Oct 28 '19 at 21:15
  • $\begingroup$ Why would you rather use stability selection out of interest? Glmnet should z-score normalise the features by default. $\endgroup$ – Christopher John Oct 29 '19 at 7:47
  • $\begingroup$ @ChristopherJohn yes, glmnet normalizes under the hood, but it gives back the coefficients on the original scale. $\endgroup$ – Edgar Oct 29 '19 at 8:46
  • $\begingroup$ Does this mean I should be doing zscore normalisation beforehand to interpret the coefficients? Or how else to do this? Stability selection seems a bit unnecessary if coefficients give importance. $\endgroup$ – Christopher John Oct 30 '19 at 9:00

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