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Shrinkage approach like elastic net can produce predictive, sparse models when p >> n and when there's correlation between the predictors. In Zou and Hastie's paper on the elastic net, the simulation results show that elastic net out performed OLS.

So my question is, (and I know this depends on the actual research goals) in what situation does regression outperform the elastic net?

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    $\begingroup$ Well elastic net is a superset of ols, no so you have to more clearly define your terms. I think what is missing is the causal analysis /significance testing framework (eg for individual coefficients) $\endgroup$ – seanv507 Jan 14 '17 at 21:01
  • $\begingroup$ What do you mean by outperform? Time-wise OLS is always faster. To that extent, OLS will offer equally good $\beta$ estimates compared to EN in less time if the sample is large and all the predictors are relevant and reasonably uncorrelated. Can you make the question clearer please? $\endgroup$ – usεr11852 Jan 15 '17 at 1:27
  • $\begingroup$ @usεr11852 It could be in any way that is advantageous, whether it be predictive power, computing time (like you have mentioned), interpretability, extrapolation, etc. $\endgroup$ – Adrian Jan 17 '17 at 16:06
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Time-wise OLS is always faster. To that extent, OLS will offer equally good β estimates compared to EN in less time if the sample is large and all the predictors are relevant and reasonably uncorrelated. - usεr11852

elastic net is a superset of ols, so you have to more clearly define your terms. I think what is missing is the causal analysis /significance testing framework (eg for individual coefficients) – seanv507

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  • $\begingroup$ I've copied these comments by usεr11852 and seanv507 as a community wiki answer because the comments are, more or less, answers to this question. We have a dramatic gap between answers and questions. At least part of the problem is that some questions are answered in comments: if comments which answered the question were answers instead, we would have fewer unanswered questions. $\endgroup$ – mkt Aug 14 '18 at 9:51

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