Sample size calculation for elastic net regression I am using elastic net regression to investigate the effect of preditors on the response variable while accounting for multicollinearity among the predictors. But I wish to perform a sample size calculation in advance. I cannot find relevant materials on this issue. Is it fine to do sample size calculation based on multiple linear regression? Will elastic net regression require less or more samples compared with multiple linear regression given the same data? Anyway, I wish to know how to do sample size calculation for elastic net regression.
 A: It is unlikely that you can calculate the required sample size, as you would need to assume not only effect sizes and variance, but also covariance (i.e. to what extent are explanatory variables correlated) and have an idea of what the hyperparameter ($\lambda$) might be. Instead, you could take some rule of thumb or try and simulate some data (but beware, for simulation you will need at least an idea of all of the aforementioned as well). Of course if you have previous data of a similar experiment, you might be able to estimate some of these things.
As for your other question, regularized models in general require fewer samples$^*$ to obtain estimates of the same number of variables. In fact, you can even estimate more parameters than you have observations (i.e. $n < p $). 
The real question is what you want to do with your model. You can estimate as much as you'd like with as little samples as you like, but the quality of those estimates will be poor and the bias of regularisation might become problematic. If you want to report significance, then you should be aware that $p$-values, on top of their usual issues, are generally unreliable in regularized models.

$^*$ See for example the original paper on elastic net:   


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*Zou & Hastie (2005): Regularization and variable selection via the
elastic net
