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How can I determine significant predictors from a multi-variate lasso model specifically using glmnet package? The dataset has 11 variables in the output space and 300 variables in the input space. There is also a lot of collinearity amongst the predictors. Is it possible to get p-values? or Should I just use beta coefficients of reduced variables of the final model? Does it make sense to fit a linear model from the reduced set of input variables of the lasso model and then compute their statistical significance?

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  • $\begingroup$ It would probably help if you clarified what you want to use the p-values for. You've already used LASSO to select variables... $\endgroup$ – Gregor Thomas Jun 15 '20 at 13:47
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Is it possible to get p-values?

From glmnet, no. Because the model is purposefully biased, traditional tests of hypothesis are invalid.

Does it make sense to fit a linear model from the reduced set of input variables of the lasso model and then compute their statistical significance?

I would recommend against this, as the test would be conditional on the fact that the variable is selected. People do this none the less, but it really doesn't tell the whole story transparently.

Ryan Tibshirani wrote this paper and a corresponding R package to do post selection inference for the lasso. The package returns confidence intervals, but I haven't had the time to play with it and check the coverage properties myself.

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  • $\begingroup$ Thanks! The fact that it is multivariate regression makes it a little more challenging. Each output variable would have its own set of beta coefficients. Is it enough if I just use beta coefficients for the inference? $\endgroup$ – Mohamad Sahil Jun 15 '20 at 15:41
  • $\begingroup$ The inference you usually do won't work. You'd have to read Tibshirani's paper to answer your question from that perspective $\endgroup$ – Demetri Pananos Jun 15 '20 at 16:04
  • $\begingroup$ Thanks, I'll look into it. Hope it can also be extended to multivariate lasso regression. $\endgroup$ – Mohamad Sahil Jun 15 '20 at 16:38

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