[R] question on lasso

[Constantine Frangakis]

I would appreciate any comments to the following question.
I am trying to build a model for survival based on 155 patients and 70 covariates using lasso. Lasso picks, three variables only, say X1,X2,X3, and  omits the others. I wanted to check why a particular (clinically important) variable, say X4, is omitted by lasso. One of the things I did was I ran lasso on X1,X2,X3 and X4 only. The results (coefs) I get are different from running all 70 variables, and in fact now X4 is not omitted.
Why is that ? should it not be that the global (among all 70 variables) optimum, which is X1,X2,X3 and not X4, be also the local (among the four only) optimum ?
Thank you for your consideration


Constantine Frangakis, PhD
Professor
Departments of Biostatistics
Psychiatry, and Radiology
Johns Hopkins University






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