What does it mean when the solution path for Elastic Net is not single-valued?

SDF1 — Sat, 10 Jun 2023 23:26:10 GMT

Dear JMP Community,

(W10, 64-bit, JMP Pro 15.2.1)

I am running a model to assess the active predictors. I am doing this by using the Autovalidation add-in to generate a Null Factor for my data. I then use the GenReg platform to find estimates for each possible X-factor and then Bootstrap those estimates to get a better assessment of the contributions to the response. I came across a very strange behavior when running the Elastic Net with 400 grid points, 5-fold cross validation, and an Alpha of 0 (I actually ran it with Alpha empty, and the best fitting result came back with Alpha=0.

The result for the solution path of the -logliklihood came back with both the validation and training sets showing non-single-valued responses. To me, this doesn't make sense, as for a fixed "magnitude of scaled parameter estimates" I would expect a single value of the -logliklihood, not multiple values.

Any clue as to why this happened? It doesn't happen when I have the grid points set to other values, or even all the time. Was it just a random fluke, or is there some other reason? Any feedback to prevent this from happening in the future would be helpful.

Thanks!,

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What does it mean when the solution path for Elastic Net is not single-valued?