Ordinal outcome survey regularization and variable selection I am analyzing some survey data with many thousands of respondants. My main dependent variable of interest is a three-level Likert scale (very/pretty/not-so-much).
I have ~50 predictors. I would like to use a cross-validated LASSO to select variables and 'explain' the response. I don't have a lot of prior knowledge about the predictors.
My current inclination is to just treat the response variable as continuous 0-1-2, and use cv.glmnet to run the LASSO. 
My understanding is that means two things:


*

*Assuming the difference between 'very' and 'pretty' is the same as the difference between 'pretty' and 'not so'

*I won't be able to evaluate the predictive error so easily (on my test set), because the predictions will be on a continuous interval while the results are discrete. (Though I suppose I could round the predictions?)
My questions:


*

*Is the above sensible?

*Is there a better way I can use LASSO for this sort of response variable?

*Is there a better approach altogether?
 A: I don't know if this is an "ANSWER" in the traditional sense.  More of a suggestion for consideration.
You might try running your LASSO on the forward continuation ratio (CR) flags formed by considering $CR_0$ to be 0 for responses={0} and to be 1 for responses={1,2} (first continuation ratio).  And $CR_1$ to be 0 for responses={1} and 1 for responses={2}.
If your response data are considered from a multinomial, the $CR_i$ values are both binomial and independent and your LASSO on $CR_0$ would be evaluating the important predictors for 'SO' versus 'NOT SO' while your LASSO on $CR_1$ would be evaluating the important predictors for 'VERY' versus 'NOT VERY'.
Maybe put simpler: The continuation ratio models the transition probabilities from NOT-SO to SO and the transition probabilities from PRETTY-MUCH-SO to VERY-MUCH-SO.
These are true ordinal models with more typical distributions.  Both can be LASSO'd separately because the questions being answered are not, after all, the same.  Predictors for why people transition from HATE-LOBSTER-BISQUE to either LIKE-LOBSTER-BISQUE or LOVE-LOBSTER-BISQUE is likely to be "I don't like lobster".  But people who transition from LIKE to LOVE already like lobster.  So this transition is likely to relate to something else.
In other words, my concern for you is not so much about the usual ordinal-versus-continuous caveats as it is that you are one-dimensionalizing a scale that has deeper structure.  The CR's capture this but forcing them to an interval scale does not.
