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I have an Elastic Net model that is selecting a number of variables from X, for prediction of Y. The assumption for Elastic Net is that X is standardized (I'm using Z-Scores), and Y is centered around zero (I'm using Y-mean(Y)). So, I am wondering if my Elastic Net model will act differently if I use both standardized X and Y (i.e., z-scores for both X and Y)?

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I figured out that one should stick with the assumption of ElasticNet, and use standardized predictors and CENTERED outcome. Standardized outcome should not be used and it will lead to different results.

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I'm not sufficiently familiar w/ the elastic net to answer this, but I've noticed across your questions that you seem to have an innate skepticism towards standardized response variables that is inexplicable to me. Standardizing a variable (whether a response variable or a covariate) is a linear transformation; it should have no meaningful effect on an analysis. – gung Oct 27 '12 at 23:23
I do believe that when predictors (X) are standardized, and the outcome (Y) is non-standardized, then there is no effect on the analysis. That is because Y=X.B+C is gonna change to Y=[(X-mean(X))/SD(X)].B'+C. The latter is Y=X.B''+C' whose right side is not dependent on Y. However, when you standardizing Y, you are affecting the X coefficients. The coefficients are going to be multiplied by SD(Y), right? Having said that, prediction is going to change in that the estimated Y (i.e., from test set) is going to be dependent on the SD of Y from training set. – Niousha Oct 28 '12 at 0:57
Continue:: I think this is making a bias, and by only CENTERING Y, and not standardizing it, we will avoid the bias. What do you think? – Niousha Oct 28 '12 at 0:57
If you want to do out of sample prediction later, using centered Y means you will be using the mean from the training data, &/or using the mean & SD from the training data w/ standardized Y. Neither should induce any bias, nor cause any other problems I'm familiar with; in both cases, these are just linear transformations. – gung Oct 28 '12 at 2:13

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