Modeling techniques such as the Elastic Net and the Lasso are particularly promising for large data sets, where collinearity is typically a problem. In fact, modern data sets often include more variables than observations. This situation is sometimes referred to as the p > n problem, where n is the number of observations and p is the number of predictors. Such data sets require variable selection if traditional modeling techniques are to be used.
 • Maximum Likelihood
 • Forward Selection
 • Lasso
 • Elastic Net
 • Ridge Regression
 • Double Lasso
 • Two-Stage Forward Selection
The Elastic Net and Lasso are relatively recent techniques (Tibshirani, 1996, Zou and Hastie, 2005). Both techniques penalize the size of the model coefficients, resulting in a continuous shrinkage. The amount of shrinkage is determined by a tuning parameter. An optimal level of shrinkage is determined by one of several validation methods. Both techniques have the ability to shrink coefficients to zero. In this way, variable selection is built into the modeling procedure. The Elastic Net model subsumes both the Lasso and ridge regression as special cases. For details, see Statistical Details for Estimation Methods.
 • The Maximum Likelihood method is a classical approach. It provides a baseline to which you can compare the other techniques.
 • The Lasso has two shortcomings. When several variables are highly correlated, it tends to select only one variable from that group. When the number of variables, p, exceeds the number of observations, n, the Lasso selects at most n predictors.
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 • Ridge regression was among the first of the penalized regression methods proposed (Hoerl, 1962, Hoerl and Kennard, 1970). Ridge regression does not shrink coefficients to zero, so it does not perform variable selection.
The Generalized Regression personality also fits an adaptive version of the Lasso and the Elastic Net. These adaptive versions attempt to penalize variables in the true active set less than variables not contained in the true active set. The true active set refers to the set of terms in a model that have an actual effect on the response. The adaptive versions of the Lasso and Elastic Net were developed to ensure that the oracle property holds. The oracle property guarantees the following: Asymptotically, your estimates are what they would have been had you fit the model to the true active set of predictors. More specifically, your model correctly identifies the predictors that should have zero coefficients. Your estimates converge to those that would have been obtained had you started with only the true active set. See Adaptive Methods.

Help created on 9/19/2017