# Categorical Regression Regularization

Method. Regularization methods can improve the predictive error of the model by reducing the variability in the estimates of regression coefficient by shrinking the estimates toward 0. The Lasso and Elastic Net will shrink some coefficient estimates to exactly 0, thus providing a form of variable selection. When a regularization method is requested, the regularized model and coefficients for each penalty coefficient value are written to an external IBM® SPSS® Statistics data file or dataset in the current session. See the topic Categorical Regression Save for more information.

• Ridge regression. Ridge regression shrinks coefficients by introducing a penalty term equal to the sum of squared coefficients times a penalty coefficient. This coefficient can range from 0 (no penalty) to 1; the procedure will search for the "best" value of the penalty if you specify a range and increment.
• Lasso. The Lasso's penalty term is based on the sum of absolute coefficients, and the specification of a penalty coefficient is similar to that of Ridge regression; however, the Lasso is more computationally intensive.
• Elastic net. The Elastic Net simply combines the Lasso and Ridge regression penalties, and will search over the grid of values specified to find the "best" Lasso and Ridge regression penalty coefficients. For a given pair of Lasso and Ridge regression penalties, the Elastic Net is not much more computationally expensive than the Lasso.

Display regularization plots. These are plots of the regression coefficients versus the regularization penalty. When searching a range of values for the "best" penalty coefficient, it provides a view of how the regression coefficients change over that range.

Elastic Net Plots. For the Elastic Net method, separate regularization plots are produced by values of the Ridge regression penalty. All possible plots uses every value in the range determined by the minimum and maximum Ridge regression penalty values specified. For some Ridge penalties allows you to specify a subset of the values in the range determined by the minimum and maximum. Simply type the number of a penalty value (or specify a range of values) and click Add.

To Specify CATREG Regularization

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