Elastic Net Wrappers

Elastic net regularized regression can be a powerful machine learning technique that reduces overfitting and can work with high-dimensional data. Furthermore, it can also provide information on the strength and nature of the relation between different predictors and the outcome. It does so by combining two regularization methods, ridge regression (L2) which shrinks model estimates and LASSO regression (L1) which removes variables that don’t contribute to the model. The amount of ridge and lasso regression is expressed by a variable alpha which varies from 0 (exclusively ridge regression) to 1 (exclusively LASSO). The strength of the regularization is defined by a variable lambda with higher values of lambda leading to more shrinkage of the coefficients. The best alpha and lambda are selected through a grid search.

Wrappers

The wrappers can perform a train test split or a cross-validation. This can be done is a stratified or non-stratified manner. The wrappers can handle binary and continuous outcomes. For binary outcomes, the area under the curve (AUD), sensitivity, specifivity, positive predictive value (PPV), and negative predictive value (NPV) are calculated. for continuous outcomes, the R2, the root mean squared error (RMSE), mean squared error (MSE), and mean absolute error (MAE) are calculated. The wrappers can work with continuous and categorical predictors, both at the within-subject and between-subject level.

Arguments

• data

Dataframe which includes the outcome and the predictor variables

• by

Only included in the pooled wrapper. A list of elements by which the data is grouped.

• predictors_con

A list of continuous predictors that will be used to predict the outcome. In the pooled wrapper, the within-subject continuous predictors have to be entered here.

• predictors_cat

A list of categorical predictors that will be used to predict the outcome. In the pooled wrapper, the within-subject categorical predictors have to be entered here.

• between_predictors_con

A list of between-subject continuous predictors that will be used to predict the outcome. Only available in the pooled wrapper.

• between_predictors_cat

A list of between-subject categorical predictors that will be used to predict the outcome. Only available in the pooled wrapper.

• split

A number indicating the percentage of the data that will be used as training data. The rest of the data is used as test data. This argument is ignored when nested cross-validation is used. The default value is 80.

• outer_cv

A number defining how many folds will be used in the outer cross-validation loop. Specifying a number here will make the wrapper use nested cross-validation.

• stratified

A logical indicating whether the train test split or cross-validation needs to be stratified. The default is TRUE.

• scaling

A logical defining whether the continuous predictors need to be scaled. In the pooled wrapper, the within-subject continuous predictors are scaled at the within-person level and the between-subject continuous predictors are scaled at the between-subject level. The default is TRUE.

• repeated_cv

A number indicating how many times the inner cross-validation loop needs to be repeated. The default value is 1, meaning that the inner cross-validation loop is not repeated.

• ensr_cv

A number defining how many folds will be used in the inner cross-validation loop. The default value is 10.

• ensr_alphas

A list of numbers ranging between 0 and 1 that will be used in in the grid search to find the best alpha and lambda. The default values are 0.0000000 0.1111111, 0.2222222, 0.3333333, 0.4444444, 0.5555556, 0.6666667, 0.7777778, 0.8888889, 1.0000000.

• ensr_lambdas

A number identifying how many lambda values will be used in the grid search to find the best alpha and lambda. The default value is 100.

• stop_train

A number specifying the minimum number of observations the train data needs to have before the model is trained.

• stop_test

A number defining the minimum number of observations the test data needs to have before the model is evaluated.

• family

A character specifying whether the outcome is 'binary' or 'contiunous'. The default is 'binary'.

• shuffle

A logical identifying whether the data need to be shuffled before the cross-validation

• seed

A number defining the seed which is used for the steps of the wrapper that are random.

• pred_min

A number defining the lower end of the predictions for continuous outcomes.

• pred_max

A number specifying the upper end of the predictions for continuous outcomes.