# Select Auxiliary Variables via LASSO with Cross-Validation (Binary and Continuous Outcomes) This function performs LASSO-penalized regression (logistic regression for binary outcomes or linear regression for continuous outcomes) with cross-validation to select auxiliary variables for modeling one or more outcome variables. It allows for the inclusion of all two-way interactions among the auxiliary variables and the option to force certain variables to remain in the model through the use of zero penalty factors. ```r select_auxiliary_variables_lasso_cv( df, outcome_vars, auxiliary_vars, must_have_vars = NULL, check_twoway_int = TRUE, nfolds = 5, verbose = TRUE, standardize = TRUE, return_models = FALSE, parallel = FALSE ) ``` ## Arguments - `df`: A data frame containing the data for modeling. - `outcome_vars`: Character vector of outcome variable names to model. These can be either binary or continuous outcomes. Each must exist in `df` and have at least two unique values (after factor conversion for binary outcomes). - `auxiliary_vars`: Character vector of auxiliary variable names to be used as predictors. - `must_have_vars`: Optional character vector of variable names that must be included in the model (penalty factor 0). If interactions are included, any interaction containing a must-have variable is also assigned zero penalty. The variables in `must_have_vars` should refer to either individual variables or the main effect part of interaction terms. - `check_twoway_int`: Logical; include all two-way interactions among auxiliary variables. Defaults to `TRUE`. - `nfolds`: Number of folds for cross-validation. Defaults to 5. - `verbose`: Logical; print progress messages. Defaults to `TRUE`. - `standardize`: Logical; standardize predictors before fitting. Defaults to `TRUE`. - `return_models`: Logical; return fitted `cv.glmnet` objects. Defaults to `FALSE`. - `parallel`: Logical; run cross-validation in parallel (requires doParallel ). Defaults to `FALSE`. ## Returns An object of class `"select_auxiliary_variables_lasso_cv"` with the following components: - **selected_variables**: Character vector of variables selected across all outcome models. This includes the main effect variables and any interaction terms. - **by_outcome**: Named list of character vectors, each containing the selected variables for each outcome. - **selected_lambdas**: Named numeric vector of lambda values (specifically, lambda.min) for each outcome. - **penalty_factors**: Named numeric vector with penalty factors (0 for must-keep, 1 otherwise). - **models**: List of `cv.glmnet` objects per outcome if `return_models = TRUE`, otherwise an empty list. - **goodness_of_fit**: Named list per outcome with cross-validation metrics (cv_error, cv_error_sd) and full data metrics (deviance_explained for binary outcomes, auc, accuracy, brier_score, rss, mse, r_squared, raw_coefs). - **interaction_metadata**: List containing metadata on interaction terms, main effects in interactions, and the full formula used. ## Details The function supports both binary and continuous outcomes. For binary outcomes, logistic regression is used, and for continuous outcomes, linear regression is used. The function outputs a list with the selected variables across outcomes, the associated lambda values, the goodness-of-fit statistics, and optionally the fitted models and interaction terms. The function supports two types of outcome variables: * Binary outcomes : LASSO logistic regression is used. The outcome variable must have exactly two levels after missing values are removed. * Continuous outcomes : LASSO linear regression is used. The outcome variable should be numeric. For factor variables in `auxiliary_vars`, dummy variables are created to represent each level of the factor. If a factor variable is specified in `must_have_vars`, its dummy variables will be included in the model, ensuring that any interactions containing those variables are also forced into the model. ## Examples ```r ## ------------------------------------------------------------ ## Example 1: Binary + continuous outcomes, with interactions ## and must-have variables (factor expanded to dummies) ## ------------------------------------------------------------ set.seed(123) n <- 150 x1 <- rnorm(n) x2 <- rnorm(n) group <- factor(sample(c("A", "B", "C"), n, replace = TRUE)) ## Generate outcomes with some signal in x1, x2 and group, plus an interaction eta_bin <- -0.5 + 1.2 * x2 - 0.8 * (group == "C") + 0.5 * x1 * x2 p <- 1 / (1 + exp(-eta_bin)) y_bin <- rbinom(n, 1, p) y_cont <- 1.5 * x1 - 2 * (group == "B") + 0.7 * x1 * x2 + rnorm(n, sd = 0.7) df <- data.frame(y_bin = y_bin, y_cont = y_cont, x1 = x1, x2 = x2, group = group) res1 <- select_auxiliary_variables_lasso_cv( df = df, outcome_vars = c("y_bin", "y_cont"), auxiliary_vars = c("x1", "x2", "group"), must_have_vars = c("x1", "group"), # 'group' (factor) expands to its dummies check_twoway_int = TRUE, nfolds = 3, verbose = FALSE, standardize = TRUE, return_models = FALSE ) ## Inspect selections and metadata res1$selected_variables res1$by_outcome res1$selected_lambdas names(which(res1$penalty_factors == 0)) # must-keep terms (incl. factor dummies & interactions) res1$interaction_metadata$full_formula ## ------------------------------------------------------------ ## Example 2: Single continuous outcome, main effects only ## ------------------------------------------------------------ set.seed(456) n2 <- 120 a <- rnorm(n2) b <- rnorm(n2) f <- factor(sample(c("a", "b"), n2, replace = TRUE)) y <- 2 * a - 1 * (f == "b") + rnorm(n2, sd = 1) toy <- data.frame(y = y, a = a, b = b, f = f) res2 <- select_auxiliary_variables_lasso_cv( df = toy, outcome_vars = "y", auxiliary_vars = c("a", "b", "f"), check_twoway_int = FALSE, # main effects only nfolds = 3, verbose = FALSE ) res2$selected_variables res2$selected_lambdas res2$goodness_of_fit$y ```

select_auxiliary_variables_lasso_cv function