# Fit a glmnet Model with Repeated Cross-Validation Repeated K-fold cross-validation over a per-alpha lambda path, with a combined 1-SE rule across repeats. Preserves fields expected by `predict.svem_model()` and internal prediction helpers. Optionally uses `glmnet`'s built-in relaxed elastic net for both the warm-start path and each CV fit. When `relaxed = TRUE`, the final coefficients are taken from a `cv.glmnet()` object at the chosen lambda so that the returned model reflects the relaxed solution (including its chosen gamma). ```r glmnet_with_cv( formula, data, glmnet_alpha = c(0.5, 1), standardize = TRUE, nfolds = 10, repeats = 5, choose_rule = c("min", "1se"), seed = NULL, exclude = NULL, relaxed = FALSE, relax_gamma = NULL, family = c("gaussian", "binomial"), ... ) ``` ## Arguments - `formula`: Model formula. - `data`: Data frame containing the variables in the model. - `glmnet_alpha`: Numeric vector of Elastic Net mixing parameters (alphas) in `[0,1]`; default `c(0.5, 1)`. When `relaxed = TRUE`, any `alpha = 0` (ridge) is dropped with a warning. - `standardize`: Logical passed to `glmnet()` and `cv.glmnet()` (default `TRUE`). - `nfolds`: Requested number of CV folds (default `10`). Internally constrained so that there are at least about 3 observations per fold and at least 5 folds when possible. - `repeats`: Number of independent CV repeats (default `5`). Each repeat reuses the same folds across all alphas for paired comparisons. - `choose_rule`: Character; how to choose lambda within each alpha: * `"min"`: lambda minimizing the cross-validated criterion. * `"1se"`: largest lambda within 1 combined SE of the minimum, where the SE includes both within- and between-repeat variability. Default is `"min"`. In small-mixture simulations, the 1-SE rule tended to increase RMSE on held-out data, so `"min"` is used as the default here. - `seed`: Optional integer seed for reproducible fold IDs (and the ridge fallback, if used). - `exclude`: Optional vector or function for `glmnet`'s `exclude=` argument. If a function, `cv.glmnet()` applies it inside each training fold (requires `glmnet` >= 4.1-2). - `relaxed`: Logical; if `TRUE`, call `glmnet()` and `cv.glmnet()` with `relax = TRUE` and optionally a `gamma` path (default `FALSE`). If `cv.glmnet(relax = TRUE)` fails for a particular repeat/alpha, the function retries that fit without relaxation; the number of such fallbacks is recorded in `meta$relax_cv_fallbacks`. - `relax_gamma`: Optional numeric vector passed as `gamma=` to `glmnet()` and `cv.glmnet()` when `relaxed = TRUE`. If `NULL`, glmnet's internal default gamma grid is used. - `family`: Model family: either `"gaussian"` or `"binomial"`, or the corresponding `stats::gaussian()` or `stats::binomial()` family objects with canonical links. For Gaussian, `y` must be numeric. For binomial, `y` must be 0/1 numeric, logical, or a factor with exactly 2 levels (the second level is treated as 1). Non-canonical links are not supported. - `...`: Additional arguments forwarded to both `cv.glmnet()` and `glmnet()`, for example: `weights`, `parallel`, `type.measure`, `intercept`, `maxit`, `lower.limits`, `upper.limits`, `penalty.factor`, `offset`, `standardize.response`, `keep`, and so on. If `family` is supplied here, it is ignored in favor of the explicit `family` argument. ## Returns A list of class `c("svem_cv","svem_model")` with elements: * `parms` Named numeric vector of coefficients (including `"(Intercept)"`). * `glmnet_alpha` Numeric vector of alphas searched. * `best_alpha` Numeric; winning alpha. * `best_lambda` Numeric; winning lambda. * `y_pred` In-sample predictions from the returned coefficients (fitted values for Gaussian; probabilities for binomial). * `debias_fit` For Gaussian, an optional `lm(y ~ y_pred)` calibration model; `NULL` otherwise. * `y_pred_debiased` If `debias_fit` exists, its fitted values; otherwise `NULL`. * `cv_summary` Named list (one element per alpha) of data frames with columns `lambda`, `mean_cvm`, `sd_cvm`, `se_combined`, `n_repeats`, `idx_min`, `idx_1se`. * `formula` Original modeling formula. * `terms` Training `terms` object with environment set to `baseenv()`. * `training_X` Training design matrix (without intercept column). * `actual_y` Training response vector used for glmnet: numeric `y` for Gaussian, or 0/1 numeric `y` for binomial. * `xlevels` Factor and character levels seen during training (for safe prediction). * `contrasts` Contrasts used for factor predictors during training. * `schema` List `list(feature_names, terms_str, xlevels, contrasts, terms_hash)` for deterministic prediction. * `note` Character vector of notes (for example, dropped rows, intercept-only path, ridge fallback, relaxed-coefficient source). * `meta` List with fields such as `nfolds`, `repeats`, `rule`, `family`, `relaxed`, `relax_cv_fallbacks`, and `cv_object` (the final `cv.glmnet()` object when `relaxed = TRUE` and `keep = TRUE`, otherwise `NULL`). * `diagnostics` List of simple diagnostics for the selected model, currently including: * `k_final`: number of coefficients estimated as nonzero **including** the intercept. * `k_final_no_intercept`: number of nonzero slope coefficients (excludes the intercept). * `family` Character scalar giving the resolved family (`"gaussian"` or `"binomial"`), mirroring `meta$family`. ## Details This function is a convenience wrapper around `glmnet()` and `cv.glmnet()` that returns an object in the same structural format as `SVEMnet()` (class `"svem_model"`). It is intended for: * direct comparison of standard cross-validated glmnet fits to SVEMnet models using the same prediction and schema tools, or * users who want a repeated-`cv.glmnet()` workflow without any SVEM weighting or bootstrap ensembling. It is not called internally by the SVEM bootstrap routines. The basic workflow is: 1. For each `alpha` in `glmnet_alpha`, generate a set of CV fold IDs (shared across alphas and repeats). 2. For that alpha, run `repeats` independent `cv.glmnet()` fits, align the lambda paths, and aggregate the CV curves. 3. At each lambda, compute a combined SE that accounts for both within-repeat and between-repeat variability. 4. Apply `choose_rule` (`"min"` or `"1se"`) to select lambda for that alpha, then choose the best alpha by comparing these per-alpha scores. Special cases and fallbacks: * If there are no predictors after `model.matrix()` (an intercept-only model), the function returns an intercept-only fit without calling `glmnet()`, along with a minimal schema for safe prediction. * If all `cv.glmnet()` attempts fail for every alpha (a rare edge case), the function falls back to a manual ridge (`alpha = 0`) CV search over a fixed lambda grid and returns the best ridge solution. For Gaussian models this search uses a mean-squared-error criterion; for binomial models it uses a negative log-likelihood (deviance-equivalent) criterion. Family-specific behavior: * For the Gaussian family, an optional calibration `lm(y ~ y_pred)` is fit on the training data (when there is sufficient variation), and both `y_pred` and `y_pred_debiased` are stored. * For the binomial family, `y_pred` is always on the probability (response) scale and debiasing is not applied. Both the primary cross-validation and any ridge fallback use deviance-style criteria (binomial negative log-likelihood) rather than squared error. Design-matrix schema and contrasts: * The training `terms` are stored with environment set to `baseenv()`. * Factor and character levels are recorded in `xlevels` for safe prediction. * Per-factor contrasts are stored in `contrasts`, normalized so that any contrasts recorded as character names are converted back to contrast functions at prediction time. The returned object inherits classes `"svem_cv"` and `"svem_model"` and is designed to be compatible with SVEMnet prediction and schema utilities. It is a standalone, standard glmnet CV workflow that does not use SVEM-style bootstrap weighting or ensembling. ## Acknowledgments OpenAI's GPT models (o1-preview through GPT-5 Pro) were used to assist with coding and roxygen documentation; all content was reviewed and finalized by the author. ## Examples ```r set.seed(123) n <- 100; p <- 10 X <- matrix(rnorm(n * p), n, p) beta <- c(1, -1, rep(0, p - 2)) y <- as.numeric(X %*% beta + rnorm(n)) df_ex <- data.frame(y = y, X) colnames(df_ex) <- c("y", paste0("x", 1:p)) # Gaussian example, v1-like behavior: choose_rule = "min" fit_min <- glmnet_with_cv( y ~ ., df_ex, glmnet_alpha = 1, nfolds = 5, repeats = 1, choose_rule = "min", seed = 42, family = "gaussian" ) # Gaussian example, relaxed path with gamma search fit_relax <- glmnet_with_cv( y ~ ., df_ex, glmnet_alpha = 1, nfolds = 5, repeats = 1, relaxed = TRUE, seed = 42, family = "gaussian" ) # Binomial example (numeric 0/1 response) set.seed(456) n2 <- 150; p2 <- 8 X2 <- matrix(rnorm(n2 * p2), n2, p2) beta2 <- c(1.0, -1.5, rep(0, p2 - 2)) linpred <- as.numeric(X2 %*% beta2) prob <- plogis(linpred) y_bin <- rbinom(n2, size = 1, prob = prob) df_bin <- data.frame(y = y_bin, X2) colnames(df_bin) <- c("y", paste0("x", 1:p2)) fit_bin <- glmnet_with_cv( y ~ ., df_bin, glmnet_alpha = c(0.5, 1), nfolds = 5, repeats = 2, seed = 99, family = "binomial" ) ``` ## References Gotwalt, C., & Ramsey, P. (2018). Model Validation Strategies for Designed Experiments Using Bootstrapping Techniques With Applications to Biopharmaceuticals. **JMP Discovery Conference**. [https://community.jmp.com/t5/Abstracts/Model-Validation-Strategies-for-Designed-Experiments-Using/ev-p/849873/redirect_from_archived_page/true](https://community.jmp.com/t5/Abstracts/Model-Validation-Strategies-for-Designed-Experiments-Using/ev-p/849873/redirect_from_archived_page/true) Karl, A. T. (2024). A randomized permutation whole-model test heuristic for Self-Validated Ensemble Models (SVEM). **Chemometrics and Intelligent Laboratory Systems**, **249**, 105122. tools:::Rd_expr_doi("10.1016/j.chemolab.2024.105122") Karl, A., Wisnowski, J., & Rushing, H. (2022). JMP Pro 17 Remedies for Practical Struggles with Mixture Experiments. JMP Discovery Conference. tools:::Rd_expr_doi("10.13140/RG.2.2.34598.40003/1") Lemkus, T., Gotwalt, C., Ramsey, P., & Weese, M. L. (2021). Self-Validated Ensemble Models for Design of Experiments. **Chemometrics and Intelligent Laboratory Systems**, 219, 104439. tools:::Rd_expr_doi("10.1016/j.chemolab.2021.104439") Xu, L., Gotwalt, C., Hong, Y., King, C. B., & Meeker, W. Q. (2020). Applications of the Fractional-Random-Weight Bootstrap. **The American Statistician**, 74(4), 345–358. tools:::Rd_expr_doi("10.1080/00031305.2020.1731599") Ramsey, P., Gaudard, M., & Levin, W. (2021). Accelerating Innovation with Space Filling Mixture Designs, Neural Networks and SVEM. **JMP Discovery Conference**. [https://community.jmp.com/t5/Abstracts/Accelerating-Innovation-with-Space-Filling-Mixture-Designs/ev-p/756841](https://community.jmp.com/t5/Abstracts/Accelerating-Innovation-with-Space-Filling-Mixture-Designs/ev-p/756841) Ramsey, P., & Gotwalt, C. (2018). Model Validation Strategies for Designed Experiments Using Bootstrapping Techniques With Applications to Biopharmaceuticals. **JMP Discovery Conference - Europe**. 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Meinshausen, N. (2007). Relaxed Lasso. Computational Statistics & Data Analysis, 52(1), 374-393. Kish, L. (1965). **Survey Sampling**. Wiley. Lumley, T. (2004). Analysis of complex survey samples. **Journal of Statistical Software**, 9(1), 1–19. Lumley, T. and Scott, A. (2015). AIC and BIC for modelling with complex survey data. **Journal of Survey Statistics and Methodology**, 3(1), 1–18.

glmnet_with_cv function