Type:	Package
Title:	Self-Validated Ensemble Models with Lasso and Relaxed-Elastic Net Regression
Version:	2.1.3
Date:	2025-09-08
Maintainer:	Andrew T. Karl <akarl@asu.edu>
Description:	Implements Self-Validated Ensemble Models (SVEM, Lemkus et al. (2021) <doi:10.1016/j.chemolab.2021.104439>) using Elastic Net regression via 'glmnet' (Friedman et al. <doi:10.18637/jss.v033.i01>). SVEM averages predictions from multiple models fitted to fractionally weighted bootstraps of the data, tuned with anti-correlated validation weights. Also implements the randomized permutation whole model test for SVEM (Karl (2024) <doi:10.1016/j.chemolab.2024.105122>). \\Code for the whole model test was taken from the supplementary material of Karl (2024). Development of this package was assisted by 'GPT o1-preview' for code structure and documentation.
Depends:	R (≥ 3.5.0)
Imports:	glmnet, stats, gamlss, gamlss.dist, ggplot2, lhs, doParallel, parallel, foreach
VignetteBuilder:	knitr
Suggests:	knitr, rmarkdown
License:	GPL-2 | GPL-3
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-09-08 21:50:02 UTC; andre
Author:	Andrew T. Karl [cre, aut]
Repository:	CRAN
Date/Publication:	2025-09-09 06:50:30 UTC

SVEMnet: Self-Validated Ensemble Models with Relaxed Lasso and Elastic-Net Regression

Description

The SVEMnet package implements Self-Validated Ensemble Models (SVEM) using Elastic Net (including lasso and ridge) regression via glmnet. SVEM averages predictions from multiple models fitted to fractionally weighted bootstraps of the data, tuned with anti-correlated validation weights.

Functions

SVEMnet

Fit an SVEMnet model using Elastic Net regression.

predict.svem_model

Predict method for SVEM models.

svem_significance_test

Whole-model significance test.

svem_significance_test_parallel

Parallel whole-model test.

plot.svem_model

Plot actual vs predicted for a model.

coef.svem_model

Coefficient nonzero percentages (bootstrap).

plot_svem_significance_tests

Plotting helper for multiple tests.

glmnet_with_cv

Wrapper around cv.glmnet() with repeats.

Acknowledgments

Development of this package was assisted by GPT o1-preview, which helped in constructing the structure of some of the code and the roxygen documentation. The code for the significance test is taken from the supplementary material of Karl (2024) (it was handwritten by that author).

Author(s)

Maintainer: Andrew T. Karl akarl@asu.edu (ORCID)

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

Karl, A. T. (2024). A randomized permutation whole-model test heuristic for Self-Validated Ensemble Models (SVEM). Chemometrics and Intelligent Laboratory Systems, 249, 105122. 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. 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. 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. 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

Ramsey, P., & Gotwalt, C. (2018). Model Validation Strategies for Designed Experiments Using Bootstrapping Techniques With Applications to Biopharmaceuticals. JMP Discovery Conference - Europe. https://community.jmp.com/t5/Abstracts/Model-Validation-Strategies-for-Designed-Experiments-Using/ev-p/849647/redirect_from_archived_page/true

Ramsey, P., Levin, W., Lemkus, T., & Gotwalt, C. (2021). SVEM: A Paradigm Shift in Design and Analysis of Experiments. JMP Discovery Conference - Europe. https://community.jmp.com/t5/Abstracts/SVEM-A-Paradigm-Shift-in-Design-and-Analysis-of-Experiments-2021/ev-p/756634

Ramsey, P., & McNeill, P. (2023). CMC, SVEM, Neural Networks, DOE, and Complexity: It's All About Prediction. JMP Discovery Conference.

Fit an SVEMnet Model (with optional relaxed elastic net)

Description

Wrapper for glmnet (Friedman et al. 2010) to fit an ensemble of Elastic Net models using the Self-Validated Ensemble Model method (SVEM; Lemkus et al. 2021), with an option to use glmnet's built-in relaxed elastic net (Meinshausen 2007). Supports searching over multiple alpha values in the Elastic Net penalty.

Usage

SVEMnet(
  formula,
  data,
  nBoot = 200,
  glmnet_alpha = c(0.25, 0.5, 0.75, 1),
  weight_scheme = c("SVEM", "FWR", "Identity"),
  objective = c("auto", "wAIC", "wBIC", "wGIC", "wSSE"),
  auto_ratio_cutoff = 1.3,
  gamma = 2,
  relaxed = TRUE,
  ...
)

Arguments

Details

SVEM applies fractional bootstrap weights to training data and anti-correlated weights for validation when weight_scheme = "SVEM". For each bootstrap, glmnet paths are fit for each alpha in glmnet_alpha, and the lambda (and, if relaxed = TRUE, relaxed gamma) minimizing a weighted validation criterion is selected.

Predictors are always standardized internally via glmnet::glmnet(..., standardize = TRUE).

When relaxed = TRUE, coef(fit, s = lambda, gamma = g) is used to obtain the coefficient path at each relaxed gamma in the internal grid. Metrics are computed from validation-weighted errors and model size is taken as the number of nonzero coefficients including the intercept (support size), keeping selection consistent between standard and relaxed paths. When relaxed = FALSE, gamma is fixed at 1.

Automatic objective rule ("auto"): This function uses a single ratio cutoff, auto_ratio_cutoff, applied to r = n_X / p_X, where p_X is computed from the model matrix with the intercept column removed. If r >= auto_ratio_cutoff the selection criterion is wAIC; otherwise it is wBIC.

Implementation notes for safety:

• The training terms object is stored with environment set to baseenv() to avoid accidental lookups in the calling environment.

• A compact schema (feature names, xlevels, contrasts) is stored to let predict() reconstruct the design matrix deterministically.

• A lightweight sampling schema (numeric ranges and factor levels for raw predictors) is cached to enable random-table generation without needing the original data.

Value

An object of class svem_model with elements:

• parms: averaged coefficients (including intercept).

• parms_debiased: averaged coefficients adjusted by the calibration fit.

• debias_fit: lm(y ~ y_pred) calibration model used for debiasing (or NULL).

• coef_matrix: per-bootstrap coefficient matrix.

• nBoot, glmnet_alpha, best_alphas, best_lambdas, weight_scheme, relaxed.

• best_relax_gammas: per-bootstrap relaxed gamma chosen (NA if relaxed = FALSE).

• objective_input, objective_used, objective (same as objective_used), auto_used, auto_decision, auto_rule, gamma (when wGIC).

• dropped_alpha0_for_relaxed: whether alpha = 0 was removed because relaxed = TRUE.

• schema: list(feature_names, terms_str, xlevels, contrasts, terms_hash) for safe predict.

• sampling_schema: list( predictor_vars, var_classes, num_ranges = rbind(min=..., max=...) for numeric raw predictors, factor_levels = list(...) for factor/character raw predictors).

• diagnostics: list with k_summary (median and IQR of selected size), fallback_rate, n_eff_summary, alpha_freq, relax_gamma_freq.

• actual_y, training_X, y_pred, y_pred_debiased, nobs, nparm, formula, terms, xlevels, contrasts.

Acknowledgments

Development of this package was assisted by GPT o1-preview for structuring parts of the code and documentation.

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

Karl, A. T. (2024). A randomized permutation whole-model test heuristic for Self-Validated Ensemble Models (SVEM). Chemometrics and Intelligent Laboratory Systems, 249, 105122. 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. 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. 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. 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

Ramsey, P., & Gotwalt, C. (2018). Model Validation Strategies for Designed Experiments Using Bootstrapping Techniques With Applications to Biopharmaceuticals. JMP Discovery Conference - Europe. https://community.jmp.com/t5/Abstracts/Model-Validation-Strategies-for-Designed-Experiments-Using/ev-p/849647/redirect_from_archived_page/true

Ramsey, P., Levin, W., Lemkus, T., & Gotwalt, C. (2021). SVEM: A Paradigm Shift in Design and Analysis of Experiments. JMP Discovery Conference - Europe. https://community.jmp.com/t5/Abstracts/SVEM-A-Paradigm-Shift-in-Design-and-Analysis-of-Experiments-2021/ev-p/756634

Ramsey, P., & McNeill, P. (2023). CMC, SVEM, Neural Networks, DOE, and Complexity: It's All About Prediction. JMP Discovery Conference.

Friedman, J. H., Hastie, T., & Tibshirani, R. (2010). Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1), 1-22.

Meinshausen, N. (2007). Relaxed Lasso. Computational Statistics & Data Analysis, 52(1), 374-393.

Examples

set.seed(42)

n  <- 30
X1 <- rnorm(n)
X2 <- rnorm(n)
X3 <- rnorm(n)
eps <- rnorm(n, sd = 0.5)
y <- 1 + 2*X1 - 1.5*X2 + 0.5*X3 + 1.2*(X1*X2) + 0.8*(X1^2) + eps
dat <- data.frame(y, X1, X2, X3)

mod_relax <- SVEMnet(
  y ~ (X1 + X2 + X3)^2 + I(X1^2) + I(X2^2),
  data          = dat,
  glmnet_alpha  = c(1, 0.5),
  nBoot         = 75,
  objective     = "auto",
  weight_scheme = "SVEM",
  relaxed       = FALSE #to run faster to pass CRAN checks
)

pred_in_raw <- predict(mod_relax, dat, debias = FALSE)
pred_in_db  <- predict(mod_relax, dat, debias = TRUE)

Coefficient Nonzero Percentages from an SVEM Model

Description

Calculates the percentage of bootstrap iterations in which each coefficient (excluding the intercept) is nonzero, using a small tolerance.

Usage

## S3 method for class 'svem_model'
coef(object, tol = 1e-07, ...)

Arguments

Value

Invisibly returns a data frame with variables and percentages.

Fit a glmnet Model with Cross-Validation

Description

Repeated K-fold CV over a per-alpha lambda path, with a proper 1-SE rule across repeats. Preserves fields expected by predict_cv(). 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 gamma).

Usage

glmnet_with_cv(
  formula,
  data,
  glmnet_alpha = c(0, 0.25, 0.5, 0.75, 1),
  standardize = TRUE,
  nfolds = 10,
  repeats = 5,
  choose_rule = c("min", "1se"),
  seed = NULL,
  exclude = NULL,
  relaxed = FALSE,
  relax_gamma = NULL,
  ...
)

Arguments

Details

To avoid duplicate-argument errors, arguments like x, y, alpha, lambda, foldid, and exclude are passed explicitly and removed from the dots before calling glmnet::cv.glmnet().

Value

A list 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.

• debias_fit Optional lm(y ~ y_pred) for Gaussian family.

• y_pred_debiased If debias_fit exists, its fitted values.

• cv_summary Per-alpha data frames with lambda, mean_cvm, sd_cvm, se_combined, n_repeats, idx_min, idx_1se.

• formula Original formula.

• terms Cleaned training terms (environment set to baseenv()).

• training_X Training design matrix without intercept.

• actual_y Training response vector.

• xlevels Factor levels seen during training (for safe predict).

• contrasts Contrasts used during training (for safe predict).

• schema list(feature_names, terms_str, xlevels, contrasts, terms_hash) for deterministic predict.

• note Character vector of notes (e.g., dropped rows, relaxed-coef source).

• meta List: nfolds, repeats, rule, family, relaxed, relax_cv_fallbacks, cv_object (if keep=TRUE for the final fit).

Examples

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))

# Default: 1SE rule, repeats=1, non-relaxed
fit_1se <- glmnet_with_cv(y ~ ., df_ex, glmnet_alpha = c(0.5, 1),
                          nfolds = 5, repeats = 1, seed = 42)
str(fit_1se$parms)

# 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)

# Relaxed path with gamma search
fit_relax <- glmnet_with_cv(y ~ ., df_ex, glmnet_alpha = 1,
                            nfolds = 5, repeats = 1, relaxed = TRUE, seed = 42)

Plot Method for SVEM Models

Description

Plots actual versus predicted values for an svem_model.

Usage

## S3 method for class 'svem_model'
plot(x, plot_debiased = FALSE, ...)

Arguments

Value

A ggplot object.

Plot SVEM Significance Test Results for Multiple Responses

Description

Plots the Mahalanobis-like distances for original and permuted data from one or more SVEM significance test results.

Usage

## S3 method for class 'svem_significance_test'
plot(x, ..., labels = NULL)

Arguments

Details

If additional svem_significance_test objects are provided via ..., they will be combined into a single plot alongside x.

Value

A ggplot object showing the distributions of distances.

Predict Method for SVEM Models

Description

Generates predictions from a fitted svem_model.

Usage

## S3 method for class 'svem_model'
predict(
  object,
  newdata,
  debias = FALSE,
  se.fit = FALSE,
  agg = c("parms", "mean"),
  ...
)

Arguments

Details

The function uses the training terms, factor levels (xlevels), and contrasts saved by SVEMnet(). The terms object environment is set to baseenv() to avoid unexpected lookup of objects in the original environment.

Column handling is strict but robust:

• We require that the set of columns produced by model.matrix on newdata matches the set used in training.

• If model.matrix drops some training columns (e.g., a factor collapses to a single level in newdata), we add those missing columns as zeros so coefficients align.

• We then reorder columns to the exact training order before multiplying.

Rows in newdata that contain unseen factor levels will yield NA predictions (and NA standard errors if se.fit=TRUE); a warning is issued indicating how many rows were affected.

When agg="mean", the predictive SE is the bootstrap spread (row-wise sd of member predictions). If debias=TRUE and the calibration slope is available and finite, SEs are scaled by abs(slope).

Value

A numeric vector of predictions, or a list with components fit and se.fit when se.fit = TRUE.

Examples

set.seed(1)
n  <- 40
X1 <- rnorm(n); X2 <- rnorm(n); X3 <- rnorm(n)
y  <- 1 + 0.8*X1 - 0.5*X2 + 0.2*X3 + rnorm(n, 0, 0.3)
dat <- data.frame(y, X1, X2, X3)
fit <- SVEMnet(y ~ (X1 + X2 + X3)^2, dat, nBoot = 30, relaxed = TRUE)
pred <- predict(fit, dat)
head(pred)

# With SEs and debias
out <- predict(fit, dat, debias = TRUE, se.fit = TRUE, agg = "mean")
str(out)

Predict for svem_cv objects (and convenience wrapper)

Description

Generates predictions from a fitted object returned by glmnet_with_cv().

Usage

predict_cv(object, newdata, debias = FALSE, strict = FALSE, ...)

## S3 method for class 'svem_cv'
predict(object, newdata, debias = FALSE, strict = FALSE, ...)

Arguments

Details

The design matrix for newdata is rebuilt using the training terms (with environment set to baseenv()), along with the saved factor xlevels and contrasts (stored in object$schema). Columns are aligned robustly to the training order:

• Any training columns that model.matrix() drops for newdata (e.g., a factor collapses to a single level) are added back as zero columns.

• Columns are reordered to exactly match the training order.

• Rows with unseen factor levels are warned about and return NA.

If debias = TRUE and a calibration fit lm(y ~ y_pred) exists with a finite slope, predictions are transformed by a + b * pred.

Value

A numeric vector of predictions.

Examples

set.seed(1)
n <- 50; p <- 5
X <- matrix(rnorm(n * p), n, p)
y <- X[,1] - 0.5 * X[,2] + rnorm(n)
df_ex <- data.frame(y = as.numeric(y), X)
colnames(df_ex) <- c("y", paste0("x", 1:p))
fit <- glmnet_with_cv(y ~ ., df_ex, glmnet_alpha = 1, nfolds = 5, repeats = 2, seed = 9)
preds_raw <- predict_cv(fit, df_ex)
preds_db  <- predict_cv(fit, df_ex, debias = TRUE)
cor(preds_raw, df_ex$y)

Print Method for SVEM Significance Test

Description

Prints the median p-value from an object of class svem_significance_test.

Usage

## S3 method for class 'svem_significance_test'
print(x, ...)

Arguments

Generate a Random Prediction Table from a Fitted SVEMnet Model (no refit)

Description

Samples the original predictor factor space using ranges and levels cached inside a fitted svem_model (from SVEMnet()) and computes predictions at those points. Optional mixture groups let you sample composition variables on a (possibly truncated) simplex via a Dirichlet draw. No refitting is performed.

Usage

svem_random_table_from_model(
  object,
  n = 1000,
  mixture_groups = NULL,
  debias = FALSE
)

Arguments

Details

This function uses:

• object$sampling_schema$num_ranges for uniform sampling of numeric variables.

• object$sampling_schema$factor_levels for categorical sampling.

• object$terms, object$xlevels, and object$contrasts (via predict.svem_model) to encode the model matrix consistently.

Mixture groups are handled by drawing Dirichlet weights and mapping them to the truncated simplex defined by lower, upper, and total; proposals violating upper bounds are rejected (with oversampling to keep it efficient).

Value

A data frame with sampled predictors and a predicted response column. The response column name matches the left-hand side of object$formula.

See Also

SVEMnet, predict.svem_model, svem_significance_test, svem_significance_test_parallel

Examples

set.seed(1)
n <- 40
X1 <- runif(n); X2 <- runif(n)
A <- runif(n); B <- runif(n); C <- pmax(0, 1 - A - B)  # simple mixture-ish
F <- factor(sample(c("lo","hi"), n, TRUE))
y <- 1 + 2*X1 - X2 + 3*A + 1.5*B + 0.5*C + (F=="hi") + rnorm(n, 0, 0.3)
d <- data.frame(y, X1, X2, A, B, C, F)

fit <- SVEMnet(y ~ X1 + X2 + A + B + C + F, d, nBoot = 50, glmnet_alpha = 1)

# No mixture constraints (independent sampling using cached ranges/levels)
tbl1 <- svem_random_table_from_model(fit, n = 50)
head(tbl1)

# With mixture constraints for A,B,C that sum to 1 and have bounds
mix <- list(list(vars = c("A","B","C"),
                 lower = c(0.1, 0.1, 0.1),
                 upper = c(0.7, 0.7, 0.7),
                 total = 1.0))
tbl2 <- svem_random_table_from_model(fit, n = 50, mixture_groups = mix)
head(tbl2)

SVEM Significance Test with Mixture Support

Description

Performs a whole-model significance test using the SVEM framework and allows the user to specify mixture factor groups. Mixture factors are sets of continuous variables that are constrained to sum to a constant (the mixture total) and have optional lower and upper bounds. When mixture groups are supplied, the grid of evaluation points is generated by sampling Dirichlet variates over the mixture simplex rather than by independently sampling each continuous predictor. Non-mixture continuous predictors are sampled via a maximin Latin hypercube over their observed ranges, and categorical predictors are sampled from their observed levels.

Usage

svem_significance_test(
  formula,
  data,
  mixture_groups = NULL,
  nPoint = 2000,
  nSVEM = 10,
  nPerm = 150,
  percent = 90,
  nBoot = 100,
  glmnet_alpha = c(1),
  weight_scheme = c("SVEM"),
  objective = c("auto", "wAIC", "wBIC", "wGIC", "wSSE"),
  auto_ratio_cutoff = 1.3,
  gamma = 2,
  relaxed = FALSE,
  verbose = TRUE,
  ...
)

Arguments

Details

If no mixture groups are supplied, this function behaves identically to a standard SVEM-based whole-model test, sampling non-mixture continuous variables via a maximin Latin hypercube within their observed ranges, and categorical variables from their observed levels.

Internally, predictions at evaluation points use predict.svem_model() with se.fit = TRUE. Rows with unseen categorical levels are returned as NA and are excluded from distance summaries via complete.cases().

Value

A list of class svem_significance_test containing:

• p_value: median p-value across evaluation points.

• p_values: vector of per-point p-values.

• d_Y: distances for original fits.

• d_pi_Y: distances for permutation fits.

• distribution_fit: fitted SHASHo distribution object.

• data_d: data frame combining distances and labels.

See Also

SVEMnet(), predict.svem_model()

SVEM Significance Test with Mixture Support (Parallel Version)

Description

Whole-model significance test using SVEM with support for mixture factor groups, parallelizing the SVEM fits for originals and permutations.

Usage

svem_significance_test_parallel(
  formula,
  data,
  mixture_groups = NULL,
  nPoint = 2000,
  nSVEM = 10,
  nPerm = 150,
  percent = 90,
  nBoot = 100,
  glmnet_alpha = c(1),
  weight_scheme = c("SVEM"),
  objective = c("auto", "wAIC", "wBIC", "wGIC", "wSSE"),
  auto_ratio_cutoff = 1.3,
  gamma = 2,
  relaxed = FALSE,
  verbose = TRUE,
  nCore = parallel::detectCores(),
  seed = NULL,
  ...
)

Arguments

Details

Identical in logic to svem_significance_test() but runs the expensive SVEM refits in parallel using foreach + doParallel. Random draws (including permutations) use RNGkind("L'Ecuyer-CMRG") for parallel-suitable streams.

Value

A list of class svem_significance_test containing the test results.

See Also

svem_significance_test

Examples

  set.seed(1)

  # Small toy data with a 3-component mixture A, B, C
  n <- 40
  sample_trunc_dirichlet <- function(n, lower, upper, total) {
    k <- length(lower)
    stopifnot(length(upper) == k, total >= sum(lower), total <= sum(upper))
    avail <- total - sum(lower)
    if (avail <= 0) return(matrix(rep(lower, each = n), nrow = n))
    out <- matrix(NA_real_, n, k)
    i <- 1L
    while (i <= n) {
      g <- rgamma(k, 1, 1)
      w <- g / sum(g)
      x <- lower + avail * w
      if (all(x <= upper + 1e-12)) { out[i, ] <- x; i <- i + 1L }
    }
    out
  }

  lower <- c(0.10, 0.20, 0.05)
  upper <- c(0.60, 0.70, 0.50)
  total <- 1.0
  ABC   <- sample_trunc_dirichlet(n, lower, upper, total)
  A <- ABC[, 1]; B <- ABC[, 2]; C <- ABC[, 3]
  X <- runif(n)
  F <- factor(sample(c("red", "blue"), n, replace = TRUE))
  y <- 2 + 3*A + 1.5*B + 1.2*C + 0.5*X + 1*(F == "red") + rnorm(n, sd = 0.3)
  dat <- data.frame(y = y, A = A, B = B, C = C, X = X, F = F)

  mix_spec <- list(list(
    vars  = c("A", "B", "C"),
    lower = lower,
    upper = upper,
    total = total
  ))

  # Parallel significance test (default relaxed = FALSE)
  res <- svem_significance_test_parallel(
    y ~ A + B + C + X + F,
    data           = dat,
    mixture_groups = mix_spec,
    glmnet_alpha   = c(1),
    weight_scheme  = "SVEM",
    objective      = "auto",
    auto_ratio_cutoff = 1.3,
    relaxed        = FALSE,   # default, shown for clarity
    nCore          = 2,
    seed           = 123,
    verbose        = FALSE
  )
  print(res$p_value)