Data and reproducibility

Know your inputs

lambert() and cv.lambert() take a finite dense numeric matrix x and a numeric response vector y. Rows represent observations; columns represent predictors. Predictor names, when present, must be unique. Prediction data must use the same names and column order. Missing values are not imputed, and columns must vary in every training sample.

The package centers and RMS-scales predictors separately in each training sample, centers the response, and leaves the intercept unpenalized. The returned coefficients and predictions are in the original units. The introduction gives the precise transformation and penalty scale.

Demonstration data dictionary

The example generator uses set.seed(42) and generates 100 independent observations. Its response is 2*x1 - x2 + 0.5*x3 + noise, with independent standard-normal noise. The eight predictors are independent standard-normal variables. The demonstration has no physical units.

File	Fields	Meaning
predictors.csv	x1–x8	Eight synthetic predictors; 100 rows in observation order.
observations.csv	id, y, sample, fold	Response, training/test split, and CV fold; fold is missing for held-out rows.
configuration.rds	seed, train, foldid, lambda_fraction, controls, package_version	Frozen example settings and fitting controls.
cv_path.csv	lambda, fraction, cv_mse, selected	Full-training penalty scale, mean fold MSE, and selected-variable count.
coefficients.csv	predictor, s1–s60	Original-scale coefficient paths, excluding the intercept.
summary.csv	lambda, selected, cv_mse, test_rmse, test_mae	Selected model and held-out errors for this demonstration.
fit.rds	A cv.lambert object	Stored paths, CV losses, preprocessing, and numerical diagnostics.
versions.txt, manifest.csv	Versions; file, bytes, sha256	Software record and output integrity checks.

The first 80 observations form the training sample and the final 20 form a held-out test sample. Training rows receive an explicit balanced five-fold partition. The test rows do not affect scaling, tuning, or selection. No observations are removed and no missing values are generated in predictors or responses.

Reproduce the gallery

The example archive contains the synthetic inputs, stored model, plots, configuration, and checksum manifest listed above. The generator recreates these files from the frozen seed.

Install lambertReg and make the documentation dependency digest available. Run the following in R, using a new output directory:

source(system.file("examples", "showcase.R", package = "lambertReg"))
example <- lambert_showcase("lambert-example-v1")
example$summary

The generator refuses an existing directory. It saves the input data, folds, controls, fit, CV curve, coefficient paths, two PNG plots, software versions, and a SHA-256 manifest. It verifies the selected fit and the completeness of the demonstration’s CV and full-training paths. This is one small example; it does not launch a Monte Carlo study.

To verify saved files:

out <- "lambert-example-v1"
manifest <- read.csv(file.path(out, "manifest.csv"))
paths <- file.path(out, manifest$file)
stopifnot(all(file.info(paths)$size == manifest$bytes))
hashes <- vapply(paths, function(p) digest::digest(file = p, algo = "sha256"), "")
stopifnot(identical(unname(hashes), manifest$sha256))

Reproduce an independent analysis

Record the input source and any preprocessing outside the package, the training/test split, foldid, penalty grid, fitting controls, and software versions. Preserve raw data separately. Use an independent test sample or outer CV for evaluation; the tuning minimum is not an external prediction error. This guide reproduces the package demonstration. The manuscript’s simulation and QSAR study use their separately recorded designs and inputs.

Cite the software

citation("lambertReg")

## To cite package 'lambertReg' in publications use:
## 
##   Yuzbasi B (2026). lambertReg: Sparse Gaussian Regression with the
##   Lambert Penalty. R package version 0.1.10
## 
##   Yuzbasi B (2026). The Lambert Penalty: Logarithmic Shrinkage for
##   Sparse Regression. arXiv preprint arXiv:2610.09627 [stat.ME].
##   https://arxiv.org/abs/2610.09627
## 
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.

The source repository provides CITATION.cff with the associated paper as the preferred citation. The paper is The Lambert Penalty: Logarithmic Shrinkage for Sparse Regression, by Bahadir Yuzbasi (2026), arXiv preprint arXiv:2610.09627 [stat.ME], first posted on 7 October 2026. citation("lambertReg") returns both the software and paper citations.