{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:28:56Z","timestamp":1788362936367,"version":"build-2803163510"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T00:00:00Z","timestamp":1707696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["22K11948"],"award-info":[{"award-number":["22K11948"]}]},{"name":"JSPS KAKENHI","award":["20H04147"],"award-info":[{"award-number":["20H04147"]}]},{"name":"JSPS KAKENHI","award":["22K11948"],"award-info":[{"award-number":["22K11948"]}]},{"name":"JSPS KAKENHI","award":["20H04147"],"award-info":[{"award-number":["20H04147"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package \u201cg.ridge\u201d (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package \u201cglmnet\u201d. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data.<\/jats:p>","DOI":"10.3390\/sym16020223","type":"journal-article","created":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T11:30:12Z","timestamp":1707737412000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3904-4014","authenticated-orcid":false,"given":"Takeshi","family":"Emura","sequence":"first","affiliation":[{"name":"Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan"},{"name":"Biostatistics Center, Kurume University, Kurume 830-0011, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Koutarou","family":"Matsumoto","sequence":"additional","affiliation":[{"name":"Biostatistics Center, Kurume University, Kurume 830-0011, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9546-9869","authenticated-orcid":false,"given":"Ryuji","family":"Uozumi","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Economics, Tokyo Institute of Technology, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4494-2529","authenticated-orcid":false,"given":"Hirofumi","family":"Michimae","sequence":"additional","affiliation":[{"name":"Department of Clinical Medicine (Biostatistics), School of Pharmacy, Kitasato University, Tokyo 108-8641, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge regression: Biased estimation for nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"ref_2","unstructured":"Montgomery, D.C., Peck, E.A., and Vining, G.G. 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