Super Learner

<!DOCTYPE html> <html lang="en" xmlns:mml="http://www.w3.org/1998/Math/MathML"> <head> <meta charset="utf-8"> <meta http-equiv="x-ua-compatible" content="ie=edge"> <title>Super Learner</title>  <link rel="preload" href="/assets/fonts/montserrat-v15-latin-ext_cyrillic-ext-regular.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/montserrat-v25-latin-ext_cyrillic-ext-500.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/montserrat-v15-latin-ext_cyrillic-ext-700.woff2" as="font" type="font/woff2" crossorigin="anonymous">  <link rel="preload" href="/assets/fonts/merriweather-v30-latin-ext_cyrillic-ext-300.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/merriweather-v22-latin-ext_cyrillic-ext-regular.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/merriweather-v22-latin-ext_cyrillic-ext-700.woff2" as="font" type="font/woff2" crossorigin="anonymous">  <link rel="preload" href="/assets/stylesheets/fontawesome.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="stylesheet" media="all" href='/assets/stylesheets/02f295d1f6a8e9c282e7831cd493e8ff-bootstrap.purged.min.css' /> <link rel="stylesheet" media="all" href='/assets/stylesheets/5337b0511e7530e28f005276f70cde44-main.min.css' /> <link rel="stylesheet" media="all" href='/assets/stylesheets/13761c60ba5201f465803f3005ccd7ef-fontawesome-codes.css' /> <link rel="shortcut icon" type="image/x-icon" href='/assets/images/ec7d7606b4e2f3f921b5e1700948efb6-favicon.ico' /> <link rel="alternate" hreflang="en" href="https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html?lang=en" /> <link rel="alternate" hreflang="de" href="https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html?lang=de" /> <link rel="alternate" hreflang="x-default" href="https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html" />  <link rel="schema.dcterms" href="http://purl.org/dc/terms/"> <meta name="dcterms.rightsHolder" content="Walter de Gruyter GmbH"> <meta name="dcterms.rights" content="De Gruyter expressly reserves the right to use all content for commercial text and data mining within the meaning of Section 44b of the German Copyright Act."> <link rel="dns-prefetch" href="https://www.google-analytics.com" /> <meta name="google" content="notranslate" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="description" content="When trying to learn a model for the prediction of an outcome given a set of covariates, a statistician has many estimation procedures in their toolbox. A few examples of these candidate learners are: least squares, least angle regression, random forests, and spline regression. Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) theoretically validated the use of cross validation to select an optimal learner among many candidate learners. Motivated by this use of cross validation, we propose a new prediction method for creating a weighted combination of many candidate learners to build the super learner. This article proposes a fast algorithm for constructing a super learner in prediction which uses V-fold cross-validation to select weights to combine an initial set of candidate learners. In addition, this paper contains a practical demonstration of the adaptivity of this so called super learner to various true data generating distributions. This approach for construction of a super learner generalizes to any parameter which can be defined as a minimizer of a loss function."/> <meta property="og:url" content="https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html"/><meta property="og:site_name" content="De Gruyter"/><meta property="og:title" content="Super Learner"/><meta property="og:type" content="article"/><meta property="og:locale" content="en"/><meta property="og:image" content="https://www.degruyter.com/document/cover/journal_key/SAGMB/product"/><meta property="og:image:type" content="image/jpeg"/><meta property="og:description" content="When trying to learn a model for the prediction of an outcome given a set of covariates, a statistician has many estimation procedures in their toolbox. A few examples of these candidate learners are: least squares, least angle regression, random forests, and spline regression. Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) theoretically validated the use of cross validation to select an optimal learner among many candidate learners. Motivated by this use of cross validation, we propose a new prediction method for creating a weighted combination of many candidate learners to build the super learner. This article proposes a fast algorithm for constructing a super learner in prediction which uses V-fold cross-validation to select weights to combine an initial set of candidate learners. In addition, this paper contains a practical demonstration of the adaptivity of this so called super learner to various true data generating distributions. This approach for construction of a super learner generalizes to any parameter which can be defined as a minimizer of a loss function."/><meta property="og:locale:alternate" content="de"/><meta property="article:author" content="Mark J. van der Laan"/><meta property="article:author" content="Eric C Polley"/><meta property="article:author" content="Alan E. Hubbard"/><meta property="article:tag" content="cross-validation"/><meta property="article:tag" content="loss-based estimation"/><meta property="article:tag" content="machine learning"/><meta property="article:tag" content="prediction"/><meta property="article:published_time" content="2007-09-16"/><meta property="article:section" content="Statistical Applications in Genetics and Molecular Biology"/> <meta name="citation_issue" content="1" /> <meta name="citation_issn" content="1544-6115" /> <meta name="citation_language" content='en' /> <meta name="citation_volume" content="6" /> <meta name="citation_publisher" content='De Gruyter' /> <meta name="citation_keywords" content='cross-validation; loss-based estimation; machine learning; prediction' /> <meta name="citation_author" content="Mark J. van der Laan" /> <meta name="citation_author" content="Eric C Polley" /> <meta name="citation_author" content="Alan E. Hubbard" /> <meta name="citation_title" content='Super Learner' /> <meta name="citation_xml_url" content="https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/xml" /> <meta name="citation_journal_title" content="Statistical Applications in Genetics and Molecular Biology" /> <meta name="citation_publication_date" content='2007/09/16' /> <meta name="citation_doi" content="10.2202/1544-6115.1309" /> <script type="application/ld+json">{"author":[{"@type":"Person","name":"Mark J. van der Laan"},{"@type":"Person","name":"Eric C Polley"},{"@type":"Person","name":"Alan E. Hubbard"}],"editor":[],"audience":null,"datePublished":"2007-09-16","headline":"","keywords":"keyword,keyword,keyword,keyword","isAccessibleForFree":false,"publisher":{"@type":"Organization","name":"De Gruyter"},"@context":"https://schema.org","@type":"Article","name":"Super Learner","image":"https://www.degruyter.com/document/cover/journal_key/SAGMB/thumbnail","url":"https://doi.org/10.2202/1544-6115.1309"}</script> <script nonce="C+LUmrHTMReisY5AgKmEcg=="> // Define dataLayer and the gtag function. window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} function getCookieValue(name){ const regex = new RegExp(`(^| )${name}=([^;]+)`) const match = document.cookie.match(regex) if (match) { return match[2] } } // Set default consent to 'denied' as a placeholder // Determine actual values based on your own requirements const acceptCookies = getCookieValue('acceptcookies') === "true"; const defaultSettings = (acceptCookies) => ({ 'ad_storage': acceptCookies ? 'granted': 'denied', 'analytics_storage': acceptCookies ? 'granted' : 'denied', 'ad_user_data': acceptCookies ? 'granted': 'denied', 'ad_personalization': acceptCookies ? 'granted' : 'denied', }) gtag('consent', 'default', defaultSettings(acceptCookies)) </script> </head> <body data-pagecategory="article" data-foxydomain="checkout.degruyter.com"> <a href="#document-main-content" class="visually-hidden-focusable" id="skip-to-content">Skip to content</a> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PMNKTQ5&gtm_auth=JraP3pn8iVUkqNIGYl03AA&gtm_preview=env-2&subjects=LF%7CLF-01%7CLF-03%7CMT%7CMT-09&publisherCode=DEG&license=restricted&publisher=De+Gruyter&contentName=Super+Learner&doi=10.2202%2F1544-6115.1309&parentIdentifier=SAGMB&parentName=Statistical+Applications+in+Genetics+and+Molecular+Biology&languages=en" title="Google tag manager iframe" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <header id="mainHeader"> <div class="position-relative d-none d-md-block z-2"> <ajax-frame src="/login/banner" class="authBannerDesktop"> <div class="authBanner d-flex flex-wrap invisible auth-banner-warning"> <span class="fa fas fa-attention text-warning d-none d-md-inline"></span> <span>Should you have <strong>institutional access?</strong></span> <a href="/how-access-works">Here's how to get it ...</a> </div> </ajax-frame> <nav class="navbar navbar-expand-md navbar-dark bg-dark dg-navbar px-md-4 pt-3 align-items-center" aria-label="site"> <a id="homepageLogoLink" class="ga_homepage_logo navbar-brand mx-0 mx-lg-3 pe-4 py-0" href="/" aria-label='De Gruyter logo with link to home page'> <img src='/assets/images/84ad0073fb7b59ebc46b966dbf03a4bb-dg-logo-nav-search.svg' width="32px" height="64px" class="d-none d-sm-inline-block" alt="De Gruyter" /> </a> <div class="d-flex flex-wrap flex-md-nowrap align-items-center w-100"> <div class="mainNavbarSearchContainer w-100 me-md-2 me-lg-5 mt-2 mt-md-0"> <form class="form-inline" action='/search?query='> <div class="input-group flex-grow-1"> <input class="mainNavbarSearchInput form-control input-header rounded-start py-1" type="search" aria-label='Search' name="query" placeholder='Search De Gruyter' value='' /> <div class="input-group-append"> <button class="btn btn-primary rounded-end analyticsButton" aria-label='Search' type="submit"><span class="fa fas fa-search ga_main_search_button"></span></button> </div> </div> </form> </div> <div class='d-flex flex-wrap flex-md-nowrap justify-content-between mt-2 mt-md-0 '> <div class="dropdown d-flex align-items-center font-size-14"> <button class="dropdown-toggle text-white text-decoration-none mainNavbarOptionsBg p-2" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> <current-currency></current-currency> </button> <div class="mt-2 py-0 dropdown-menu font-size-14" aria-labelledby="currencyPickerLink"> <select-currency currency="EUR"><div class="dropdown-item">€ EUR - Euro</div></select-currency> <select-currency currency="GBP"><div class="dropdown-item">£ GBP - Pound</div></select-currency> <select-currency currency="USD"><div class="dropdown-item">$ USD - Dollar</div></select-currency> </div> </div> <div class="dropdown show d-flex align-items-center font-size-14"> <a class="dropdown-toggle text-white text-decoration-none mainNavbarOptionsBg p-2" href="#" role="button" id="desktopLanguagePickerLink" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> EN </a> <div class="mt-2 py-2 dropdown-menu font-size-14" id="languageSelector" aria-labelledby="desktopLanguagePickerLink"> <a class="languageSelector_en ga_language_selector dropdown-item" href="/_language/en?uri=%2Fdocument%2Fdoi%2F10.2202%2F1544-6115.1309%2Fhtml"> English </a> <a class="languageSelector_de ga_language_selector dropdown-item" href="/_language/de?uri=%2Fdocument%2Fdoi%2F10.2202%2F1544-6115.1309%2Fhtml"> Deutsch </a> </div> </div> <div class="cartSummary d-flex align-items-center"> <a href="" class="mainNavbarOptionsBg pe-2 d-flex align-items-center text-decoration-none"> <span class="fa fas fa-shopping-cart"></span> <span data-fc-id="minicart-quantity" class="shopping-cart-badge badge font-family-standard font-size-12">0</span> </a></div> <div id="currentLoginContent" class="d-flex align-items-center font-size-14"></div> </div> </div> </nav> <nav id="navbar" aria-label="site"> <a href='/publishing/subjects' id='mega-one-subject' aria-haspopup="true" aria-expanded="false" > Subjects </a> <div class="d-none" aria-labelledby="mega-one-subject"> <div><a href="#mega-one-for-authors" class="linkAnimation visually-hidden-focusable">Skip section</a></div> <a href='/publishing/subjects' class="fw-bold linkAnimation"> Browse Publications By Subject </a> <div class="col dropdown-divider"></div> <div class="row my-row" id="subjectsSubjects"> <div class="col-4"> <ul class="list-unstyled"> <li> <a href='/search?query=*&subjectFacet=AD' class="linkAnimation"> Architecture and Design </a> </li> <li> <a href='/search?query=*&subjectFacet=AR' class="linkAnimation"> Arts </a> </li> <li> <a href='/search?query=*&subjectFacet=AS' class="linkAnimation"> Asian and Pacific Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=EC' class="linkAnimation"> Business and Economics </a> </li> <li> <a href='/search?query=*&subjectFacet=CH' class="linkAnimation"> Chemistry </a> </li> <li> <a href='/search?query=*&subjectFacet=CL' class="linkAnimation"> Classical and Ancient Near Eastern Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=CO' class="linkAnimation"> Computer Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=CS' class="linkAnimation"> Cultural Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=EN' class="linkAnimation"> Engineering </a> </li> <li> <a href='/search?query=*&subjectFacet=GL' class="linkAnimation"> General Interest </a> </li> </ul> </div> <div class="col-4"> <ul class="list-unstyled"> <li> <a href='/search?query=*&subjectFacet=GS' class="linkAnimation"> Geosciences </a> </li> <li> <a href='/search?query=*&subjectFacet=HI' class="linkAnimation"> History </a> </li> <li> <a href='/search?query=*&subjectFacet=IC' class="linkAnimation"> Industrial Chemistry </a> </li> <li> <a href='/search?query=*&subjectFacet=IS' class="linkAnimation"> Islamic and Middle Eastern Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=JS' class="linkAnimation"> Jewish Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=LA' class="linkAnimation"> Law </a> </li> <li> <a href='/search?query=*&subjectFacet=LB' class="linkAnimation"> Library and Information Science, Book Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=LF' class="linkAnimation"> Life Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=LS' class="linkAnimation"> Linguistics and Semiotics </a> </li> <li> <a href='/search?query=*&subjectFacet=LT' class="linkAnimation"> Literary Studies </a> </li> </ul> </div> <div class="col-4"> <ul class="list-unstyled"> <li> <a href='/search?query=*&subjectFacet=MS' class="linkAnimation"> Materials Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=MT' class="linkAnimation"> Mathematics </a> </li> <li> <a href='/search?query=*&subjectFacet=MD' class="linkAnimation"> Medicine </a> </li> <li> <a href='/search?query=*&subjectFacet=MU' class="linkAnimation"> Music </a> </li> <li> <a href='/search?query=*&subjectFacet=PM' class="linkAnimation"> Pharmacy </a> </li> <li> <a href='/search?query=*&subjectFacet=PL' class="linkAnimation"> Philosophy </a> </li> <li> <a href='/search?query=*&subjectFacet=PY' class="linkAnimation"> Physics </a> </li> <li> <a href='/search?query=*&subjectFacet=SN' class="linkAnimation"> Social Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=SR' class="linkAnimation"> Sports and Recreation </a> </li> <li> <a href='/search?query=*&subjectFacet=TL' class="linkAnimation"> Theology and Religion </a> </li> </ul> </div> </div> </div> <a href='/publishing/for-authors' id='mega-one-for-authors' aria-haspopup="true" aria-expanded="false" > For Authors </a> <div class="row d-none" aria-labelledby="mega-one-for-authors"> <div class="col-12"><a href="#mega-one-services" class="linkAnimation visually-hidden-focusable">Skip section</a></div> <div class="col-sm-6 col-lg-4 mb-3 mb-lg-0"> <a href='/publishing/for-authors/for-journal-authors' class="fw-bold linkAnimation"> For Journal Authors </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/for-authors/for-journal-authors/publish-your-article' class='linkAnimation'> Publish your article </a></li> <li><a href='/publishing/for-authors/for-journal-authors/role-of-authors' class='linkAnimation'> The role of authors </a></li> <li><a href='/publishing/for-authors/for-journal-authors/promoting-your-article' class='linkAnimation'> Promoting your article </a></li> <li><a href='/publishing/for-authors/for-journal-authors/abstracting-and-indexing' class='linkAnimation'> Abstracting & indexing </a></li> <li><a href='/publishing/for-authors/for-journal-authors/publishing-ethics' class='linkAnimation'> Publishing Ethics </a></li> </ul> </div> <div class="col-sm-6 col-lg-4 mb-3 mb-lg-0"> <a href='/publishing/for-authors/for-book-authors' class="fw-bold linkAnimation"> For Book Authors </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/for-authors/for-book-authors/why-publish-with-de-gruyter' class='linkAnimation'> Why publish with De Gruyter </a></li> <li><a href='/publishing/for-authors/for-book-authors/how-to-publish-with-de-gruyter' class='linkAnimation'> How to publish with De Gruyter </a></li> <li><a href='/publishing/for-authors/for-book-authors/our-book-series' class='linkAnimation'> Our book series </a></li> <li><a href='/publishing/for-authors/for-book-authors/our-subject-areas' class='linkAnimation'> Our subject areas </a></li> </ul> </div> <div class="col-sm-6 col-lg-4"> <a href='/publishing/for-authors/for-database-authors' class="fw-bold linkAnimation"> For Database Authors </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/for-authors/for-database-authors/digital-product' class='linkAnimation'> Your digital product at De Gruyter </a></li> <li><a href='/publishing/for-authors/for-database-authors/contribute-reference-works' class='linkAnimation'> Contribute to our reference works </a></li> </ul> </div> </div> <a href='/publishing/services' id='mega-one-services' aria-haspopup="true" aria-expanded="false" > Services </a> <div class="row d-none" aria-labelledby="mega-one-services"> <div class="col-12"><a href="#mega-one-publications" class="linkAnimation visually-hidden-focusable">Skip section</a></div> <div class="col-sm-6 col-lg-4 mb-3 mb-lg-0"> <a href='/publishing/services/for-librarians' class="fw-bold linkAnimation"> For Librarians </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/services/for-librarians/product-information' class='linkAnimation'> Product information </a></li> <li><a href='/publishing/services/for-librarians/tools-resources' class='linkAnimation'> Tools & resources </a></li> <li><a href='/publishing/services/for-librarians/faqs' class='linkAnimation'> FAQs </a></li> <li><a href='/publishing/about-us/contact/sales' class='linkAnimation'> Contacts </a></li> </ul> </div> <div class="col-sm-6 col-lg-4 mb-3 mb-lg-0"> <a href='/publishing/services/book-sellers-library-suppliers' class="fw-bold linkAnimation"> For Book Sellers & Library Suppliers </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/services/book-sellers-library-suppliers/product-information-marketing-tools' class='linkAnimation'> Product Information </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/promotional-materials' class='linkAnimation'> Promotional Materials </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/orders-and-inquiries' class='linkAnimation'> Orders and Inquiries </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/faq-library-suppliers-and-book-sellers' class='linkAnimation'> FAQ for Library Suppliers and Book Sellers </a></li> </ul> </div> <div class="col-sm-6 col-lg-4"> <a href='/publishing/services/rights-and-permissions' class="fw-bold linkAnimation"> Rights & Permissions </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/services/rights-and-permissions/repositorypolicy' class='linkAnimation'> Repository Policy </a></li> <li><a href='/publishing/services/rights-and-permissions/freeaccesspolicy' class='linkAnimation'> Free access policy </a></li> </ul> </div> </div> <a href='/publishing/publications' id='mega-one-publications' aria-haspopup="true" aria-expanded="false" > Publications </a> <div class="row d-none" aria-labelledby="mega-one-publications"> <div class="col-12"><a href="#mega-one-about" class="linkAnimation visually-hidden-focusable">Skip section</a></div> <div class="col-sm-6 col-lg-2 my-col mb-3 mb-lg-0"> <a href='/publishing/publications/openaccess' class="fw-bold linkAnimation"> Open Access </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/publications/openaccess/open-access-books' class='linkAnimation'> Books </a></li> <li><a href='/publishing/publications/openaccess/open-access-articles' class='linkAnimation'> Articles </a></li> <li><a href='/publishing/publications/openaccess/open-access-agreements' class='linkAnimation'> Open Access agreements </a></li> </ul> </div> <div class="col-sm-6 col-lg-2 my-col mb-3 mb-lg-0"> <a href='/publishing/publications/publicationtypes' class="fw-bold linkAnimation"> Publication types </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/search?query=*&sortBy=mostrecent&documentTypeFacet=book&publisherFacet=De+Gruyter%7EDe+Gruyter+Mouton%7EDe+Gruyter+Oldenbourg%7EDe+Gruyter+Saur%7EBirkh%C3%A4user%7EDeutscher+Kunstverlag%7ED%C3%BCsseldorf+University+Press%7EJovis%7EKlaus+Schwarz+Verlag' class="linkAnimation"> Books </a></li> <li><a href='/search?query=*&sortBy=mostrecent&documentTypeFacet=journal&publisherFacet=De+Gruyter%7EDe+Gruyter+Mouton%7EDe+Gruyter+Oldenbourg%7EDe+Gruyter+Saur%7EBirkh%C3%A4user%7EDeutscher+Kunstverlag%7ED%C3%BCsseldorf+University+Press%7EJovis%7EKlaus+Schwarz+Verlag' class="linkAnimation"> Journals </a></li> <li><a href='/search?query=*&sortBy=relevance&documentTypeFacet=database' class="linkAnimation"> Databases </a></li> <li><a href='/publishing/publications/publicationtypes/database-portals' class='linkAnimation'> Database portals </a></li> </ul> </div> <div class="col-sm-12 col-lg-8 my-col"> <div class="row my-row"> <div class="col-lg-12 my-col"> <a href='/publishing/subjects' class="fw-bold linkAnimation"> Subjects we publish </a> <div class="dropdown-divider"></div> </div> </div> <div class="row my-row" id="publicationsSubjects"> <div class="col-4"> <ul class="list-unstyled"> <li><a href='/search?query=*&subjectFacet=AD' class="linkAnimation">Architecture and Design</a></li> <li><a href='/search?query=*&subjectFacet=AR' class="linkAnimation">Arts</a></li> <li><a href='/search?query=*&subjectFacet=AS' class="linkAnimation">Asian and Pacific Studies</a></li> <li><a href='/search?query=*&subjectFacet=EC' class="linkAnimation">Business and Economics</a></li> <li><a href='/search?query=*&subjectFacet=CH' class="linkAnimation">Chemistry</a></li> <li><a href='/search?query=*&subjectFacet=CL' class="linkAnimation">Classical and Ancient Near Eastern Studies</a></li> <li><a href='/search?query=*&subjectFacet=CO' class="linkAnimation">Computer Sciences</a></li> <li><a href='/search?query=*&subjectFacet=CS' class="linkAnimation">Cultural Studies</a></li> <li><a href='/search?query=*&subjectFacet=EN' class="linkAnimation">Engineering</a></li> <li><a href='/search?query=*&subjectFacet=GL' class="linkAnimation">General Interest</a></li> </ul> </div> <div class="col-4"> <ul class="list-unstyled"> <li><a href='/search?query=*&subjectFacet=GS' class="linkAnimation">Geosciences</a></li> <li><a href='/search?query=*&subjectFacet=HI' class="linkAnimation">History</a></li> <li><a href='/search?query=*&subjectFacet=IC' class="linkAnimation">Industrial Chemistry</a></li> <li><a href='/search?query=*&subjectFacet=IS' class="linkAnimation">Islamic and Middle Eastern Studies</a></li> <li><a href='/search?query=*&subjectFacet=JS' class="linkAnimation">Jewish Studies</a></li> <li><a href='/search?query=*&subjectFacet=LA' class="linkAnimation">Law</a></li> <li><a href='/search?query=*&subjectFacet=LB' class="linkAnimation">Library and Information Science, Book Studies</a></li> <li><a href='/search?query=*&subjectFacet=LF' class="linkAnimation">Life Sciences</a></li> <li><a href='/search?query=*&subjectFacet=LS' class="linkAnimation">Linguistics and Semiotics</a></li> <li><a href='/search?query=*&subjectFacet=LT' class="linkAnimation">Literary Studies</a></li> </ul> </div> <div class="col-4"> <ul class="list-unstyled"> <li><a href='/search?query=*&subjectFacet=MS' class="linkAnimation">Materials Sciences</a></li> <li><a href='/search?query=*&subjectFacet=MT' class="linkAnimation">Mathematics</a></li> <li><a href='/search?query=*&subjectFacet=MD' class="linkAnimation">Medicine</a></li> <li><a href='/search?query=*&subjectFacet=MU' class="linkAnimation">Music</a></li> <li><a href='/search?query=*&subjectFacet=PM' class="linkAnimation">Pharmacy</a></li> <li><a href='/search?query=*&subjectFacet=PL' class="linkAnimation">Philosophy</a></li> <li><a href='/search?query=*&subjectFacet=PY' class="linkAnimation">Physics</a></li> <li><a href='/search?query=*&subjectFacet=SN' class="linkAnimation">Social Sciences</a></li> <li><a href='/search?query=*&subjectFacet=SR' class="linkAnimation">Sports and Recreation</a></li> <li><a href='/search?query=*&subjectFacet=TL' class="linkAnimation">Theology and Religion</a></li> </ul> </div> </div> </div> </div> <a href='/publishing/about-us' id='mega-one-about' aria-haspopup="true" aria-expanded="false" > About </a> <div class="row d-none" aria-labelledby="mega-one-about"> <div class="col-12"><a href="#main" class="linkAnimation visually-hidden-focusable">Skip section</a></div> <div class="col-lg-6 my-col mb-3 mb-lg-0"> <div class="row my-row"> <div class="col-lg-12 my-col justify-content-start"> <a href='/publishing/about-us/contact' class="fw-bold linkAnimation"> Contact </a> <div class="dropdown-divider"></div> </div> </div> <div class="row my-row"> <div class="col-6 my-col"> <ul class="list-unstyled"> <li><a href='/publishing/about-us/contact/contact-for-authors' class='linkAnimation'> For Authors </a></li> <li><a href='/publishing/about-us/contact/contact-customer-services' class='linkAnimation'> Customer service </a></li> <li><a href='/publishing/about-us/contact/contact-hr' class='linkAnimation'> People + Culture </a></li> <li><a href='/publishing/about-us/press' class='linkAnimation'> Press </a></li> <li><a href='/publishing/about-us/contact/sales' class='linkAnimation'> Sales </a></li> <li><a href='/publishing/about-us/contact/journal-management' class='linkAnimation'> Journal Management </a></li> </ul> </div> <div class="col-6 my-col"> <ul class="list-unstyled"> <li><a href='/publishing/about-us/contact/partner-publishers' class='linkAnimation'> Partner Publishers </a></li> <li><a href='/publishing/about-us/contact/contact-openaccess' class='linkAnimation'> Open Access </a></li> <li><a href='/publishing/about-us/contact/advertising' class='linkAnimation'> Advertising </a></li> <li><a href='/publishing/about-us/contact/review-copies' class='linkAnimation'> Review Copies </a></li> <li><a href='/publishing/about-us/contact/inspection-copies' class='linkAnimation'> Inspection Copies </a></li> <li><a href='/publishing/about-us/contact/legal' class='linkAnimation'> Legal </a></li> </ul> </div> </div> </div> <div class="col-sm-4 col-lg-2 my-col"> <a href='/publishing/about-us/careers' class="fw-bold linkAnimation">Career</a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/about-us/careers/how-to-join' class='linkAnimation'> How to join us </a></li> <li><a href='/publishing/about-us/careers/vacancies' class='linkAnimation'> Vacancies </a></li> <li><a href='/publishing/about-us/careers/working-at-dg' class='linkAnimation'> Working at De Gruyter </a></li> </ul> </div> <div class="col-sm-4 col-lg-2 my-col"> <a href='/publishing/about-us/about-dg' class="fw-bold linkAnimation"> About De Gruyter </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/about-us/about-dg/vision-mission' class='linkAnimation'> Mission & Vision </a></li> <li><a href='/publishing/about-us/about-dg/our-imprints' class='linkAnimation'> Imprints </a></li> <li><a href='/publishing/about-us/about-dg/history' class='linkAnimation'> History </a></li> <li><a href='/publishing/about-us/about-dg/dg-foundation' class='linkAnimation'> De Gruyter Foundation </a></li> <li><a href='/publishing/about-us/about-dg/degruyter-ebound' class='linkAnimation'> De Gruyter Ebound </a></li> <li><a href='/publishing/about-us/about-dg/locations' class='linkAnimation'> Locations </a></li> <li><a href='/publishing/about-us/our-responsibility' class='linkAnimation'> Our Responsibility </a></li> </ul> </div> <div class="col-sm-4 col-lg-2 my-col"> <a href='/publishing/about-us/publisher-partners' class="fw-bold linkAnimation"> Partnerships </a> <div class="dropdown-divider"></div> <ul class="list-unstyled"> <li><a href='/publishing/about-us/publisher-partners' class='linkAnimation'> Partner publishers </a></li> <li><a href='/publishing/about-us/press' class='fw-bold linkAnimation'> Press </a></li> <li><a href='/publishing/about-us/faqs' class='fw-bold linkAnimation'> FAQs </a></li> <li><a href='/publishing/subscribe-newsletter' class='fw-bold linkAnimation'> Newsletter </a></li> </ul> </div> </div> </nav> </div> <div class="position-relative d-md-none d-block z-2"> <nav class="navbar navbar-expand-md navbar-dark bg-dark dg-navbar p-3 align-items-center" aria-label="site"> <span class="pe-2"> <dg-toggle target="megaMenu" state="open"> <button type="button" class="navbar-toggler border-0 px-1 ml--1" aria-controls="megaMenu" aria-label='Display site navigation, currency and language options'> <span class="fa fas fa-hamburger-icon text-white hamburgerIcon"></span> </button> </dg-toggle> </span> <span class="flex-grow-2"> <a id="homepageLogoLinkMobile" class="ga_homepage_logo navbar-brand mx-0 py-0" href="/" aria-label='De Gruyter logo with link to home page'> <img src='/assets/images/b8fcea517b20e08ecf20a1c14e8b5dfb-dg-logo-nav-small.svg' alt="De Gruyter" /> </a> </span> <span> <div class="cartSummary d-inline-block"> <a href="" class="mainNavbarOptionsBg pe-2 d-flex align-items-center text-decoration-none"> <span class="fa fas fa-shopping-cart"></span> <span data-fc-id="minicart-quantity" class="shopping-cart-badge badge font-family-standard font-size-12">0</span> </a></div> <button id="navbarProfileBtn" class="navbar-toggler border-0 px-1 collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#navbarProfile" aria-controls="navbarProfile" aria-expanded="false" aria-label="Toggle navigation"> <span class="fa fas fa-solid fa-user text-white"></span> <span class="fa fas fa-solid fa-close-icon text-white"></span> </button> </span> <div class="mainNavbarSearchContainer w-100 me-md-2 me-lg-5 mt-2 mt-md-0"> <form class="form-inline" action='/search?query='> <div class="input-group flex-grow-1"> <input class="mainNavbarSearchInput form-control input-header rounded-start py-1" type="search" aria-label='Search' name="query" placeholder='Search De Gruyter' value='' /> <div class="input-group-append"> <button class="btn btn-primary rounded-end analyticsButton" aria-label='Search' type="submit"><span class="fa fas fa-search ga_main_search_button"></span></button> </div> </div> </form> </div> <div id="wrap"> <div class="accordion-collapse collapse accordion navbar-collapse" data-bs-parent="#wrap" id="navbarProfile"> <div id="mobileLoginContent" class="mt-3"></div> <ajax-frame src="/login/banner" class="authBannerMobile mb-3"></ajax-frame> </div> </div> </nav> </div>  <mega-menu id="megaMenu" tabindex="-1" class="d-md-none"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <img class="logo" src="/assets/images/dg-logo-nav-small.svg" alt="De Gruyter"> <dg-toggle target="megaMenu" state="close"> <button class="btn-close" aria-label='Close Navigation Menu'></button> </dg-toggle> </div> <div class="modal-body scrollWatch"> <div class="accordion accordion-flush mega-menu-accordion" data-bs-parent="#wrap" id="mobileCorpMenu"> <div class="accordion-item"> <div class="accordion-header" id="mobileCorpMenu-headingOne"> <button class="accordion-button collapsed lvl1" type="button" data-bs-toggle="collapse" data-bs-target="#mobileCorpMenu-collapseOne" aria-expanded="false" aria-controls="mobileCorpMenu-collapseOne"> <div class="button-text"> SUBJECTS </div> </button> </div> <div id="mobileCorpMenu-collapseOne" class="accordion-collapse collapse" aria-labelledby="mobileCorpMenu-headingOne" data-bs-parent="#mobileCorpMenu"> <div class="accordion-body"> <a class="lvl2"href='/publishing/subjects' > Browse Publications By Subject </a> <ul class="list-unstyled subsection"> <li> <a href='/search?query=*&subjectFacet=AD' class="linkAnimation"> Architecture and Design </a> </li> <li> <a href='/search?query=*&subjectFacet=AR' class="linkAnimation"> Arts </a> </li> <li> <a href='/search?query=*&subjectFacet=AS' class="linkAnimation"> Asian and Pacific Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=EC' class="linkAnimation"> Business and Economics </a> </li> <li> <a href='/search?query=*&subjectFacet=CH' class="linkAnimation"> Chemistry </a> </li> <li> <a href='/search?query=*&subjectFacet=CL' class="linkAnimation"> Classical and Ancient Near Eastern Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=CO' class="linkAnimation"> Computer Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=CS' class="linkAnimation"> Cultural Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=EN' class="linkAnimation"> Engineering </a> </li> <li> <a href='/search?query=*&subjectFacet=GL' class="linkAnimation"> General Interest </a> </li> <li> <a href='/search?query=*&subjectFacet=GS' class="linkAnimation"> Geosciences </a> </li> <li> <a href='/search?query=*&subjectFacet=HI' class="linkAnimation"> History </a> </li> <li> <a href='/search?query=*&subjectFacet=IC' class="linkAnimation"> Industrial Chemistry </a> </li> <li> <a href='/search?query=*&subjectFacet=IS' class="linkAnimation"> Islamic and Middle Eastern Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=JS' class="linkAnimation"> Jewish Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=LA' class="linkAnimation"> Law </a> </li> <li> <a href='/search?query=*&subjectFacet=LB' class="linkAnimation"> Library and Information Science, Book Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=LF' class="linkAnimation"> Life Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=LS' class="linkAnimation"> Linguistics and Semiotics </a> </li> <li> <a href='/search?query=*&subjectFacet=LT' class="linkAnimation"> Literary Studies </a> </li> <li> <a href='/search?query=*&subjectFacet=MS' class="linkAnimation"> Materials Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=MT' class="linkAnimation"> Mathematics </a> </li> <li> <a href='/search?query=*&subjectFacet=MD' class="linkAnimation"> Medicine </a> </li> <li> <a href='/search?query=*&subjectFacet=MU' class="linkAnimation"> Music </a> </li> <li> <a href='/search?query=*&subjectFacet=PM' class="linkAnimation"> Pharmacy </a> </li> <li> <a href='/search?query=*&subjectFacet=PL' class="linkAnimation"> Philosophy </a> </li> <li> <a href='/search?query=*&subjectFacet=PY' class="linkAnimation"> Physics </a> </li> <li> <a href='/search?query=*&subjectFacet=SN' class="linkAnimation"> Social Sciences </a> </li> <li> <a href='/search?query=*&subjectFacet=SR' class="linkAnimation"> Sports and Recreation </a> </li> <li> <a href='/search?query=*&subjectFacet=TL' class="linkAnimation"> Theology and Religion </a> </li> </ul> </div> </div> </div> <div class="accordion-item"> <div class="accordion-header" id="mobileCorpMenu-headingTwo"> <button class="accordion-button collapsed lvl1" type="button" data-bs-toggle="collapse" data-bs-target="#mobileCorpMenu-collapseTwo" aria-expanded="false" aria-controls="mobileCorpMenu-collapseTwo"> FOR AUTHORS </button> </div> <div id="mobileCorpMenu-collapseTwo" class="accordion-collapse collapse" aria-labelledby="mobileCorpMenu-headingTwo" data-bs-parent="#mobileCorpMenu"> <div class="accordion-body mvertical"> <div class="accordion accordion-flush" id="services-accordion"> <a class="lvl2 linkAnimation" href='/publishing/for-authors/for-journal-authors'> For Journal Authors </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/for-authors/for-journal-authors/publish-your-article' class='linkAnimation'> Publish your article </a></li> <li><a href='/publishing/for-authors/for-journal-authors/role-of-authors' class='linkAnimation'> The role of authors </a></li> <li><a href='/publishing/for-authors/for-journal-authors/promoting-your-article' class='linkAnimation'> Promoting your article </a></li> <li><a href='/publishing/for-authors/for-journal-authors/abstracting-and-indexing' class='linkAnimation'> Abstracting & indexing </a></li> <li><a href='/publishing/for-authors/for-journal-authors/publishing-ethics' class='linkAnimation'> Publishing Ethics </a></li> </ul> <a class="lvl2 linkAnimation" href='/publishing/for-authors/for-book-authors'> For Book Authors </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/for-authors/for-book-authors/why-publish-with-de-gruyter' class='linkAnimation'> Why publish with De Gruyter </a></li> <li><a href='/publishing/for-authors/for-book-authors/how-to-publish-with-de-gruyter' class='linkAnimation'> How to publish with De Gruyter </a></li> <li><a href='/publishing/for-authors/for-book-authors/our-book-series' class='linkAnimation'> Our book series </a></li> <li><a href='/publishing/for-authors/for-book-authors/our-subject-areas' class='linkAnimation'> Our subject areas </a></li> </ul> <a class="lvl2 linkAnimation" href='/publishing/for-authors/for-database-authors'> For Database Authors </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/for-authors/for-database-authors/digital-product' class='linkAnimation'> Your digital product at De Gruyter </a></li> <li><a href='/publishing/for-authors/for-database-authors/contribute-reference-works' class='linkAnimation'> Contribute to our reference works </a></li> </ul> </div> </div> </div> </div> <div class="accordion-item"> <div class="accordion-header" id="mobileCorpMenu-headingThree"> <button class="accordion-button collapsed lvl1" type="button" data-bs-toggle="collapse" data-bs-target="#mobileCorpMenu-collapseThree" aria-expanded="false" aria-controls="mobileCorpMenu-collapseThree"> SERVICES </button> </div> <div id="mobileCorpMenu-collapseThree" class="accordion-collapse collapse" aria-labelledby="mobileCorpMenu-headingThree" data-bs-parent="#mobileCorpMenu"> <div class="accordion-body mvertical"> <div class="accordion accordion-flush" id="services-accordion"> <a class="lvl2 linkAnimation" href='/publishing/services/for-librarians'> For Librarians </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/services/for-librarians/product-information' class='linkAnimation'> Product information </a></li> <li><a href='/publishing/services/for-librarians/tools-resources' class='linkAnimation'> Tools & resources </a></li> <li><a href='/publishing/services/for-librarians/faqs' class='linkAnimation'> FAQs </a></li> <li><a href='/publishing/about-us/contact/sales' class='linkAnimation'> Contacts </a></li> </ul> <a class="lvl2 linkAnimation" href='/publishing/services/book-sellers-library-suppliers'> For Book Sellers & Library Suppliers </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/services/book-sellers-library-suppliers/product-information-marketing-tools' class='linkAnimation'> Product Information </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/promotional-materials' class='linkAnimation'> Promotional Materials </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/orders-and-inquiries' class='linkAnimation'> Orders and Inquiries </a></li> <li><a href='/publishing/services/book-sellers-library-suppliers/faq-library-suppliers-and-book-sellers' class='linkAnimation'> FAQ for Library Suppliers and Book Sellers </a></li> </ul> <a class="lvl2 linkAnimation" href='/publishing/services/rights-and-permissions'> Rights & Permissions </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/services/rights-and-permissions/repositorypolicy' class='linkAnimation'> Repository Policy </a></li> <li><a href='/publishing/services/rights-and-permissions/freeaccesspolicy' class='linkAnimation'> Free access policy </a></li> </ul> </div> </div> </div> </div> <div class="accordion-item"> <div class="accordion-header" id="mobileCorpMenu-headingFour"> <button class="accordion-button collapsed lvl1" type="button" data-bs-toggle="collapse" data-bs-target="#mobileCorpMenu-collapseFour" aria-expanded="false" aria-controls="mobileCorpMenu-collapseFour"> PUBLICATIONS </button> </div> <div id="mobileCorpMenu-collapseFour" class="accordion-collapse collapse" aria-labelledby="mobileCorpMenu-headingFour" data-bs-parent="#mobileCorpMenu"> <div class="accordion-body"> <div class="accordion accordion-flush" id="publications-accordion"> <a href='/publishing/publications/openaccess' class="lvl2 linkAnimation"> Open Access </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/publications/openaccess/open-access-books' class='linkAnimation'> Books </a></li> <li><a href='/publishing/publications/openaccess/open-access-articles' class='linkAnimation'> Articles </a></li> <li><a href='/publishing/publications/openaccess/open-access-agreements' class='linkAnimation'> Open Access agreements </a></li> </ul> <a href='/publishing/publications/publicationtypes' class="lvl2 linkAnimation"> Publication types </a> <ul class="list-unstyled subsection"> <li><a href='/search?query=*&sortBy=mostrecent&documentTypeFacet=book&publisherFacet=De+Gruyter%7EDe+Gruyter+Mouton%7EDe+Gruyter+Oldenbourg%7EDe+Gruyter+Saur%7EBirkh%C3%A4user%7EDeutscher+Kunstverlag%7ED%C3%BCsseldorf+University+Press%7EJovis%7EKlaus+Schwarz+Verlag' class="linkAnimation"> Books </a></li> <li><a href='/search?query=*&sortBy=mostrecent&documentTypeFacet=journal&publisherFacet=De+Gruyter%7EDe+Gruyter+Mouton%7EDe+Gruyter+Oldenbourg%7EDe+Gruyter+Saur%7EBirkh%C3%A4user%7EDeutscher+Kunstverlag%7ED%C3%BCsseldorf+University+Press%7EJovis%7EKlaus+Schwarz+Verlag' class="linkAnimation"> Journals </a></li> <li><a href='/search?query=*&sortBy=relevance&documentTypeFacet=database' class="linkAnimation"> Databases </a></li> <li><a href='/publishing/publications/publicationtypes/database-portals' class='linkAnimation'> Database portals </a></li> </ul> <a href='/publishing/subjects' class="lvl2 linkAnimation"> Subjects we publish </a> <ul class="list-unstyled subsection"> <li><a href='/search?query=*&subjectFacet=AD' class="linkAnimation">Architecture and Design</a></li> <li><a href='/search?query=*&subjectFacet=AR' class="linkAnimation">Arts</a></li> <li><a href='/search?query=*&subjectFacet=AS' class="linkAnimation">Asian and Pacific Studies</a></li> <li><a href='/search?query=*&subjectFacet=EC' class="linkAnimation">Business and Economics</a></li> <li><a href='/search?query=*&subjectFacet=CH' class="linkAnimation">Chemistry</a></li> <li><a href='/search?query=*&subjectFacet=CL' class="linkAnimation">Classical and Ancient Near Eastern Studies</a></li> <li><a href='/search?query=*&subjectFacet=CO' class="linkAnimation">Computer Sciences</a></li> <li><a href='/search?query=*&subjectFacet=CS' class="linkAnimation">Cultural Studies</a></li> <li><a href='/search?query=*&subjectFacet=EN' class="linkAnimation">Engineering</a></li> <li><a href='/search?query=*&subjectFacet=GL' class="linkAnimation">General Interest</a></li> </ul> <ul class="list-unstyled subsection"> <li><a href='/search?query=*&subjectFacet=GS' class="linkAnimation">Geosciences</a></li> <li><a href='/search?query=*&subjectFacet=HI' class="linkAnimation">History</a></li> <li><a href='/search?query=*&subjectFacet=IC' class="linkAnimation">Industrial Chemistry</a></li> <li><a href='/search?query=*&subjectFacet=IS' class="linkAnimation">Islamic and Middle Eastern Studies</a></li> <li><a href='/search?query=*&subjectFacet=JS' class="linkAnimation">Jewish Studies</a></li> <li><a href='/search?query=*&subjectFacet=LA' class="linkAnimation">Law</a></li> <li><a href='/search?query=*&subjectFacet=LB' class="linkAnimation">Library and Information Science, Book Studies</a></li> <li><a href='/search?query=*&subjectFacet=LF' class="linkAnimation">Life Sciences</a></li> <li><a href='/search?query=*&subjectFacet=LS' class="linkAnimation">Linguistics and Semiotics</a></li> <li><a href='/search?query=*&subjectFacet=LT' class="linkAnimation">Literary Studies</a></li> </ul> <ul class="list-unstyled subsection"> <li><a href='/search?query=*&subjectFacet=MS' class="linkAnimation">Materials Sciences</a></li> <li><a href='/search?query=*&subjectFacet=MT' class="linkAnimation">Mathematics</a></li> <li><a href='/search?query=*&subjectFacet=MD' class="linkAnimation">Medicine</a></li> <li><a href='/search?query=*&subjectFacet=MU' class="linkAnimation">Music</a></li> <li><a href='/search?query=*&subjectFacet=PM' class="linkAnimation">Pharmacy</a></li> <li><a href='/search?query=*&subjectFacet=PL' class="linkAnimation">Philosophy</a></li> <li><a href='/search?query=*&subjectFacet=PY' class="linkAnimation">Physics</a></li> <li><a href='/search?query=*&subjectFacet=SN' class="linkAnimation">Social Sciences</a></li> <li><a href='/search?query=*&subjectFacet=SR' class="linkAnimation">Sports and Recreation</a></li> <li><a href='/search?query=*&subjectFacet=TL' class="linkAnimation">Theology and Religion</a></li> </ul> </div> </div> </div> </div> <div class="accordion-item"> <div class="accordion-header" id="mobileCorpMenu-headingFive"> <button class="accordion-button collapsed lvl1" type="button" data-bs-toggle="collapse" data-bs-target="#mobileCorpMenu-collapseFive" aria-expanded="false" aria-controls="mobileCorpMenu-collapseFive"> ABOUT </button> </div> <div id="mobileCorpMenu-collapseFive" class="accordion-collapse collapse" aria-labelledby="mobileCorpMenu-headingFive" data-bs-parent="#mobileCorpMenu"> <div class="accordion-body"> <div class="accordion accordion-flush" id="aboutAccordion"> <a href='/publishing/about-us/contact' class="lvl2 linkAnimation"> Contact </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/about-us/contact/contact-for-authors' class='linkAnimation'> For Authors </a></li> <li><a href='/publishing/about-us/contact/contact-customer-services' class='linkAnimation'> Customer service </a></li> <li><a href='/publishing/about-us/contact/contact-hr' class='linkAnimation'> People + Culture </a></li> <li><a href='/publishing/about-us/press' class='linkAnimation'> Press </a></li> <li><a href='/publishing/about-us/contact/sales' class='linkAnimation'> Sales </a></li> <li><a href='/publishing/about-us/contact/journal-management' class='linkAnimation'> Journal Management </a></li> </ul> <a href='/publishing/about-us/careers' class="lvl2 linkAnimation"> Career </a> <ul class="list-unstyled subsection"> <li><a href='/publishing/about-us/careers/how-to-join' class='linkAnimation'> How to join us </a></li> <li><a href='/publishing/about-us/careers/vacancies' class='linkAnimation'> Vacancies </a></li> <li><a href='/publishing/about-us/careers/working-at-dg' class='linkAnimation'> Working at De Gruyter </a></li> </ul> <a href='/publishing/about-us/about-dg' class="lvl2 linkAnimation"> About De Gruyter </a> <ul class="subsection list-unstyled"> <li><a href='/publishing/about-us/about-dg/vision-mission' class='linkAnimation'> Mission & Vision </a></li> <li><a href='/publishing/about-us/about-dg/our-imprints' class='linkAnimation'> Imprints </a></li> <li><a href='/publishing/about-us/about-dg/history' class='linkAnimation'> History </a></li> <li><a href='/publishing/about-us/about-dg/dg-foundation' class='linkAnimation'> De Gruyter Foundation </a></li> <li><a href='/publishing/about-us/about-dg/degruyter-ebound' class='linkAnimation'> De Gruyter Ebound </a></li> <li><a href='/publishing/about-us/about-dg/locations' class='linkAnimation'> Locations </a></li> <li><a href='/publishing/about-us/our-responsibility' class='linkAnimation'> Our Responsibility </a></li> </ul> <a href='/publishing/about-us/publisher-partners' class="lvl2 linkAnimation"> Partnerships </a> <ul class="list-unstyled"> <ul class="list-unstyled subsection"> <li><a href='/publishing/about-us/publisher-partners' class='linkAnimation'> Partner publishers </a></li> </ul> <ul class="list-unstyled subsection"> <li><a href='/publishing/about-us/press' class='fw-bold linkAnimation'> Press </a></li> </ul> <ul class="list-unstyled subsection"> <li><a href='/publishing/about-us/faqs' class='fw-bold linkAnimation'> FAQs </a></li> </ul> <ul class="list-unstyled subsection"> <li><a href='/publishing/subscribe-newsletter' class='fw-bold linkAnimation'> Newsletter </a></li> </ul> </ul> </div> </div> </div> </div> </div> <div class="mt-3"> <span class="selectorHeader"> Change language </span> <div class="grid-2 mobile-selector mt-2 mb-3"> <a class="languageSelector_en ga_language_selector mobile-option mobile-active" href="/_language/en?uri=%2Fdocument%2Fdoi%2F10.2202%2F1544-6115.1309%2Fhtml"> <span>English</span> </a> <a class="languageSelector_de ga_language_selector mobile-option " href="/_language/de?uri=%2Fdocument%2Fdoi%2F10.2202%2F1544-6115.1309%2Fhtml"> <span>Deutsch</span> </a> </div> <span class="selectorHeader"> Change currency </span> <div class="grid-3 mobile-selector mt-2 mb-5"> <select-currency class="mobile-option" selected-class="mobile-active" currency="EUR"><span>€ EUR</span></select-currency> <select-currency class="mobile-option" selected-class="mobile-active" currency="GBP"><span>£ GBP</span></select-currency> <select-currency class="mobile-option" selected-class="mobile-active" currency="USD"><span>$ USD</span></select-currency> </div> </div> </div> </div> </div> </mega-menu> <div class="accordion-collapse collapse accordion navbar-collapse" data-bs-parent="#wrap" id="navbarSupportedContentnope"> </div> </header>  <div class="modal" id="orderCompleteModal" tabindex="-1" role="dialog" aria-label='Purchase Complete' aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-lg" role="document"> <div class="modal-content bg-white"> <div class="modal-body"> <button type="button" class="btn-close float-end btn-modal-close" data-bs-dismiss="modal" aria-label='Close'></button> <p>Your purchase has been completed. Your documents are now available to view.</p> <div id="orderCompleteItemList"> </div> </div> </div> </div> </div> <main id="main" class='language_en min-vh-100 '> <div class="row no-theme-gutter-x g-0 " id="docContent"> <div class='offset-lg-1 col-lg-8 pb-2'> <div class='row g-0 '> <div class="col p-3 pt-5"> <div class="d-flex flex-wrap flex-column flex-md-row justify-content-between"> <div> <div class="mb-2"> <span class="d-none itemAuthorized"> <span class="fa fas fa-icon-authorized"></span> <span class="accessAccessible me-2">Licensed</span> </span> <span class="d-none itemNotAuthorized"> <span class="fa fas fa-icon-not-authorized"></span> <span class="d-none notAuthUserLoggedIn accessRequireAuth me-2">Unlicensed</span> <span class="d-none notAuthUserLoggedOut accessRequireAuth me-2">Requires Authentication</span> </span> <span class="publisherAndPublicationDate metadataInfoMainContent"> <span class="publisher"> Published by <a class="ga_published_by ga_published_by_header" href='/search?query=*&publisherFacet=De+Gruyter'>De Gruyter</a> </span> <span class="publicationDate">September 16, 2007</span> </span> </div> <div id="mobilePurchaseDiv" class="d-none"> <a class="mobilePurchaseButton" href="#"> Purchase article <svg width="17" height="16" viewBox="0 0 17 16" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M12.75 10.3238L11.4513 9L9.5 11.1469L9.5 1L7.5 1L7.5 11.1473L5.54829 9L4.24962 10.3238L8.49981 15L12.75 10.3238Z" fill="#007596"/> </svg> </a> </div> <h1>Super Learner</h1> <ul class="contributors list-unstyled mb-2"> <li class="contributors-AUTHOR mb-2"> <span class="metadataAndContributorsFont"><span class="contributor"> <span class="displayName linkAnimation">Mark J. van der Laan</span> <contributor-popdown name="Mark J. van der Laan" position="1" email="" affiliations="" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Eric C Polley</span> <contributor-popdown name="Eric C Polley" position="2" email="" affiliations="" > </contributor-popdown> </span> and <span class="contributor"> <span class="displayName linkAnimation">Alan E. Hubbard</span> <contributor-popdown name="Alan E. Hubbard" position="3" email="" affiliations="" > </contributor-popdown> </span></span> </li> </ul> <div class="subTitleInfoProductPage">From the journal <a class="ga_parent ga_parent_journal" href="/journal/key/sagmb/html">Statistical Applications in Genetics and Molecular Biology</a></div> <div class="doi"><a href="https://doi.org/10.2202/1544-6115.1309" class="linkWithoutStyle subTitleInfoProductPage ga_doi" target="_blank">https://doi.org/10.2202/1544-6115.1309</a></div> </div> </div> </div> <div class="d-flex align-items-center flex-wrap px-4 px-lg-2 "> <button id='citationsModalButton' type="button" class="btn btn-main-content ga_cite_this me-2" href='#citationsModal' data-bs-toggle="modal" data-bs-target="#citationsModal" data-doi="10.2202/1544-6115.1309" aria-controls='citationsModal'> Cite this </button> <button id="socialModalButton" type="button" class="btn btn-main-content ga_share_this me-2" href="#socialModal" data-bs-toggle="modal" data-bs-target="#socialModal" aria-controls="socialModal"> Share this </button> <div class="dimensions __dimensions_badge_embed__ ga_dimensions_citation me-2" data-doi="10.2202/1544-6115.1309" data-hide-zero-citations="true" data-legend="never" data-style="large_rectangle"></div> </div> <div id="div-document-progress-bar" class="sticky-top d-none"> <div class="row"> <div class="col-12"> <div class="progress progress-bar-toolbar"> <div id="document-progress-bar" class="progress-bar bg-primary" role="progressbar" aria-label="Document progress bar" aria-valuenow="0" aria-valuemin="0" aria-valuemax="100"></div> </div> </div> </div> </div> <div id="document-main-content" class='row'> <div class="container-fluid px-3 px-lg-0 py-2"> <div class="col"> <div class="d-none analyticsHolder" data-subjects='LF|LF-01|LF-03|MT|MT-09' data-publisherCode='DEG' data-license='restricted' data-publisher='De Gruyter' data-contentName='Super Learner' data-doi='10.2202/1544-6115.1309' data-parentIdentifier='SAGMB' data-parentName='Statistical Applications in Genetics and Molecular Biology' data-languages='en' ></div> <div id="documentContent" class="content py-2" data-doi='10.2202/1544-6115.1309' data-accessrestricted="true" data-countertype="document"> <div class="px-2"> <div class="alert alert-info-box" role="alert"> <div id="noAccessReasonSpinner"> <div class="spinner-border text-primary" role="status"></div> </div> <div id="noAccessReasonContent"> <small class="fa fas fa-block"></small> <small id="noAccessReason"></small> <div class="previewAlertContainer"> <small class="previewAlert">Showing a limited preview of this publication:</small> </div> </div> </div> <div id="text-container"> <div xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" xmlns:dgpm="http://degruyter.com/resources/fetched-pubmed-id" class="contentWrapper"><div class="article" lang="en"><div class="abstract"><p>When trying to learn a model for the prediction of an outcome given a set of covariates, a statistician has many estimation procedures in their toolbox. A few examples of these candidate learners are: least squares, least angle regression, random forests, and spline regression. Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) theoretically validated the use of cross validation to select an optimal learner among many candidate learners. Motivated by this use of cross validation, we propose a new prediction method for creating a weighted combination of many candidate learners to build the super learner. This article proposes a fast algorithm for constructing a super learner in prediction which uses V-fold cross-validation to select weights to combine an initial set of candidate learners. In addition, this paper contains a practical demonstration of the adaptivity of this so called super learner to various true data generating distributions. This approach for construction of a super learner generalizes to any parameter which can be defined as a minimizer of a loss function.</p></div><div class="keywords mb-3">Keywords: <a href="/search?query=keywordValues%3A%28%22cross-validation%22%29%20AND%20journalKey%3A%28%22SAGMB%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">cross-validation</a>; <a href="/search?query=keywordValues%3A%28%22loss-based%20estimation%22%29%20AND%20journalKey%3A%28%22SAGMB%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">loss-based estimation</a>; <a href="/search?query=keywordValues%3A%28%22machine%20learning%22%29%20AND%20journalKey%3A%28%22SAGMB%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">machine learning</a>; <a href="/search?query=keywordValues%3A%28%22prediction%22%29%20AND%20journalKey%3A%28%22SAGMB%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">prediction</a></div><div class="contrib-group"></div><div class="publicationDates mb-3"><div class="publishedOnlineDate"><span class="label-publishedOnline"><span><strong>Published Online: </strong></span></span>2007-9-16</div></div><div class="copyrightStatement"><p>©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston</p></div></div></div> </div> </div> </div> <div class="modal" id="citationsModal" tabindex="-1" role="dialog" aria-label='Cite this' aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-lg" role="document"> <div class="modal-content bg-white"> <div class="modal-body"> <button type="button" class="btn-close float-end btn-modal-close" data-bs-dismiss="modal" aria-label='Close'></button> <div id="citations"> <div class="row pb-2"> <div class="col"> <div class="text-dark fw-bold">Cite this article</div> </div> </div> <div class="row p-2"> <div class="col-lg-auto ps-4 mb-3 mb-lg-0"> <ul class="nav d-flex flex-lg-column" id="citationSelector" role="tablist"> <li class="nav-item py-1" role="presentation"> <a class="nav-link citations py-0 font-size-14 active" id="MLA-tab" data-bs-toggle="tab" href="#MLA" role="tab" aria-controls="MLA" aria-selected="true"> <span class="text-primary fa fas fa-ok me-2"></span> <span class="font-family-standard text-dark">MLA</span> </a> </li> <li class="nav-item py-1" role="presentation"> <a class="nav-link citations py-0 font-size-14 " id="APA-tab" data-bs-toggle="tab" href="#APA" role="tab" aria-controls="APA" aria-selected="true"> <span class="text-primary fa fas fa-ok me-2"></span> <span class="font-family-standard text-dark">APA</span> </a> </li> <li class="nav-item py-1" role="presentation"> <a class="nav-link citations py-0 font-size-14 " id="Harvard-tab" data-bs-toggle="tab" href="#Harvard" role="tab" aria-controls="Harvard" aria-selected="true"> <span class="text-primary fa fas fa-ok me-2"></span> <span class="font-family-standard text-dark">Harvard</span> </a> </li> <li class="nav-item py-1" role="presentation"> <a class="nav-link citations py-0 font-size-14 " id="Chicago-tab" data-bs-toggle="tab" href="#Chicago" role="tab" aria-controls="Chicago" aria-selected="true"> <span class="text-primary fa fas fa-ok me-2"></span> <span class="font-family-standard text-dark">Chicago</span> </a> </li> <li class="nav-item py-1" role="presentation"> <a class="nav-link citations py-0 font-size-14 " id="Vancouver-tab" data-bs-toggle="tab" href="#Vancouver" role="tab" aria-controls="Vancouver" aria-selected="true"> <span class="text-primary fa fas fa-ok me-2"></span> <span class="font-family-standard text-dark">Vancouver</span> </a> </li> </ul> </div> <div class="col"> <div class="tab-content border pt-4 px-4" id="citationContent"> <div class="tab-pane fade show active" id="MLA" role="tabpanel" aria-labelledby="MLA-tab">van der Laan, Mark J., Polley, Eric C and Hubbard, Alan E.. "Super Learner" <i>Statistical Applications in Genetics and Molecular Biology</i>, vol. 6, no. 1, 2007. <a href='https://doi.org/10.2202/1544-6115.1309'>https://doi.org/10.2202/1544-6115.1309</a></div> <div class="tab-pane fade " id="APA" role="tabpanel" aria-labelledby="APA-tab">van der Laan, M., Polley, E. & Hubbard, A. (2007). Super Learner. <i>Statistical Applications in Genetics and Molecular Biology</i>, <i>6</i>(1). <a href='https://doi.org/10.2202/1544-6115.1309'>https://doi.org/10.2202/1544-6115.1309</a></div> <div class="tab-pane fade " id="Harvard" role="tabpanel" aria-labelledby="Harvard-tab">van der Laan, M., Polley, E. and Hubbard, A. (2007) Super Learner. Statistical Applications in Genetics and Molecular Biology, Vol. 6 (Issue 1). <a href='https://doi.org/10.2202/1544-6115.1309'>https://doi.org/10.2202/1544-6115.1309</a></div> <div class="tab-pane fade " id="Chicago" role="tabpanel" aria-labelledby="Chicago-tab">van der Laan, Mark J., Polley, Eric C and Hubbard, Alan E.. "Super Learner" <i>Statistical Applications in Genetics and Molecular Biology</i> 6, no. 1 (2007). <a href='https://doi.org/10.2202/1544-6115.1309'>https://doi.org/10.2202/1544-6115.1309</a></div> <div class="tab-pane fade " id="Vancouver" role="tabpanel" aria-labelledby="Vancouver-tab">van der Laan M, Polley E, Hubbard A. Super Learner. <i>Statistical Applications in Genetics and Molecular Biology</i>. 2007;6(1). <a href='https://doi.org/10.2202/1544-6115.1309'>https://doi.org/10.2202/1544-6115.1309</a></div> <div class="d-flex justify-content-center"><span id="citationCopied" aria-hidden="true">Copied to clipboard</span></div> </div> <div class="d-flex justify-content-between mt-2"> <div><a href="#" id="citationCopy" class="font-size-14">Copy to clipboard</a></div> <div> <span class="font-size-14">Download:</span> <a title='Download in BibTeX format' aria-label='Download in BibTeX format' class="ms-1 font-size-14" href="/document/doi/10.2202/1544-6115.1309/machineReadableCitation/BibTeX">BibTeX</a> <a title='Download in EndNote format' aria-label='Download in EndNote format' class="ms-1 font-size-14" href="/document/doi/10.2202/1544-6115.1309/machineReadableCitation/EndNote">EndNote</a> <a title='Download in RIS format' aria-label='Download in RIS format' class="ms-1 font-size-14" href="/document/doi/10.2202/1544-6115.1309/machineReadableCitation/RIS">RIS</a> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="modal" id="socialModal" tabindex="-1" role="dialog" aria-label='Share this' aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-sm" role="document"> <div class="modal-content bg-white"> <div class="modal-body"> <button type="button" class="btn-close float-end btn-modal-close" data-bs-dismiss="modal" aria-label='Close'></button> <div id="share-this"> <div class="row bg-white"> <div class="text-dark fw-bold pb-2"> Share this article </div> <ul class="list-unstyled m-0"> <li> <a href="http://www.facebook.com/sharer.php?u=https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html" class="btn btn-default linkToShare facebookColor ga_share_this_facebook" target="_blank"> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex"> <path fill-rule="evenodd" clip-rule="evenodd" d="M13.5655 22V12.877H16.6612L17.1247 9.32165H13.5655V7.05176C13.5655 6.0224 13.8544 5.32092 15.3467 5.32092L17.25 5.32009V2.14013C16.9208 2.0968 15.791 2 14.4765 2C11.7324 2 9.85365 3.65689 9.85365 6.69965V9.32165H6.75V12.877H9.85365V22H13.5655Z" fill="#555558" /> </svg> <span class="ms-2">Facebook</span> </a> </li> <li> <a href="http://twitter.com/intent/tweet?text=Super+Learner+-+Read+on+https%3A%2F%2Fwww.degruyter.com%2Fdocument%2Fdoi%2F10.2202%2F1544-6115.1309%2Fhtml+%40degruyter_brill" class="btn btn-default linkToShare twitterColor ga_share_this_twitter" target="_blank"> <svg width="24px" height="24px" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex"> <path d="M13.941 10.441 21.524 1.815H19.727L13.141 9.302 7.882 1.815H1.815L9.768 13.14 1.815 22.185H3.612L10.565 14.274 16.12 22.185H22.185L13.941 10.441ZM11.479 13.24 10.673 12.113 4.26 3.142H7.02L12.195 10.386 12.998 11.513 19.724 20.925H16.965L11.479 13.24Z" fill="#555558"/> </svg> <span class="ms-2">X / Twitter</span> </a> </li> <li> <a href="http://www.linkedin.com/shareArticle?url=https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html" class="btn btn-default linkToShare linkedinColor ga_share_this_Linkedin" target="_blank"> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex"> <path fill-rule="evenodd" clip-rule="evenodd" d="M3.47796 2C2.66169 2 2 2.64164 2 3.43268V20.5673C2 21.3586 2.66169 22 3.47796 22H20.522C21.3383 22 22 21.3586 22 20.5673V3.43268C22 2.64164 21.3383 2 20.522 2H3.47796ZM8.48683 6.90621C8.48683 7.76646 7.85538 8.45482 6.84087 8.45482L6.75734 8.45381C5.81786 8.42414 5.21429 7.74734 5.21429 6.90621C5.21429 6.0266 5.86495 5.35734 6.86012 5.35734C7.85538 5.35734 8.46792 6.0266 8.48683 6.90621ZM8.29551 9.67875V18.6431H5.38626V9.67875H8.29551ZM9.90536 18.6431H12.8145V13.637C12.8145 13.3691 12.8334 13.1014 12.9102 12.9099C13.1205 12.3746 13.5992 11.8202 14.4029 11.8202C15.4556 11.8202 15.8767 12.6423 15.8767 13.8474V18.6431H18.7857V13.503C18.7857 10.7496 17.3505 9.46839 15.4364 9.46839C13.8931 9.46839 13.2012 10.3371 12.8146 10.9479V9.67874H9.90536C9.94354 10.5199 9.90536 18.6431 9.90536 18.6431Z" fill="#555558"/> </svg> <span class="ms-2">LinkedIn</span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="modal" id="supplementaryModal" tabindex="-1" role="dialog" aria-label='Supplementary Materials' aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-l" role="document"> <div class="modal-content bg-white"> <div class="modal-body"> <button type="button" class="btn-close float-end btn-modal-close" data-bs-dismiss="modal" aria-label='Close'></button> <h3>Supplementary Materials</h3> <ul class="list-unstyled"> </ul> </div> </div> </div> </div> <div class="modal" id="loginToPurchase" tabindex="-1" role="dialog" aria-label='Please login or register with De Gruyter to order this product.' aria-hidden="true"> <div class="modal-dialog modal-dialog-centered modal-md" role="document"> <div class="modal-content bg-white"> <div class="modal-body"> <button type="button" class="btn-close float-end btn-modal-close" data-bs-dismiss="modal" aria-label='Close'></button> <div class="text-center"> <p>Please login or register with De Gruyter to order this product.</p> <a id="registerButtonSubmit" href="/register" class="btn btn-outline-primary">Register</a> <a id="loginButtonSubmit" href="/login" class="btn btn-primary">Log in</a> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="col-lg-3 bg-light"> <div class="sidebar py-5 px-4"> <div class="accessBroughtToYouBy" data-idtype="doi" data-id="10.2202/1544-6115.1309"><div class="reservedForAccessBroughtToYou"></div></div> <div id="currentPriceDiv"><current-price doi="10.2202/1544-6115.1309"><div class='reservedForCurrentPrice'></div></current-price></div> <div class="mb-3 subTitleGraySidebar">From the journal</div> <div class="d-flex pb-4"> <div class="d-inline-flex"> <a href="/journal/key/sagmb/html" title="Statistical Applications in Genetics and Molecular Biology"><img class="coverImage ga_cover_image_product" alt="Statistical Applications in Genetics and Molecular Biology" src="/document/cover/journal_key/SAGMB/thumbnail" srcset="/document/cover/journal_key/SAGMB/product 2x" width="100" height="auto" loading="lazy"/></a> </div> <div class="flex-wrap px-2"> <div class="parentJournal"> <a class="fw-bold standardLinkProduct ga_product ga_parent ga_parent_journal" href="/journal/key/sagmb/html">Statistical Applications in Genetics and Molecular Biology</a> </div> <div class="parentJournalIssue"> <a href="/journal/key/sagmb/6/1/html" class="standardLinkProduct ga_parent"> Volume 6 Issue 1 </a> </div> </div> </div> <div class="pb-4"> <a href="http://mc.manuscriptcentral.com/dgsagmb" class="btn btn-outline-primary fw-bold w-100 ga_submit">Submit manuscript</a> </div> <h2 class="subTitleProductPage"> Journal and Issue </h2> <div class="searchJournal"> <form class="pt-2 font-family-standard" action='/search/series/sagmb?query='> <div class="input-group"> <input class="form-control rounded-start placeholderSmallText font-size-14 py-1" type="text" name="query" aria-label='Search journal' placeholder='Search journal'> <div class="input-group-append"> <button class="btn btn-primary rounded-end analyticsButton" aria-label='Search journal' type="submit"> <span class="fa fas fa-search ga_parent_search_button"></span> </button> </div> </div> <div class="form-check ps-0 pt-3 d-flex font-size-14"> <div class="custom-control custom-radio me-3"> <input class="custom-control-input" autocomplete="off" type="radio" aria-label='This issue' name="volumeIssue" id="searchThisJournalIssue" value="6|1" checked="checked"> <label class="custom-control-label" for="searchThisJournalIssue"> This issue </label> </div> <div class="custom-control custom-radio me-3"> <input class="custom-control-input" autocomplete="off" type="radio" aria-label='All issues' name="volumeIssue" id="searchAllJournalIssues" value=""> <label class="custom-control-label" for="searchAllJournalIssues"> All issues </label> </div> </div> <label><input hidden="hidden" name="documentVisibility" value="all"></label> </form> </div> <div class="listTocItems"> <h2 class="subTitleProductPage">Articles in the same Issue</h2> <div class="mt-3 tocItems border-bottom"> <div class='item '> <div class="tocItemContent w-100"> <span class="tocSectionHeader fw-bold two-line-ellipsis linkRegularSidebar my-2">Article</span> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1212/html">Accounting for Dependence in Similarity Data from DNA Fingerprinting</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1228/html">Normalization of Dye Bias in Microarray Data Using the Mixture of Splines Model</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1247/html">A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1251/html">Using Duplicate Genotyped Data in Genetic Analyses: Testing Association and Estimating Error Rates</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1266/html">Likelihood-Based Inference for Multi-Color Optical Mapping</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1248/html">Sparse Logistic Regression with Lp Penalty for Biomarker Identification</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1240/html">Super Learning: An Application to the Prediction of HIV-1 Drug Resistance</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1260/html">Supervised Detection of Conserved Motifs in DNA Sequences with Cosmo</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1252/html">Accurate Ranking of Differentially Expressed Genes by a Distribution-Free Shrinkage Approach</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1253/html">Statistical Inference for Quantitative Polymerase Chain Reaction Using a Hidden Markov Model: A Bayesian Approach</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1152/html">A Bayesian Model of AFLP Marker Evolution and Phylogenetic Inference</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1264/html">Sequential Quantitative Trait Locus Mapping in Experimental Crosses</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1270/html">Case-Control Inference of Interaction between Genetic and Nongenetic Risk Factors under Assumptions on Their Distribution</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1285/html">Inference on the Limiting False Discovery Rate and the P-value Threshold Parameter Assuming Weak Dependence between Gene Expression Levels within Subject</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1282/html">Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1153/html">Cox Survival Analysis of Microarray Gene Expression Data Using Correlation Principal Component Regression</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1281/html">A Method for Meta-Analysis of Case-Control Genetic Association Studies Using Logistic Regression</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1296/html">Approximating the Variance of the Conditional Probability of the State of a Hidden Markov Model</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1249/html">Using Linear Mixed Models for Normalization of cDNA Microarrays</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1245/html">Experimental Design for Two-Color Microarrays Applied in a Pre-Existing Split-Plot Experiment</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1286/html">The Cyclohedron Test for Finding Periodic Genes in Time Course Expression Studies</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1272/html">H-Tuple Approach to Evaluate Statistical Significance of Biological Sequence Comparison with Gaps</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1295/html">Multiple Testing Issues in Discriminating Compound-Related Peaks and Chromatograms from High Frequency Noise, Spikes and Solvent-Based Noise in LC - MS Data Sets</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1299/html">A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <span class="fw-bold two-line-ellipsis linkRegularSidebar my-2">Super Learner</span> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1283/html">Testing for Trends in Dose-Response Microarray Experiments: A Comparison of Several Testing Procedures, Multiplicity and Resampling-Based Inference</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1302/html">On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1310/html">A Comparison of Methods to Control Type I Errors in Microarray Studies</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1312/html">Selection of Biologically Relevant Genes with a Wrapper Stochastic Algorithm</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1303/html">T-BAPS: A Bayesian Statistical Tool for Comparison of Microbial Communities Using Terminal-restriction Fragment Length Polymorphism (T-RFLP) Data</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1305/html">Population Structure and Covariate Analysis Based on Pairwise Microsatellite Allele Matching Frequencies</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1236/html">Estimating the Arm-Wise False Discovery Rate in Array Comparative Genomic Hybridization Experiments</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1321/html">An Expectation Maximization Approach to Estimate Malaria Haplotype Frequencies in Multiply Infected Children</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1244/html">Estimation of Expression Levels in Spotted Microarrays with Saturated Pixels</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1313/html">Improving Divergence Time Estimation in Phylogenetics: More Taxa vs. Longer Sequences</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1314/html">Fully Bayesian Mixture Model for Differential Gene Expression: Simulations and Model Checks</a> </div> </div> <div class='item border-top'> <div class="tocItemContent w-100"> <a class="ga_same_issue_article two-line-ellipsis linkRegularSidebar my-2 linkAnimation" href="/document/doi/10.2202/1544-6115.1315/html">Multiple Testing for SNP-SNP Interactions</a> </div> </div> </div> </div> </div> </div> </div> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/lib/pdfjs-dist/build/b48eed8da5b6208c90435ec6e9e1a295-pdf.min.js'></script> </main> <footer class="bg-dark" role="contentinfo"> <nav class="content-wrapper" aria-label="Static pages"> <div class="footerContainer"> <div class="row"> <div class="col-12 col-lg-6 pb-3"> <div class="border-bottom pb-3 mb-3"><a class="ga_footer text-white footerLevel1Font linkAnimation" href="/publishing/subjects">Subjects</a></div> <div class="row"> <div class="col-12 col-sm-4"> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=AD">Architecture and Design</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=AR">Arts</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=AS">Asian and Pacific Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=EC">Business and Economics</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=CH">Chemistry</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=CL">Classical and Ancient Near Eastern Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=CO">Computer Sciences</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=CS">Cultural Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=EN">Engineering</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=GL">General Interest</a></li> </ul> </div> <div class="col-12 col-sm-4"> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=GS">Geosciences</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=HI">History</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=IC">Industrial Chemistry</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=IS">Islamic and Middle Eastern Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=JS">Jewish Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=LA">Law</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=LB">Library and Information Science, Book Studies</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=LF">Life Sciences</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=LS">Linguistics and Semiotics</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=LT">Literary Studies</a></li> </ul> </div> <div class="col-12 col-sm-4"> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=MS">Materials Sciences</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=MT">Mathematics</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=MD">Medicine</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=MU">Music</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=PM">Pharmacy</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=PL">Philosophy</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=PY">Physics</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=SN">Social Sciences</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=SR">Sports and Recreation</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/search?query=*&subjectFacet=TL">Theology and Religion</a></li> </ul> </div> </div> </div> <div class="col-12 col-lg-6 pb-3"> <div class="row"> <div class="col-12 col-sm-4 pb-3"> <div class="border-bottom pb-3 mb-3"><a class="ga_footer text-white footerLevel1Font linkAnimation" href="/publishing/services">Services</a></div> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/for-authors/for-journal-authors">For Journal Authors</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/for-authors/for-book-authors">For Book Authors</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/services/for-librarians">For Librarians</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/services/rights-and-permissions">Rights & Permissions</a></li> </ul> </div> <div class="col-12 col-sm-4 pb-3"> <div class="border-bottom pb-3 mb-3"><a class="ga_footer text-white footerLevel1Font linkAnimation" href="/publishing/publications">Publications</a></div> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/publications/publicationtypes">Publication types</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/publications/openaccess">Open Access</a></li> </ul> </div> <div class="col-12 col-sm-4 pb-3"> <div class="border-bottom pb-3 mb-3"><a class="ga_footer text-white footerLevel1Font linkAnimation" href="/publishing/about-us">About</a></div> <ul class="list-unstyled"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/contact">Contact</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/careers">Career</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/about-dg">About De Gruyter</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/publisher-partners">Partnerships</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/press">Press</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/faqs">FAQs</a></li> </ul> </div> </div> <div class="row d-none d-sm-flex"> <div class="col-6"> <div class="border-bottom pb-3 mb-3 text-white footerLevel1Font">Social</div> <ul class="list-unstyled" style="columns: 2;"> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.facebook.com/degruyter.publishers" target="_blank" aria-label='Link to Facebook'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to Facebook'> <path fill-rule="evenodd" clip-rule="evenodd" d="M13.5655 22V12.877H16.6612L17.1247 9.32165H13.5655V7.05176C13.5655 6.0224 13.8544 5.32092 15.3467 5.32092L17.25 5.32009V2.14013C16.9208 2.0968 15.791 2 14.4765 2C11.7324 2 9.85365 3.65689 9.85365 6.69965V9.32165H6.75V12.877H9.85365V22H13.5655Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">Facebook</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.instagram.com/degruyter_brill/" target="_blank" aria-label='Link to Instagram'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to Instagram'> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.87709 2.05993C8.94354 2.01127 9.28421 1.99976 12 1.99976C14.7159 1.99976 15.0566 2.01127 16.1231 2.06013C17.1875 2.10852 17.9144 2.27755 18.5505 2.52458C19.2179 2.77573 19.8224 3.16945 20.3219 3.67826C20.8306 4.17776 21.2242 4.78223 21.4753 5.44949C21.7225 6.08558 21.8915 6.81249 21.9401 7.87694C21.9888 8.94341 22.0003 9.28412 22.0003 12C22.0003 14.7159 21.9888 15.0564 21.9401 16.1231C21.8915 17.1875 21.7225 17.9144 21.4753 18.5505C20.9558 19.8938 19.8939 20.9557 18.5506 21.4752C17.9146 21.7224 17.1877 21.8914 16.1232 21.94C15.0568 21.9887 14.7161 22.0002 12.0002 22.0002C9.28434 22.0002 8.94379 21.9887 7.87717 21.94C6.81277 21.8914 6.08587 21.7224 5.44974 21.4752C4.78248 21.2241 4.17803 20.8304 3.67853 20.3217C3.16982 19.8222 2.77619 19.2178 2.52509 18.5505C2.27787 17.9144 2.10884 17.1875 2.06025 16.1231C2.01139 15.0566 1.99988 14.7159 1.99988 12C1.99988 9.28408 2.01139 8.94341 2.06025 7.87694C2.10864 6.81249 2.27767 6.08558 2.52469 5.44945C2.77589 4.78216 3.16962 4.17769 3.67845 3.67822C4.17795 3.16951 4.78241 2.77588 5.44967 2.52477C6.08575 2.27755 6.81265 2.10852 7.87709 2.05993ZM6.99685 11.9968C6.99685 9.23536 9.23548 6.99673 11.997 6.99673C14.7584 6.99673 16.9971 9.23536 16.9971 11.9968C16.9971 14.7583 14.7584 16.9969 11.997 16.9969C9.23548 16.9969 6.99685 14.7583 6.99685 11.9968ZM12 15.2499C10.2051 15.2499 8.75 13.7948 8.75001 11.9999C8.75002 10.2049 10.2051 8.74988 12 8.74989C13.7949 8.7499 15.25 10.205 15.25 11.9999C15.25 13.7948 13.7949 15.2499 12 15.2499ZM17 6.99989C17.5523 6.99989 18 6.55217 18 5.99989C18 5.4476 17.5523 4.99989 17 4.99989C16.4477 4.99989 16 5.4476 16 5.99989C16 6.55217 16.4477 6.99989 17 6.99989Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">Instagram</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.linkedin.com/company/de-gruyter" target="_blank" aria-label='Link to Linkedin'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to LinkedIn'> <path fill-rule="evenodd" clip-rule="evenodd" d="M3.47796 2C2.66169 2 2 2.64164 2 3.43268V20.5673C2 21.3586 2.66169 22 3.47796 22H20.522C21.3383 22 22 21.3586 22 20.5673V3.43268C22 2.64164 21.3383 2 20.522 2H3.47796ZM8.48683 6.90621C8.48683 7.76646 7.85538 8.45482 6.84087 8.45482L6.75734 8.45381C5.81786 8.42414 5.21429 7.74734 5.21429 6.90621C5.21429 6.0266 5.86495 5.35734 6.86012 5.35734C7.85538 5.35734 8.46792 6.0266 8.48683 6.90621ZM8.29551 9.67875V18.6431H5.38626V9.67875H8.29551ZM9.90536 18.6431H12.8145V13.637C12.8145 13.3691 12.8334 13.1014 12.9102 12.9099C13.1205 12.3746 13.5992 11.8202 14.4029 11.8202C15.4556 11.8202 15.8767 12.6423 15.8767 13.8474V18.6431H18.7857V13.503C18.7857 10.7496 17.3505 9.46839 15.4364 9.46839C13.8931 9.46839 13.2012 10.3371 12.8146 10.9479V9.67874H9.90536C9.94354 10.5199 9.90536 18.6431 9.90536 18.6431Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">LinkedIn</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://twitter.com/degruyter_brill" target="_blank" aria-label='Link to Twitter'> <svg width="24px" height="24px" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" class="d-inline-flex" alt='Link to X / Twitter'> <path d="M13.941 10.441 21.524 1.815H19.727L13.141 9.302 7.882 1.815H1.815L9.768 13.14 1.815 22.185H3.612L10.565 14.274 16.12 22.185H22.185L13.941 10.441ZM11.479 13.24 10.673 12.113 4.26 3.142H7.02L12.195 10.386 12.998 11.513 19.724 20.925H16.965L11.479 13.24Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">X / Twitter</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.youtube.com/c/DegruyterPublishers" target="_blank" aria-label='Link to Youtube'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to YouTube'> <path fill-rule="evenodd" clip-rule="evenodd" d="M19.7885 5.42336C20.6513 5.65671 21.3252 6.33037 21.5586 7.19274C22.2192 9.85067 22.0666 14.0485 21.5715 16.809C21.338 17.6713 20.6641 18.345 19.8014 18.5784C18.2493 19.0015 12.0027 19.0015 12.0027 19.0015C12.0027 19.0015 5.75609 19.0015 4.20405 18.5784C3.34133 18.345 2.66741 17.6713 2.43396 16.809C1.76954 14.1626 1.95168 9.96222 2.42113 7.20557C2.65458 6.34319 3.3285 5.66954 4.19123 5.43618C5.74326 5.01307 11.9899 5.00024 11.9899 5.00024C11.9899 5.00024 18.2365 5.00024 19.7885 5.42336ZM15.5714 12.0009L9.85714 15.1512V8.85068L15.5714 12.0009Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">YouTube</span> </a> </li> </ul> </div> <div class="col-6"> <div><img src='/assets/images/0f0f306f30d5f2d2f68caab6976dc637-dg-logo-footer.svg' height="100%" width="auto" alt="De Gruyter" /></div> <div class="my-4"> <a class="d-flex" target="_blank" href="https://blog.degruyter.com/de-gruyter-wins-the-best-publisher-ux-award/" style="text-decoration: none;"> <img class="oa_award" src='/assets/images/80cca219a7e93410593d2bf03850db70-Open-Athens-Logo_Icon-White.svg' height="100%" width="100%" alt="Open-Athens" /> <span class="footerCopyright text-start ms-3"> <span class="linkAnimation lh-base"><b>Winner</b> of the OpenAthens<br>Best Publisher UX Award 2022</span> </span> </a> </div> </div> </div> <div class="row d-sm-none"> <div class="col-12"> <div class="border-bottom mb-5"></div> <ul class="list-unstyled d-flex justify-content-center mb-4"> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.facebook.com/degruyter.publishers" target="_blank" aria-label='Link to Facebook'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to Facebook'> <path fill-rule="evenodd" clip-rule="evenodd" d="M13.5655 22V12.877H16.6612L17.1247 9.32165H13.5655V7.05176C13.5655 6.0224 13.8544 5.32092 15.3467 5.32092L17.25 5.32009V2.14013C16.9208 2.0968 15.791 2 14.4765 2C11.7324 2 9.85365 3.65689 9.85365 6.69965V9.32165H6.75V12.877H9.85365V22H13.5655Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">Facebook</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.instagram.com/degruyter_brill/" target="_blank" aria-label='Link to Instagram'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to Instagram'> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.87709 2.05993C8.94354 2.01127 9.28421 1.99976 12 1.99976C14.7159 1.99976 15.0566 2.01127 16.1231 2.06013C17.1875 2.10852 17.9144 2.27755 18.5505 2.52458C19.2179 2.77573 19.8224 3.16945 20.3219 3.67826C20.8306 4.17776 21.2242 4.78223 21.4753 5.44949C21.7225 6.08558 21.8915 6.81249 21.9401 7.87694C21.9888 8.94341 22.0003 9.28412 22.0003 12C22.0003 14.7159 21.9888 15.0564 21.9401 16.1231C21.8915 17.1875 21.7225 17.9144 21.4753 18.5505C20.9558 19.8938 19.8939 20.9557 18.5506 21.4752C17.9146 21.7224 17.1877 21.8914 16.1232 21.94C15.0568 21.9887 14.7161 22.0002 12.0002 22.0002C9.28434 22.0002 8.94379 21.9887 7.87717 21.94C6.81277 21.8914 6.08587 21.7224 5.44974 21.4752C4.78248 21.2241 4.17803 20.8304 3.67853 20.3217C3.16982 19.8222 2.77619 19.2178 2.52509 18.5505C2.27787 17.9144 2.10884 17.1875 2.06025 16.1231C2.01139 15.0566 1.99988 14.7159 1.99988 12C1.99988 9.28408 2.01139 8.94341 2.06025 7.87694C2.10864 6.81249 2.27767 6.08558 2.52469 5.44945C2.77589 4.78216 3.16962 4.17769 3.67845 3.67822C4.17795 3.16951 4.78241 2.77588 5.44967 2.52477C6.08575 2.27755 6.81265 2.10852 7.87709 2.05993ZM6.99685 11.9968C6.99685 9.23536 9.23548 6.99673 11.997 6.99673C14.7584 6.99673 16.9971 9.23536 16.9971 11.9968C16.9971 14.7583 14.7584 16.9969 11.997 16.9969C9.23548 16.9969 6.99685 14.7583 6.99685 11.9968ZM12 15.2499C10.2051 15.2499 8.75 13.7948 8.75001 11.9999C8.75002 10.2049 10.2051 8.74988 12 8.74989C13.7949 8.7499 15.25 10.205 15.25 11.9999C15.25 13.7948 13.7949 15.2499 12 15.2499ZM17 6.99989C17.5523 6.99989 18 6.55217 18 5.99989C18 5.4476 17.5523 4.99989 17 4.99989C16.4477 4.99989 16 5.4476 16 5.99989C16 6.55217 16.4477 6.99989 17 6.99989Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">Instagram</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.linkedin.com/company/de-gruyter" target="_blank" aria-label='Link to Linkedin'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to LinkedIn'> <path fill-rule="evenodd" clip-rule="evenodd" d="M3.47796 2C2.66169 2 2 2.64164 2 3.43268V20.5673C2 21.3586 2.66169 22 3.47796 22H20.522C21.3383 22 22 21.3586 22 20.5673V3.43268C22 2.64164 21.3383 2 20.522 2H3.47796ZM8.48683 6.90621C8.48683 7.76646 7.85538 8.45482 6.84087 8.45482L6.75734 8.45381C5.81786 8.42414 5.21429 7.74734 5.21429 6.90621C5.21429 6.0266 5.86495 5.35734 6.86012 5.35734C7.85538 5.35734 8.46792 6.0266 8.48683 6.90621ZM8.29551 9.67875V18.6431H5.38626V9.67875H8.29551ZM9.90536 18.6431H12.8145V13.637C12.8145 13.3691 12.8334 13.1014 12.9102 12.9099C13.1205 12.3746 13.5992 11.8202 14.4029 11.8202C15.4556 11.8202 15.8767 12.6423 15.8767 13.8474V18.6431H18.7857V13.503C18.7857 10.7496 17.3505 9.46839 15.4364 9.46839C13.8931 9.46839 13.2012 10.3371 12.8146 10.9479V9.67874H9.90536C9.94354 10.5199 9.90536 18.6431 9.90536 18.6431Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">LinkedIn</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://twitter.com/degruyter_brill" target="_blank" aria-label='Link to Twitter'> <svg width="24px" height="24px" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" class="d-inline-flex" alt='Link to X / Twitter'> <path d="M13.941 10.441 21.524 1.815H19.727L13.141 9.302 7.882 1.815H1.815L9.768 13.14 1.815 22.185H3.612L10.565 14.274 16.12 22.185H22.185L13.941 10.441ZM11.479 13.24 10.673 12.113 4.26 3.142H7.02L12.195 10.386 12.998 11.513 19.724 20.925H16.965L11.479 13.24Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">X / Twitter</span> </a> </li> <li> <a class="ga_footer iconLinkAnimation text-nowrap" href="https://www.youtube.com/c/DegruyterPublishers" target="_blank" aria-label='Link to Youtube'> <svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="d-inline-flex" aria-hidden="true" alt='Link to YouTube'> <path fill-rule="evenodd" clip-rule="evenodd" d="M19.7885 5.42336C20.6513 5.65671 21.3252 6.33037 21.5586 7.19274C22.2192 9.85067 22.0666 14.0485 21.5715 16.809C21.338 17.6713 20.6641 18.345 19.8014 18.5784C18.2493 19.0015 12.0027 19.0015 12.0027 19.0015C12.0027 19.0015 5.75609 19.0015 4.20405 18.5784C3.34133 18.345 2.66741 17.6713 2.43396 16.809C1.76954 14.1626 1.95168 9.96222 2.42113 7.20557C2.65458 6.34319 3.3285 5.66954 4.19123 5.43618C5.74326 5.01307 11.9899 5.00024 11.9899 5.00024C11.9899 5.00024 18.2365 5.00024 19.7885 5.42336ZM15.5714 12.0009L9.85714 15.1512V8.85068L15.5714 12.0009Z" fill="#555558"/> </svg> <span class="text-white footerLevel2Font ms-2 linkAnimation d-none d-sm-inline-flex">YouTube</span> </a> </li> </ul> <div class="mx-5 mb-2"> <a class="d-flex justify-content-center" target="_blank" href="https://www.openathens.net/news/winner-best-publisher-ux-award-2022/" style="text-decoration: none;"> <img class="oa_award" src='/assets/images/80cca219a7e93410593d2bf03850db70-Open-Athens-Logo_Icon-White.svg' height="100%" width="100%" alt="Open-Athens" /> <span class="footerCopyright text-start ms-3"> <span class="linkAnimation lh-base"><b>Winner</b> of the OpenAthens<br>Best Publisher UX Award 2022</span> </span> </a> </div> </div> </div> </div> <div class="col-12"> <div class="border-bottom mb-4"></div> </div> </div> <div class="row"> <div class="col-12 col-lg-8"> <ul class="list-unstyled d-flex flex-wrap justify-content-around justify-content-lg-start paddLiRight"> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/about-us/new-website-faqs">Help/FAQ</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/our-privacy-policy">Privacy policy</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/our-cookie-policy">Cookie Policy</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/accessibility">Accessibility</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/terms-conditions">Terms & Conditions</a></li> <li><a class="ga_footer text-white footerLevel2Font linkAnimation" href="/publishing/imprints">Legal Notice</a></li> </ul> </div> <div class="col-12 col-lg-4 d-flex justify-content-center justify-content-lg-end"> <div class="footerCopyright pt-1">© Walter de Gruyter GmbH 2024</div> </div> <div class="col-12 text-center d-sm-none"> <div class="mt-5"><img src='/assets/images/dcb5aecb586bd5336d1428d326e8dccf-dg-logo-footer-mobile.svg' height="100%" width="auto" alt="De Gruyter" /></div> </div> </div> </div> </nav> </footer> <div class="printFooter"> <span>Downloaded on 27.11.2024 from https://www.degruyter.com/document/doi/10.2202/1544-6115.1309/html</span> </div>  <a class="scroll-up-button d-sm-none" id="scrollUpButton" href="#mainHeader"> <img alt='Scroll to top button' src='/assets/images/2a1093d067525528af2f87c7296d39e1-scroll-arrow.svg'> </a> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/02f217ac44f30e20572ec9be327266f9-clipboard-polyfill.js' defer="defer" crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/f4a7cebacca43a770afd837b68a7eed8-autoComplete.min.js' defer="defer" crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/f62fc03e44df2f5efad9611016f07366-custom-elements.min.js' defer="defer" crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/7ccd9d390d31af98110f74f842ea9b32-bootstrap.js' type="module" crossorigin="use-credentials"></script> <div id="lang-code" data-code="en"></div> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/99bb3afb087e75c3dca1083e14a397a0-cookie-control.js' type="module" defer="defer" crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/6acc668691121f867b851f59f7c39e66-main-immediate.js' crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='/assets/javascripts/29ddfbae4f53ec4977b4a9bcc806c99b-main.js' type="module" crossorigin="use-credentials"></script> <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='https://www.googletagmanager.com/gtm.js?id=GTM-PMNKTQ5&gtm_auth=JraP3pn8iVUkqNIGYl03AA&gtm_preview=env-2' defer="defer" async="async"></script>  <script nonce="C+LUmrHTMReisY5AgKmEcg==" src='https://connect.liblynx.com/log/js/counter5.js' async="async" defer="defer"></script>  <script nonce="C+LUmrHTMReisY5AgKmEcg==" src="https://badge.dimensions.ai/badge.js" async="async" defer="defer" charset="utf-8"></script>  <script nonce="C+LUmrHTMReisY5AgKmEcg==" src="https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js" async="async" defer="defer" charset="utf-8"></script> </body> </html>

CINXE.COM

Super Learner