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Beschikbaar in 39 talen" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">39 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%D9%8A%D9%84_%D8%B9%D8%A7%D9%85%D9%84%D9%8A" title="تحليل عاملي – Arabisch" lang="ar" hreflang="ar" data-title="تحليل عاملي" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Faktor_analizi" title="Faktor analizi – Azerbeidzjaans" lang="az" hreflang="az" data-title="Faktor analizi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%B0%D1%80%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Фактарны аналіз – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Фактарны аналіз" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B5%D0%BD_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Факторен анализ – Bulgaars" lang="bg" hreflang="bg" data-title="Факторен анализ" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Faktorov%C3%A1_anal%C3%BDza" title="Faktorová analýza – Tsjechisch" lang="cs" hreflang="cs" data-title="Faktorová analýza" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Faktoranalyse" title="Faktoranalyse – Deens" lang="da" hreflang="da" data-title="Faktoranalyse" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Faktorenanalyse" title="Faktorenanalyse – Duits" lang="de" hreflang="de" data-title="Faktorenanalyse" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Factor_analysis" title="Factor analysis – Engels" lang="en" hreflang="en" data-title="Factor analysis" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/An%C3%A1lisis_factorial" title="Análisis factorial – Spaans" lang="es" hreflang="es" data-title="Análisis factorial" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Faktoranal%C3%BC%C3%BCs" title="Faktoranalüüs – Estisch" lang="et" hreflang="et" data-title="Faktoranalüüs" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Faktore-analisi" title="Faktore-analisi – Baskisch" lang="eu" hreflang="eu" data-title="Faktore-analisi" data-language-autonym="Euskara" data-language-local-name="Baskisch" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D8%B9%D8%A7%D9%85%D9%84%DB%8C" title="تحلیل عاملی – Perzisch" lang="fa" hreflang="fa" data-title="تحلیل عاملی" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Faktorianalyysi" title="Faktorianalyysi – Fins" lang="fi" hreflang="fi" data-title="Faktorianalyysi" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Analyse_factorielle" title="Analyse factorielle – Frans" lang="fr" hreflang="fr" data-title="Analyse factorielle" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Anail%C3%ADs_facht%C3%B3ir%C3%AD" title="Anailís fachtóirí – Iers" lang="ga" hreflang="ga" data-title="Anailís fachtóirí" data-language-autonym="Gaeilge" data-language-local-name="Iers" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%99%D7%AA%D7%95%D7%97_%D7%92%D7%95%D7%A8%D7%9E%D7%99%D7%9D" title="ניתוח גורמים – Hebreeuws" lang="he" hreflang="he" data-title="ניתוח גורמים" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A4%BE%E0%A4%B0%E0%A4%95_%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A5%8D%E0%A4%B2%E0%A5%87%E0%A4%B7%E0%A4%A3" title="कारक विश्लेषण – Hindi" lang="hi" hreflang="hi" data-title="कारक विश्लेषण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Faktoranal%C3%ADzis" title="Faktoranalízis – Hongaars" lang="hu" hreflang="hu" data-title="Faktoranalízis" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Analisis_faktor" title="Analisis faktor – Indonesisch" lang="id" hreflang="id" data-title="Analisis faktor" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Analisi_fattoriale" title="Analisi fattoriale – Italiaans" lang="it" hreflang="it" data-title="Analisi fattoriale" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%9B%A0%E5%AD%90%E5%88%86%E6%9E%90" title="因子分析 – Japans" lang="ja" hreflang="ja" data-title="因子分析" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%BB%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Факторлар теориясы – Kazachs" lang="kk" hreflang="kk" data-title="Факторлар теориясы" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B8%EC%9E%90_%EB%B6%84%EC%84%9D" title="인자 분석 – Koreaans" lang="ko" hreflang="ko" data-title="인자 분석" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Faktoru_anal%C4%ABze" title="Faktoru analīze – Lets" lang="lv" hreflang="lv" data-title="Faktoru analīze" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D2%AF%D1%87%D0%B8%D0%BD_%D0%B7%D2%AF%D0%B9%D0%BB%D0%B8%D0%B9%D0%BD_%D1%88%D0%B8%D0%BD%D0%B6%D0%B8%D0%BB%D0%B3%D1%8D%D1%8D" title="Хүчин зүйлийн шинжилгээ – Mongools" lang="mn" hreflang="mn" data-title="Хүчин зүйлийн шинжилгээ" data-language-autonym="Монгол" data-language-local-name="Mongools" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Analisis_faktor" title="Analisis faktor – Maleis" lang="ms" hreflang="ms" data-title="Analisis faktor" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Faktoranalyse" title="Faktoranalyse – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Faktoranalyse" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Analiza_czynnikowa" title="Analiza czynnikowa – Pools" lang="pl" hreflang="pl" data-title="Analiza czynnikowa" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/An%C3%A1lise_fatorial" title="Análise fatorial – Portugees" lang="pt" hreflang="pt" data-title="Análise fatorial" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Факторный анализ – Russisch" lang="ru" hreflang="ru" data-title="Факторный анализ" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Factor_analysis" title="Factor analysis – Simple English" lang="en-simple" hreflang="en-simple" data-title="Factor analysis" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D1%81%D0%BA%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0" title="Факторска анализа – Servisch" lang="sr" hreflang="sr" data-title="Факторска анализа" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Analisis_faktor" title="Analisis faktor – Soendanees" lang="su" hreflang="su" data-title="Analisis faktor" data-language-autonym="Sunda" data-language-local-name="Soendanees" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Faktoranalys" title="Faktoranalys – Zweeds" lang="sv" hreflang="sv" data-title="Faktoranalys" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Analisis_ng_paktor" title="Analisis ng paktor – Tagalog" lang="tl" hreflang="tl" data-title="Analisis ng paktor" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Факторний аналіз – Oekraïens" lang="uk" hreflang="uk" data-title="Факторний аналіз" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_t%C3%ADch_nh%C3%A2n_t%E1%BB%91" title="Phân tích nhân tố – Vietnamees" lang="vi" hreflang="vi" data-title="Phân tích nhân tố" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="因素分析 – Chinees" lang="zh" hreflang="zh" data-title="因素分析" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="因素分析 – Kantonees" lang="yue" hreflang="yue" data-title="因素分析" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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lang="nl" dir="ltr"><p><b>Factoranalyse</b> is een multivariate <a href="/wiki/Statistiek" title="Statistiek">statistische</a> techniek die voor een groot aantal geobserveerde variabelen een kleiner aantal achterliggende variabelen identificeert. Deze niet geobserveerde, achterliggende variabelen worden factoren genoemd. Belangrijk is dat de factoren bijna evenveel van de variatie verklaren als de geobserveerde variabelen. Factoranalyse wordt gebruikt voor <a href="/wiki/Datareductie" title="Datareductie">datareductie</a> en om inzicht te krijgen in de structuur van de <a href="/wiki/Dataset" title="Dataset">dataset</a>. </p><p>Een goede factoroplossing bepaalt een relatief klein aantal factoren die samen een groot deel van de <a href="/wiki/Variantie" title="Variantie">variantie</a> die in de oorspronkelijke variabelen aanwezig is, verklaren. <a href="/wiki/Matrix_(wiskunde)" title="Matrix (wiskunde)">Matrixalgebra</a> is een essentieel onderdeel van factoranalyse. De factoroplossing wordt verkregen door manipulatie van de <a href="/wiki/Correlatiematrix" title="Correlatiematrix">correlatiematrix</a>. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:NYW-Scatter01.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/NYW-Scatter01.jpg/350px-NYW-Scatter01.jpg" decoding="async" width="350" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/6d/NYW-Scatter01.jpg 1.5x" data-file-width="486" data-file-height="321" /></a><figcaption>Voorbeeld met 2 variabelen en 1 factor, ieder punt stelt de scores op A en B van één proefpersoon voor.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Voorbeeld">Voorbeeld</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Factoranalyse&veaction=edit&section=1" title="Bewerk dit kopje: Voorbeeld" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Factoranalyse&action=edit&section=1" title="De broncode bewerken van de sectie: Voorbeeld"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een zeer vereenvoudigd voorbeeld verduidelijkt een en ander. </p><p>Stel dat een groep proefpersonen van een vragenlijst twee vragen, A en B, beantwoordt. Uit analyse blijkt dat er een verband is tussen A en B. Dan kan dit komen door de invloed van A op B, door de invloed van B op A, of doordat er nog een andere onbekende variabele C in het spel is. Met factoranalyse kan de onbekende <a href="/wiki/Variabele" title="Variabele">variabele</a> C opgespoord worden. </p><p>Duidelijk is te zien dat de beide variabelen A en B <a href="/wiki/Correlatie" title="Correlatie">gecorreleerd</a> zijn. De lijn die goed bij de <a href="/wiki/Puntenwolk" title="Puntenwolk">puntenwolk</a> past geeft deze samenhang tussen A en B weer. De grootste variatie vindt plaats langs de lijn, de kleinste loodrecht daarop. De lijn stelt een nieuwe variabele, in dit geval factor genaamd, voor, die de plaats van A en B kan innemen. Een lage score op die variabele komt overeen met een lage score op zowel A als B en een hoge score met een hoge score op A en B. Het doel van factoranalyse is in dit geval het bepalen van deze lijn en daarmee de onbekende factor. </p><p>Als voorbeeld nemen we een proef waarbij van een aantal personen de lengte van de armen en de lengte van de benen worden gemeten. Deze blijken goed gecorreleerd te zijn. De onbekende factor zou hier de grootte van de persoon kunnen zijn. </p> <div class="mw-heading mw-heading2"><h2 id="Doel">Doel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Factoranalyse&veaction=edit&section=2" title="Bewerk dit kopje: Doel" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Factoranalyse&action=edit&section=2" title="De broncode bewerken van de sectie: Doel"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het vinden van een of meer achterliggende (mogelijk hypothetische) variabelen is het doel van factoranalyse. In theorie kan het aantal factoren uiteenlopen van een tot het aantal oorspronkelijke variabelen. Als <a href="/wiki/Vuistregel" title="Vuistregel">vuistregel</a> geldt vaak dat een derde tot een vijfde van het aantal oorspronkelijke variabelen een nuttige factoroplossing kan betekenen. </p><p>Bij het uitvoeren van een factoranalyse wordt op elk moment in het proces veel eigen interpretatie van de uitvoerder gevraagd. Twee verschillende personen kunnen daardoor met exact dezelfde dataset tot andere conclusies komen. Waar de ene persoon drie factoren meent te onderscheiden, kan een ander van mening zijn dat het in werkelijkheid om vijf factoren gaat. Om deze reden heeft factoranalyse in een aantal wetenschappelijke disciplines aan belang ingeboet. </p><p>Factoranalyse lijkt erg op <a href="/wiki/Hoofdcomponenten" class="mw-redirect" title="Hoofdcomponenten">hoofdcomponentenanalyse</a>. Wat in factoranalyse <i>factoren</i> genoemd wordt, wordt in hoofdcomponentenanalyse <i>componenten</i> genoemd. Het verschil tussen beide analysetechnieken is dat bij factoranalyse alleen naar de gemeenschappelijke variantie in de oorspronkelijke variabelen wordt gekeken, terwijl hoofdcomponentenanalyse ook naar de unieke variantie kijkt. In de meeste gevallen zijn de verschillen tussen beide methoden niet erg groot. Mochten er wel verschillen zijn, dan komt dit dus door de unieke variantie binnen (sommige van) de geobserveerde variabelen. Een derde analysetechniek die zoekt naar achterliggende variabelen is de <a href="/wiki/Correspondentieanalyse" title="Correspondentieanalyse">correspondentieanalyse</a>, waarbij niet a priori wordt uitgegaan van lineaire verbanden. </p> <ul><li>Communaliteiten: de communaliteit van een geobserveerde variabele geeft het deel van de variantie weer dat door de factor voorspeld wordt. Omdat een communaliteit een proportie van de totale variantie is, kan deze in theorie slechts waarden tussen de 0 en 1 aannemen. Als vuistregel wordt doorgaans gehanteerd dat een variabele pas goed op een factor laadt als deze een communaliteit heeft van meer dan 0,45. In situaties waarin te weinig data aanwezig is, de startwaarden verkeerd gekozen zijn, of het aantal geëxtraheerde factoren verkeerd is, kunnen in de praktijk variabelen met een communaliteiten die groter dan 1 is voorkomen. In een dergelijke situatie spreekt men van een Heywoodgeval. De gekozen factoroplossing moet in dat geval geïnterpreteerd worden als een problematische oplossing.</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:3_factor_screeplot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/3_factor_screeplot.png/350px-3_factor_screeplot.png" decoding="async" width="350" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/3_factor_screeplot.png/525px-3_factor_screeplot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/c/ce/3_factor_screeplot.png 2x" data-file-width="694" data-file-height="459" /></a><figcaption><a href="/wiki/Screeplot" title="Screeplot">Screeplot</a> van 18 variabelen, waarbij 3 factoren een eigenwaarde hebben groter dan 1 (in de afbeelding boven de blauwe lijn). <br />Op basis van de screeplot kan ook de 'elleboog' van de grafiek bepaald worden. In dit voorbeeld ligt die bij een 2-factor oplossing; de grafiek daalt vanaf dit punt veel minder scherp</figcaption></figure> <ul><li>Aantal factoren: het aantal factoren kan onder meer op basis van de <a href="/wiki/Eigenwaarde_(wiskunde)" title="Eigenwaarde (wiskunde)">eigenwaarden</a> van de factoren bepaald worden. De eigenwaarde geeft hierbij aan hoeveel additionele variantie door de extra factor wordt verklaard. Omdat het hier gestandaardiseerde variabelen betreft, voegt elke extra factor een variantie van 1 toe. Factoren met een eigenwaarde van minder dan 1 verklaren dus minder variantie dan ze zelf toevoegen. Deze <a href="/wiki/Vuistregel" title="Vuistregel">vuistregel</a> wordt ook wel het Kaiser-criterium genoemd of ook wel het Guttman-criterium. Nadeel van de vuistregel is de aanwezige kans op overschatting van het aantal factoren. Een alternatieve beslissingsregel voor het aantal factoren kan op basis van een <a href="/wiki/Screeplot" title="Screeplot">screeplot</a> verkregen worden (zie figuur). Hierbij wordt op basis van de grafiek gekeken waar de zogenaamde 'elleboog' van de eigenwaarden zich voordoet. Dit is het punt waarop de <a href="/wiki/Richtingsco%C3%ABffici%C3%ABnt" title="Richtingscoëfficiënt">richtingscoëfficiënt</a> van de lijn door de eigenwaarden een knik vertoont.</li> <li>Factorladingen zijn de <a href="/wiki/Correlatieco%C3%ABffici%C3%ABnt" title="Correlatiecoëfficiënt">correlatiecoëfficiënten</a> tussen de gemeten variabelen en de verklarende factoren.</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:Factor_rotatie.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Factor_rotatie.jpg/350px-Factor_rotatie.jpg" decoding="async" width="350" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Factor_rotatie.jpg/525px-Factor_rotatie.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Factor_rotatie.jpg/700px-Factor_rotatie.jpg 2x" data-file-width="833" data-file-height="409" /></a><figcaption>Links een factoroplossing die hoog laadt op beide factoren; Rechts de (oblique) geroteerde factoren, waarbij duidelijk wordt dat er twee factoren zijn</figcaption></figure> <ul><li>Rotatie: Nadat factoren uit de correlatiematrix zijn geëxtraheerd is het mogelijk om de factoren te draaien met als doel de interpretatie van de factoren te vergemakkelijken. Factorrotatie verandert niets aan de oplossing, maar wijst combinaties van de oorspronkelijke factoren als nieuwe factoren aan. Vooral wanneer de factoren niet grafisch, maar in tabelvorm geïnterpreteerd worden, werkt rotatie vaak verhelderend. Draaiing van de matrix kan zo gedaan worden dat de correlatie tussen variabelen die in de oorspronkelijke matrix van factorladingen laag was, nog lager wordt, en correlatie tussen factorladingen die hoog waren, nog hoger wordt. Er zijn veel methoden om een factorrotatie uit te voeren, onderverdeeld in <a href="/wiki/Orthogonaal" title="Orthogonaal">orthogonale</a> en <a href="/w/index.php?title=Oblique&action=edit&redlink=1" class="new" title="Oblique (de pagina bestaat niet)">oblique</a> rotaties; bij het eerste type worden de verschillende factoren strikt onafhankelijk van elkaar verondersteld, bij oblique methoden kunnen de factoren gecorreleerd zijn. Een aantal specifieke rotatiemethoden is opgenomen in de populaire statistische softwarepakketten zoals SPSS en SAS. Voorbeelden van rotatiemethoden zijn Varimax, Direct Oblimin, Quartimax, Equamax en Promax.</li> <li>Factorscores: De hypothetische scores van individuen op de gevonden factoren. Deze worden uitgedrukt als <a href="/wiki/Z-scores" class="mw-redirect" title="Z-scores">Z-scores</a>, dat wil zeggen met een <a href="/wiki/Standaarddeviatie" class="mw-redirect" title="Standaarddeviatie">standaarddeviatie</a> van 1 en een <a href="/wiki/Verwachting_(wiskunde)" title="Verwachting (wiskunde)">verwachting</a> 0.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Model">Model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Factoranalyse&veaction=edit&section=3" title="Bewerk dit kopje: Model" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Factoranalyse&action=edit&section=3" title="De broncode bewerken van de sectie: Model"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het factoranalysemodel stelt dat de waargenomen variabelen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>, op een onverklaarbaar deel, de uniciteit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span>, na, uitgedrukt kunnen worden als lineaire combinaties <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> van een geringer aantal variabelen, de factoren <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X=\mu +LF+U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <mi>μ</mi> <mo>+</mo> <mi>L</mi> <mi>F</mi> <mo>+</mo> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=\mu +LF+U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98b2652bff17c0489181535552e5301f2e0a4acc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.267ex; height:2.676ex;" alt="{\displaystyle X=\mu +LF+U}"></span></dd></dl> <p>Daarin is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> de vector van de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> variabelen, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> de vector met verwachtingswaarden van de variabelen, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> de vector met de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k\ (k\leq p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>k</mi> <mo>≤</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\ (k\leq p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc1088e014fcfcf9cd66b60396df8f4be576d50d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.08ex; height:2.843ex;" alt="{\displaystyle k\ (k\leq p)}"></span> factoren, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> de matrix met coëfficiënten, factorladingen genoemd, en <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> de vector van uniciteiten. De factoren worden verondersteld gestandaardiseerd te zijn en onderling ongecorreleerd. De uniciteiten worden verondersteld verwachting 0 te hebben en ongecorreleerd te zijn met de factoren. </p><p>Voor de covariantiematrix <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e1f558f53cda207614abdf90162266c70bc5c1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Sigma }"></span> van de variabelen volgt dan: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Sigma =\operatorname {E} (X-\mu )(X-\mu )'=\operatorname {E} (LF+U)(LF+U)'=LL'+W,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Σ</mi> <mo>=</mo> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>−</mo> <mi>μ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>−</mo> <mi>μ</mi> <msup> <mo stretchy="false">)</mo> <mo>′</mo> </msup> <mo>=</mo> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>L</mi> <mi>F</mi> <mo>+</mo> <mi>U</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>L</mi> <mi>F</mi> <mo>+</mo> <mi>U</mi> <msup> <mo stretchy="false">)</mo> <mo>′</mo> </msup> <mo>=</mo> <mi>L</mi> <msup> <mi>L</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>W</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma =\operatorname {E} (X-\mu )(X-\mu )'=\operatorname {E} (LF+U)(LF+U)'=LL'+W,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04d06f26e5ceca5776f99d325f5cfcc26abbc7da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:60.856ex; height:3.009ex;" alt="{\displaystyle \Sigma =\operatorname {E} (X-\mu )(X-\mu )'=\operatorname {E} (LF+U)(LF+U)'=LL'+W,}"></span></dd></dl> <p>waarin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> de covariantiematrix van de uniciteiten is. </p><p>Het is de opgave van factoranalyse de dimensie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> en de factorladingen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> zo te bepalen dat de bijdrage aan de variantie door de uniciteiten klein blijft. Het deel van de variantie van een variabele <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> dat voor rekening van de factoren komt, heet <i>communaliteit</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d535f210cbd9b9fe6689e61427b3e213e5b2d547" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.139ex; height:2.509ex;" alt="{\displaystyle h_{i}}"></span>; het wordt gevormd door de som van de kwadraten van de betrokken factorladingen: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{i}=\sum _{j}L_{ij}^{2}=(LL')_{ii}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>L</mi> <msup> <mi>L</mi> <mo>′</mo> </msup> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{i}=\sum _{j}L_{ij}^{2}=(LL')_{ii}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/762c32cf4bb147ccc6dcff85c1cb0da6ae7cedac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:22.164ex; height:5.843ex;" alt="{\displaystyle h_{i}=\sum _{j}L_{ij}^{2}=(LL')_{ii}}"></span></dd></dl> <p>Een gebruikelijke analyse is de <a href="/wiki/Hoofdcomponenten" class="mw-redirect" title="Hoofdcomponenten">hoofdcomponenten</a> van <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle LL'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <msup> <mi>L</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LL'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cb621db404ed19e992ebebf55308b3ee3457da8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.85ex; height:2.509ex;" alt="{\displaystyle LL'}"></span> te bepalen, en daarvan de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> belangrijkste als factoren te benoemen. </p> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);text-align:center;font-size:87%}.mw-parser-output .navigatie-bewerken{margin-left:0.5em}.mw-parser-output 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/24px-OOjs_UI_icon_edit-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/32px-OOjs_UI_icon_edit-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></div></div> <div id="Ordinatie,_multidimensional_scaling" class="navigatie-titel"><a href="/wiki/Ordinatie" title="Ordinatie">Ordinatie, multidimensional scaling</a></div> <div class="navigatie-inhoud"> <style data-mw-deduplicate="TemplateStyles:r67785531">.mw-parser-output .navigatie-tabel{margin:0 auto 0 auto;text-align:left}.mw-parser-output .navigatie-tabel .links{text-align:right}.mw-parser-output .navigatie-tabel .rechts{padding-left:0.5em}@media screen and (max-width:640px){.mw-parser-output .navigatie-tabel tr{display:grid;grid-template-columns:1fr;width:100%;margin-bottom:0.5em}.mw-parser-output .navigatie-tabel tr:last-of-type{margin-bottom:0}.mw-parser-output .navigatie-tabel .links{text-align:unset}.mw-parser-output .navigatie-tabel .rechts{padding:unset}}</style><table class="navigatie-tabel vatop" cellpadding="0" cellspacing="0" style=""><tbody><tr><td class="links" style=""><b>Algemeen:</b></td><td class="rechts"><a href="/wiki/Ordinatie" title="Ordinatie">Gradiëntanalyse</a> · <a href="/wiki/Ordinatie" title="Ordinatie">Multidimensional scaling</a> · <a href="/wiki/Multivariate_statistiek" title="Multivariate statistiek">Multivariate statistiek</a> · <a href="/wiki/Ordinatie" title="Ordinatie">Ordinatie · Ordinogram</a></td></tr><tr><td class="links"><span class="nowrap"><b><a href="/wiki/Distantie_en_similariteit#Distantiematrix" title="Distantie en similariteit">Distantiematrix methoden:</a></b></span></td><td class="rechts"><a href="/wiki/Afstand" title="Afstand">Afstand</a> · <a href="/wiki/Polaire_ordinatie" title="Polaire ordinatie">Bray-Curtis ordinatie</a> · <a href="/wiki/Distantie_en_similariteit" title="Distantie en similariteit">Dissimilariteit · Distantie en similariteit</a> · <a href="/wiki/Afstand" title="Afstand">Distantie</a> · <a href="/wiki/Polaire_ordinatie" title="Polaire ordinatie">Polaire ordinatie</a> · <a href="/wiki/Principal_coordinates_analysis" class="mw-redirect" title="Principal coordinates analysis">Principal coordinates analysis</a> · <a href="/wiki/Nonmetric_multidimensional_scaling" title="Nonmetric multidimensional scaling">Nonmetric multidimensional scaling</a> · <a href="/wiki/Distantie_en_similariteit#Distantiematrix" title="Distantie en similariteit">Resemblance matrix</a> · <a href="/wiki/Distantie_en_similariteit" title="Distantie en similariteit">Similariteit</a> · <a href="/wiki/Polaire_ordinatie" title="Polaire ordinatie">Wisconsin ordinatie</a></td></tr><tr><td class="links"><span class="nowrap"><b><a href="/wiki/Eigenwaarde_(wiskunde)" title="Eigenwaarde (wiskunde)">Eigenvectormethoden:</a></b></span></td><td class="rechts"><a href="/wiki/Canonische_correspondentieanalyse" class="mw-redirect" title="Canonische correspondentieanalyse">Canonische correspondentieanalyse</a> · <a href="/wiki/Correspondentieanalyse" title="Correspondentieanalyse">Correspondentieanalyse</a> · <a href="/wiki/Detrended_canonical_correspondence_analysis" class="mw-redirect" title="Detrended canonical correspondence analysis">Detrended canonical correspondence analysis</a> · <a href="/wiki/Detrended_correspondence_analysis" title="Detrended correspondence analysis">Detrended correspondence analysis</a> · <a class="mw-selflink selflink">Factoranalyse</a> · <a href="/wiki/Hoofdcomponentenanalyse" title="Hoofdcomponentenanalyse">Hoofdcomponentenanalyse · Principale-componentenanalyse</a> · <a href="/wiki/Correspondentieanalyse" title="Correspondentieanalyse">Reciprocal Averaging</a> · <a href="/wiki/Ordinatie#Redundantieanalyse_(RDA)" title="Ordinatie">Redundantieanalyse</a> · <a href="/wiki/Screeplot" title="Screeplot">Screeplot</a></td></tr></tbody></table> </div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Factoranalyse&oldid=64391927">https://nl.wikipedia.org/w/index.php?title=Factoranalyse&oldid=64391927</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorie</a>: <ul><li><a href="/wiki/Categorie:Multivariate_statistiek" title="Categorie:Multivariate statistiek">Multivariate statistiek</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor 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