{"id":106,"date":"2008-08-20T18:28:06","date_gmt":"2008-08-20T15:28:06","guid":{"rendered":"http:\/\/www.muratakyildiz.com\/wordpress\/?p=106"},"modified":"2014-09-11T18:44:40","modified_gmt":"2014-09-11T15:44:40","slug":"multicollinearity-nedir-nasl-baa-cklr-spss-oernei","status":"publish","type":"post","link":"https:\/\/www.istatistik.gen.tr\/?p=106","title":{"rendered":"Multicollinearity nedir nas\u0131l ba\u015fa \u00e7\u0131k\u0131l\u0131r. SPSS \u00f6rne\u011fi"},"content":{"rendered":"

En basit tan\u0131m\u0131yla multicollinearity bir de\u011fi\u015fkeni yordayan (tahmin eden) en az iki de\u011fi\u015fken aras\u0131nda \u00e7ok y\u00fcksek ili\u015fkinin olmas\u0131 durumudur. Aralar\u0131ndaki ili\u015fki \u00e7ok y\u00fcksek olan iki de\u011fi\u015fken k\u0131smen birbirinin \u00e7ok benzeri olaca\u011f\u0131ndan ikisinden birisinin at\u0131lmas\u0131 uygun olacakt\u0131r. Multicollinearity tespiti i\u00e7in \u00e7e\u015fitli testler bulunmaktad\u0131r, bunlar\u0131n aras\u0131nda en kolay kulan\u0131m\u0131 olanlar SPSS istatistik program\u0131nda regresyon analizine giren de\u011fi\u015fkenlerin collinearity de\u011ferlerini hesaplamaktad\u0131r. Regresyon analizi se\u00e7eneklerinde collinearity diagnostics se\u00e7ilirse multicollinearity i\u00e7in bir tespit analizi yap\u0131lmaktad\u0131r.<\/p>\n

<\/p>\n

Bu tespitlerin ba\u015f\u0131nda varyans art\u0131\u015f fakt\u00f6r\u00fc gelir (variance inflation factor— VIF (varyans geni\u015flik fakt\u00f6r\u00fc)). Bir de\u011fi\u015fkeni yordayan iki ba\u011f\u0131ms\u0131z de\u011fi\u015fken aras\u0131ndaki ortak varyans miktar\u0131na g\u00f6re belirlenen bu fakt\u00f6r bize iki yorday\u0131c\u0131 de\u011fi\u015fken aras\u0131ndaki ortak olmayan varyans\u0131n miktar\u0131n\u0131 1 ile sonsuz aras\u0131ndaki bir \u00f6l\u00e7ek d\u00fczeyinde g\u00f6sterir. VIF’nin form\u00fcl\u00fc basittir.VIF=1\/1-R2(Rkare).\u00a0 (burada Rkare iki ba\u011f\u0131ms\u0131z yani yorday\u0131c\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi g\u00f6stermektedir. Her bir de\u011fi\u015fken grubu i\u00e7in tekrar tekrar hesaplamak gerekmektedir. Ger\u00e7i SPSS bu i\u015fi bizim i\u00e7in yap\u0131yor). Baz\u0131lar\u0131 VIF de\u011ferinin 10 ve 10’dan daha b\u00fcy\u00fck olmas\u0131n\u0131n collinearity (ya da multicollinearity) i\u00e7in yeterli oldu\u011funu s\u00f6ylmektedir. Bu durumda Rkare 0,90 \u00e7\u0131km\u015f demektir. Yani iki ba\u011f\u0131ms\u0131z de\u011fi\u015fken aras\u0131ndaki korelasyon katsay\u0131s\u0131 0,95 demektir. A\u00e7\u0131kcas\u0131 bana g\u00f6re VIF’nin 10 ve daha y\u00fcksek oldu\u011funda collinearity’yi g\u00f6stermesi \u00e7ok kabul edilebilecek bir durum de\u011fildir. \u00c7\u00fcnk\u00fc iki yorday\u0131c\u0131 de\u011fi\u015fken aras\u0131ndaki korelasyon zaten 0,95’e dayanm\u0131\u015fsa bu ikisi neredeyse birbirinin ayn\u0131s\u0131 demektir. Birini zaten \u00e7oktan atm\u0131\u015f olmam\u0131z gerekmektedir. Peki hangi de\u011fer kabul edilecektir. VIF i\u00e7in kesin bir yan\u0131t yok ama y\u00fcksek VIF de\u011ferleri size collinearity sorununu hat\u0131rlats\u0131n diyebiliriz. Collinearity i\u00e7in ba\u015fka kontrol y\u00f6ntemleri de geli\u015ftirilmi\u015f durumda. Condition index bunlardan en \u00e7ok bilinenidir. Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerin ortak varyanslar\u0131n\u0131n \u00f6zde\u011ferlerine (eigenvalues) g\u00f6re bulunmas\u0131 esas\u0131na dayan bu y\u00f6ntemde ortak varyans olu\u015fturan her bir de\u011fi\u015fkenleraras\u0131 korelasyon matrisi i\u00e7in bir \u00f6zde\u011fer hesaplan\u0131r..\u00a0 (T\u0131pk\u0131 fakt\u00f6r analizinde oldu\u011fu gibi). Bu \u00f6zde\u011ferler bize, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerimizin, kendi aralar\u0131nda olu\u015fturduklar\u0131 ortak fakt\u00f6r\u00fc\/fakt\u00f6rleri birlikte dengeli\/e\u015fit bir \u015fekilde a\u00e7\u0131klad\u0131klar\u0131na ili\u015fkin bilgi verir. (alttaki tabloya bak\u0131n\u0131z). E\u011fer t\u00fcm de\u011fi\u015fkenler olu\u015fturduklar\u0131 fakt\u00f6r\u00fc ayn\u0131 derecede\/g\u00fc\u00e7te a\u00e7\u0131kl\u0131yorlarsa \u00f6zde\u011fer y\u00fcksek \u00e7\u0131kacakt\u0131r. E\u011fer her biri olu\u015fturduklar\u0131 fakt\u00f6r\u00fc farkl\u0131 g\u00fc\u00e7lerde\/derecelerde a\u00e7\u0131kl\u0131yorlarsa \u00f6zde\u011ferleri de d\u00fc\u015f\u00fck \u00e7\u0131kacakt\u0131r. Zaten bu de\u011fer \u00f6zde\u011fer denmesinin sebebi de bu. \u00f6z-de\u011fer. Birlikte e\u015fitli\u011fi tutturabilme, birlikte ve uyumlu bir \u015fekilde “bir \u015fey” \u00fcretebilme gibi bir anlam\u0131 var.\u00a0\u00a0 Daha sonra bu \u00f6zde\u011ferlerden en b\u00fcy\u00fc\u011f\u00fc, elde edilmi\u015f t\u00fcm \u00f6zde\u011ferler i\u00e7in ayr\u0131 ayr\u0131 olmak \u00fczere di\u011fer \u00f6zde\u011ferlere b\u00f6l\u00fcnerek karek\u00f6k\u00fc al\u0131n\u0131r. Yani birlikte dengeli bir \u015fekilde bulunabilme g\u00fc\u00e7lerinin en y\u00fcksek oldu\u011fu durum birlikte dengeli bir \u015fekilde bulunabilmenin di\u011fer ko\u015fullar\u0131na oranlan\u0131r. Bu condition index de\u011feri \u00e7ok y\u00fcksek \u00e7\u0131karsa de\u011fi\u015fkenlerden en az ikisi aras\u0131nda collinearity sorunu oldu\u011fu d\u00fc\u015f\u00fcn\u00fcl\u00fcr. Bu \u00e7ok y\u00fcksek nerede ba\u015flamaktad\u0131r. Neyse i bunun kesin bir cevab\u0131 var. E\u011fer condition index 15 ve daha \u00fczerinde bir de\u011fer ald\u0131ysa collinearity d\u00fc\u015f\u00fcn\u00fcl\u00fcr. Hangi de\u011fi\u015fkenler aras\u0131nda collinearity oldu\u011funu bulabilmek i\u00e7inse de\u011fi\u015fkenlerin a\u00e7\u0131klad\u0131klar\u0131 varyansa bakmak gerekecektir. Bunun i\u00e7in de yine sa\u011folsun SPSS yard\u0131mc\u0131 oluyor. A\u015fa\u011f\u0131daki spss tablosu metinden s\u0131k\u0131lanlar i\u00e7in daha yard\u0131mc\u0131 olabilir.<\/p>\n

<\/div>\n

Dimension<\/span>\u00a0 <\/span>Eigenval<\/span>\u00a0\u00a0\u00a0\u00a0 <\/span>Condition<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>Variance Proportions<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>Index<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>Constant<\/span>\u00a0\u00a0\u00a0\u00a0 <\/span>X1<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>X2<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>X3<\/span><\/span><\/p>\n

1<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>3.819<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>1.00<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.004<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.006<\/span>\u00a0\u00a0\u00a0 <\/span>.002<\/span>\u00a0\u00a0\u00a0 <\/span>.002<\/span><\/span><\/p>\n

2<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.117<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>5.707<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.043<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.384<\/span>\u00a0\u00a0\u00a0 <\/span>.041<\/span>\u00a0\u00a0\u00a0 <\/span>.087<\/span><\/span><\/p>\n

3<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.047<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>9.025<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.876<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.608<\/span>\u00a0\u00a0\u00a0 <\/span>.001<\/span>\u00a0\u00a0\u00a0 <\/span>.042<\/span><\/span><\/p>\n

4<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.017<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>15.128<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.077<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>.002<\/span>\u00a0\u00a0\u00a0 <\/span>.967<\/span>\u00a0\u00a0\u00a0 <\/span>.868<\/span><\/span><\/p>\n

G\u00f6r\u00fcld\u00fc\u011f\u00fc gibi 4 boyutta X2 ve X3 de\u011fi\u015fkenlerinin eigenvalue (\u00f6zde\u011fer) de\u011feri 15,128. a\u00e7\u0131klad\u0131klar\u0131 varyanslara bak\u0131nca ikisinin de 4 boyutu y\u00fcksek oranda benzer \u015fekilde a\u00e7\u0131klad\u0131klar\u0131 g\u00f6r\u00fcl\u00fcyor. Yani bunlardan birisine gerek yok.
\nBu t\u00fcr durumlarla kar\u015f\u0131la\u015f\u0131ld\u0131\u011f\u0131nda izlenebilecek bir ka\u00e7 yol var
\n1) Umurunuzda bile olmamas\u0131
\n2) fakt\u00f6r analizi ile iki de\u011fi\u015fkeni birle\u015ftirmek ve yeni bir ortak de\u011fi\u015fken ile regresyonu tekrarlamak
\n3) Birisini g\u00f6zden \u00e7\u0131karmak
\n4) Regresyon analizinde subsetler belirleyerek analizi buna g\u00f6re yapmak<\/p>\n

\u015fimdi size b\u00fct\u00fcn bu i\u015flemlerin SPSS’te hangi yoldan yap\u0131laca\u011f\u0131n\u0131 da anlatay\u0131m.
\nTabii ki \u00f6nce analyse men\u00fcs\u00fcne\u00a0 oradan\u00a0 regression a\u00e7\u0131lan yerden de
\nlinear k\u0131sm\u0131na t\u0131kl\u0131yoruz. A\u00e7\u0131lan dialog penceresinden (ne demekse) ba\u011f\u0131ml\u0131 ba\u011f\u0131ms\u0131z de\u011fi\u015fkenleri uygun yerlere g\u00f6nderiyoruz. bu dialog penceresinde sol altta bir statistics butonu (d\u00fc\u011fmesi) g\u00f6receksiniz oraya t\u0131kl\u0131yoruz. Sa\u011fda model fit’ten ba\u015flayan ve collinearity diagnostics’e kadar i\u015faretlenebilir kutucuklar\u0131n hepsini i\u015faretliyoruz. (bir k\u0131sm\u0131 burada anlat\u0131lmad\u0131 ama size laz\u0131m olacakt\u0131r). Ok deyip devam ediyorsunuz. Analizi yapt\u0131\u011f\u0131n\u0131zda yukar\u0131da anlatt\u0131\u011f\u0131m her \u015fey son iki tabloda kar\u015f\u0131n\u0131zda olacak.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

En basit tan\u0131m\u0131yla multicollinearity bir de\u011fi\u015fkeni yordayan (tahmin eden) en az iki de\u011fi\u015fken aras\u0131nda \u00e7ok y\u00fcksek ili\u015fkinin olmas\u0131 durumudur. Aralar\u0131ndaki ili\u015fki \u00e7ok y\u00fcksek olan iki de\u011fi\u015fken k\u0131smen birbirinin \u00e7ok benzeri olaca\u011f\u0131ndan ikisinden birisinin at\u0131lmas\u0131 uygun olacakt\u0131r. Multicollinearity tespiti i\u00e7in \u00e7e\u015fitli testler bulunmaktad\u0131r, bunlar\u0131n aras\u0131nda en kolay kulan\u0131m\u0131 olanlar SPSS istatistik program\u0131nda regresyon analizine giren de\u011fi\u015fkenlerin…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-106","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=106"}],"version-history":[{"count":1,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/106\/revisions"}],"predecessor-version":[{"id":108,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/106\/revisions\/108"}],"wp:attachment":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}