{"id":3139,"date":"2023-07-19T00:50:54","date_gmt":"2023-07-19T00:50:54","guid":{"rendered":"https:\/\/statorials.org\/tr\/ileri-secim\/"},"modified":"2023-07-19T00:50:54","modified_gmt":"2023-07-19T00:50:54","slug":"ileri-secim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ileri-secim\/","title":{"rendered":"Do\u011frudan se\u00e7im nedir? (tan\u0131m & #038; \u00f6rnek)"},"content":{"rendered":"

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\u0130statistikte, ad\u0131m ad\u0131m se\u00e7im,<\/strong> art\u0131k istatistiksel olarak ge\u00e7erli bir neden kalmayana kadar modele tahmin edicileri ad\u0131m ad\u0131m girerek ve \u00e7\u0131kararak bir dizi tahmin de\u011fi\u015fkeninden bir regresyon modeli<\/a> olu\u015fturmak i\u00e7in kullanabilece\u011fimiz bir prosed\u00fcrd\u00fcr. veya daha fazlas\u0131n\u0131 silin.<\/span><\/p>\n

Ad\u0131m ad\u0131m se\u00e7imin amac\u0131 , yan\u0131t de\u011fi\u015fkeniyle<\/a> istatistiksel olarak anlaml\u0131 d\u00fczeyde ili\u015fkili olan t\u00fcm yorday\u0131c\u0131 de\u011fi\u015fkenleri i\u00e7eren bir regresyon modeli olu\u015fturmakt\u0131r.<\/span><\/p>\n

En s\u0131k kullan\u0131lan ad\u0131m ad\u0131m se\u00e7im y\u00f6ntemlerinden biri do\u011frudan se\u00e7im<\/strong> olarak bilinir ve \u015fu \u015fekilde \u00e7al\u0131\u015f\u0131r:<\/span><\/span><\/p>\n

Ad\u0131m 1:<\/strong> Tahmin edici de\u011fi\u015fkenler olmadan yaln\u0131zca kesi\u015fme regresyon modelini yerle\u015ftirin. Model i\u00e7in AIC *<\/strong> de\u011ferini hesaplay\u0131n.<\/span><\/p>\n

Ad\u0131m 2:<\/strong> T\u00fcm olas\u0131 tek tahminli regresyon modellerini tak\u0131n. Yaln\u0131zca engelleme modeline k\u0131yasla en d\u00fc\u015f\u00fck AIC’yi \u00fcreten ve ayn\u0131 zamanda AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya sahip olan modeli belirleyin.<\/span><\/p>\n

Ad\u0131m 3:<\/strong> T\u00fcm regresyon modellerini iki olas\u0131 tahminciye uydurun. Tek tahminli modelle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda en d\u00fc\u015f\u00fck AIC’yi \u00fcreten ve ayn\u0131 zamanda AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya sahip olan modeli belirleyin.<\/span><\/p>\n

Daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken i\u00e7eren bir regresyon modelinin yerle\u015ftirilmesi art\u0131k AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya yol a\u00e7mayana kadar i\u015flemi tekrarlay\u0131n.<\/span><\/p>\n

*<\/strong> \u00c7apraz do\u011frulama tahmin hatas\u0131, Cp, BIC, AIC veya d\u00fczeltilmi\u015f R2<\/sup> dahil olmak \u00fczere, bir regresyon modelinin uyum iyili\u011fini hesaplamak i\u00e7in kullanabilece\u011finiz \u00e7e\u015fitli \u00f6l\u00e7\u00fcmler vard\u0131r.<\/span> A\u015fa\u011f\u0131daki \u00f6rnekte AIC kullanmay\u0131 se\u00e7iyoruz.<\/span><\/p>\n

A\u015fa\u011f\u0131daki \u00f6rnek, R’de do\u011frudan se\u00e7imin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir.<\/span><\/p>\n

\u00d6rnek: R’de do\u011frudan se\u00e7im<\/strong><\/span><\/h3>\n

Bu \u00f6rnek i\u00e7in R’de yerle\u015fik mtcars veri k\u00fcmesini<\/a> kullanaca\u011f\u0131z:<\/span><\/p>\n

 #view first six rows of mtcars\n<\/em><\/span>head(mtcars)\n\n                   mpg cyl disp hp drat wt qsec vs am gear carb\nMazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4\nMazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4\nDatsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1\nHornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1\nHornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2\nValiant 18.1 6 225 105 2.76 3,460 20.22 1 0 3 1\n<\/strong><\/pre>\n
 Yan\u0131t de\u011fi\u015fkeni olarak mpg’yi<\/em> (galon ba\u015f\u0131na mil) ve veri setindeki di\u011fer 10 de\u011fi\u015fkeni potansiyel \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenler olarak kullanarak \u00e7oklu do\u011frusal regresyon modelini yerle\u015ftirece\u011fiz.<\/span><\/p>\n
 A\u015fa\u011f\u0131daki kod, bir se\u00e7imin ad\u0131m ad\u0131m nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n
 #define intercept-only model\n<\/span>intercept_only <- lm(mpg ~ 1, data=mtcars)\n\n#define model with all predictors\n<\/span>all <- lm(mpg ~ ., data=mtcars)\n\n#perform forward stepwise regression\n<\/span>forward <- step(intercept_only, direction=' forward<\/span> ', scope= formula<\/span> (all), trace= 0<\/span> )\n\n#view results of forward stepwise regression<\/span>\nforward$anova\n\n   Step Df Deviance Resid. Df Resid. Dev AIC\n1 NA NA 31 1126.0472 115.94345\n2 + wt -1 847.72525 30 278.3219 73.21736\n3 + cyl -1 87.14997 29 191.1720 63.19800\n4 + hp -1 14.55145 28 176.6205 62.66456\n\n#view final model\n<\/span>forward$coefficients\n\n(Intercept) wt cyl hp \n 38.7517874 -3.1669731 -0.9416168 -0.0180381 \n<\/strong><\/pre>\n
 Sonu\u00e7lar\u0131 nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n
 \u00d6ncelikle sadece kesi\u015fme modelini uyguluyoruz. Bu modelin AIC’si 115.94345’ti<\/strong> .<\/span><\/p>\n
 Daha sonra olas\u0131 t\u00fcm modelleri bir tahminciye s\u0131\u011fd\u0131r\u0131r\u0131z. En d\u00fc\u015f\u00fck AIC’yi \u00fcreten ve ayn\u0131 zamanda wt<\/em> tahmincisini kullanan yaln\u0131zca kesi\u015fme modeline k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya sahip olan model. Bu modelin AIC’si 73.21736’yd\u0131<\/strong> .<\/span><\/p>\n
 Daha sonra, t\u00fcm olas\u0131 modelleri iki tahminciyle e\u015fle\u015ftiriyoruz. En d\u00fc\u015f\u00fck AIC’yi \u00fcreten ve ayr\u0131ca tek \u00f6ng\u00f6r\u00fcc\u00fc modele k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya sahip olan model, silindir<\/em> tahmincisini ekledi. Bu modelin AIC’si 63.19800’d\u00fc<\/strong> .<\/span><\/p>\n
 Daha sonra, t\u00fcm olas\u0131 modelleri \u00fc\u00e7 tahminciye s\u0131\u011fd\u0131r\u0131yoruz. En d\u00fc\u015f\u00fck AIC’yi \u00fcreten ve ayn\u0131 zamanda iki tahminci modele k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya sahip olan model, hp<\/em> tahmincisini ekledi. Bu modelin AIC’si 62.66456’yd\u0131<\/strong> .<\/span><\/p>\n
 Daha sonra, t\u00fcm olas\u0131 modelleri d\u00f6rt tahminciye s\u0131\u011fd\u0131r\u0131yoruz. Bu modellerden hi\u00e7birinin AIC’de \u00f6nemli bir azalma sa\u011flamad\u0131\u011f\u0131 ortaya \u00e7\u0131kt\u0131 ve bu nedenle prosed\u00fcr\u00fc durdurduk.<\/span><\/p>\n
 Dolay\u0131s\u0131yla nihai model \u015fu \u015fekilde ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n
 mpg = 38,75 \u2013 3,17*a\u011f\u0131rl\u0131k \u2013 0,94*sil \u2013 0,02*hip<\/strong><\/span><\/p>\n
 Modele daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken eklemeye \u00e7al\u0131\u015fman\u0131n AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya yol a\u00e7mad\u0131\u011f\u0131 ortaya \u00e7\u0131kt\u0131.<\/span><\/p>\n
 B\u00f6ylece, en iyi modelin \u00fc\u00e7 \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkene sahip olan model oldu\u011fu sonucuna var\u0131yoruz: wt, cyl ve hp.<\/span><\/p>\n
 AIC kullan\u0131m\u0131na ili\u015fkin bir not<\/strong><\/span><\/h3>\n
 \u00d6nceki \u00f6rnekte, \u00e7e\u015fitli regresyon modellerinin uyumunu de\u011ferlendirmek i\u00e7in AIC’yi bir \u00f6l\u00e7\u00fcm olarak kullanmay\u0131 se\u00e7tik.<\/span><\/p>\n
 AIC, Akaike Bilgi Kriteri<\/strong> anlam\u0131na gelir ve a\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n
 AIC = 2K \u2013 2 ln<\/em> (L)<\/span><\/p>\n
 Alt\u0131n:<\/span><\/p>\n