{"id":3140,"date":"2023-07-19T00:41:50","date_gmt":"2023-07-19T00:41:50","guid":{"rendered":"https:\/\/statorials.org\/tr\/arka-secim\/"},"modified":"2023-07-19T00:41:50","modified_gmt":"2023-07-19T00:41:50","slug":"arka-secim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/arka-secim\/","title":{"rendered":"Geriye 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, geriye do\u011fru se\u00e7im<\/strong> olarak bilinir ve \u015fu \u015fekilde \u00e7al\u0131\u015f\u0131r:<\/span><\/p>\n

Ad\u0131m 1:<\/strong> T\u00fcm p<\/em> tahmin de\u011fi\u015fkenlerini kullanarak bir regresyon modeli yerle\u015ftirin. Model i\u00e7in AIC *<\/strong> de\u011ferini hesaplay\u0131n.<\/span><\/p>\n

Ad\u0131m 2:<\/strong> T\u00fcm p<\/em> \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenleri i\u00e7eren modelle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda, AIC’de en b\u00fcy\u00fck azalmaya neden olan ve ayn\u0131 zamanda AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya yol a\u00e7an \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkeni kald\u0131r\u0131n.<\/span><\/p>\n

Ad\u0131m 3:<\/strong> AIC’de en b\u00fcy\u00fck azalmaya yol a\u00e7an ve ayn\u0131 zamanda p-1<\/em> \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenlere sahip modelle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya yol a\u00e7an \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkeni kald\u0131r\u0131n.<\/span><\/p>\n

Herhangi bir \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin kald\u0131r\u0131lmas\u0131 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 geriye do\u011fru se\u00e7imin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir.<\/span><\/p>\n

\u00d6rnek: R’de geriye do\u011fru 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 nas\u0131l geri ad\u0131m at\u0131laca\u011f\u0131n\u0131 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 backward stepwise regression\n<\/span>backward <- step(all, direction=' backward<\/span> ', scope= formula<\/span> (all), trace=0)\n\n#view results of backward stepwise regression<\/span>\nbackward$anova\n\n    Step Df Deviance Resid. Df Resid. Dev AIC\n1 NA NA 21 147.4944 70.89774\n2 - cyl 1 0.07987121 22 147.5743 68.91507\n3 - vs 1 0.26852280 23 147.8428 66.97324\n4 - carb 1 0.68546077 24 148.5283 65.12126\n5 - gear 1 1.56497053 25 150.0933 63.45667\n6 - drat 1 3.34455117 26 153.4378 62.16190\n7 - available 1 6.62865369 27 160.0665 61.51530\n8 - hp 1 9.21946935 28 169.2859 61.30730\n\n#view final model\n<\/span>backward$coefficients\n\n(Intercept) wt qsec am \n   9.617781 -3.916504 1.225886 2.935837\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
 \u0130lk olarak, 10 \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkeni kullanarak bir model olu\u015fturuyoruz ve modelin AIC’sini hesapl\u0131yoruz.<\/span><\/p>\n
 Daha sonra, AIC’de en b\u00fcy\u00fck azalmaya neden olan de\u011fi\u015fkeni ( cyl<\/strong> ) kald\u0131rd\u0131k ve ayr\u0131ca 10 \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken modeline k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalma elde ettik.<\/span><\/p>\n
 Daha sonra, AIC’de en b\u00fcy\u00fck azalmaya yol a\u00e7an de\u011fi\u015fkeni ( vs<\/strong> ) kald\u0131rd\u0131k ve ayr\u0131ca 9’lu \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken modeline k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalma elde ettik.<\/span><\/p>\n
 Daha sonra, AIC’de en b\u00fcy\u00fck azalmaya neden olan de\u011fi\u015fkeni ( karbonhidrat<\/strong> ) kald\u0131rd\u0131k ve ayr\u0131ca 8-predikt\u00f6r de\u011fi\u015fken modeline k\u0131yasla AIC’de istatistiksel olarak anlaml\u0131 bir azalma elde ettik.<\/span><\/p>\n
 Art\u0131k AIC’de istatistiksel olarak anlaml\u0131 bir azalmaya yol a\u00e7mayan herhangi bir de\u011fi\u015fkeni kald\u0131rana kadar bu i\u015flemi tekrarlad\u0131k.<\/span><\/p>\n
 Nihai model \u015fu \u015fekilde ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n
 mpg = 9,62 \u2013 3,92*a\u011f\u0131rl\u0131k + 1,23*qsaniye + 2,94*am<\/strong><\/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