{"id":1534,"date":"2023-07-25T23:59:19","date_gmt":"2023-07-25T23:59:19","guid":{"rendered":"https:\/\/statorials.org\/tr\/negatif-binom-vs-balik\/"},"modified":"2023-07-25T23:59:19","modified_gmt":"2023-07-25T23:59:19","slug":"negatif-binom-vs-balik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/negatif-binom-vs-balik\/","title":{"rendered":"Negatif binom vs poisson: regresyon modeli nas\u0131l se\u00e7ilir"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Negatif binom regresyon<\/strong> ve <strong>Poisson regresyon,<\/strong> <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener\">yan\u0131t de\u011fi\u015fkeni<\/a> ayr\u0131 say\u0131m sonu\u00e7lar\u0131yla temsil edildi\u011finde kullan\u0131lmas\u0131 gereken iki t\u00fcr regresyon modelidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131k say\u0131m sonu\u00e7lar\u0131n\u0131 temsil eden yan\u0131t de\u011fi\u015fkenlerinin baz\u0131 \u00f6rnekleri a\u015fa\u011f\u0131da verilmi\u015ftir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Belirli bir programdan mezun olan \u00f6\u011frenci say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir kav\u015faktaki trafik kazas\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Maratonu tamamlayan kat\u0131l\u0131mc\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir ayda bir perakende ma\u011fazas\u0131ndaki iadelerin say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Varyans yakla\u015f\u0131k olarak ortalamaya e\u015fitse, Poisson regresyon modeli genellikle veri setine iyi uyum sa\u011flar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, varyans\u0131n ortalamadan \u00f6nemli \u00f6l\u00e7\u00fcde b\u00fcy\u00fck olmas\u0131 durumunda, negatif binom regresyon modeli genellikle verilere daha iyi uyum sa\u011flayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir veri seti i\u00e7in Poisson regresyonunun mu yoksa negatif binom regresyonunun mu daha uygun oldu\u011funu belirlemek i\u00e7in kullanabilece\u011fimiz iki teknik vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Art\u0131k araziler<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir regresyon modelinden tahmin edilen de\u011ferlere kar\u015f\u0131 standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131n bir grafi\u011fini olu\u015fturabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131n \u00e7o\u011funlu\u011fu -2 ile 2 aras\u0131ndaysa Poisson regresyon modeli muhtemelen uygundur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, e\u011fer bir\u00e7ok art\u0131k bu aral\u0131\u011f\u0131n d\u0131\u015f\u0131nda kal\u0131yorsa, negatif binom regresyon modeli muhtemelen daha iyi bir uyum sa\u011flayacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Olas\u0131l\u0131k oran\u0131 testi<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayn\u0131 veri setine bir Poisson regresyon modeli ve bir negatif binom regresyon modeli yerle\u015ftirebilir ve ard\u0131ndan bir olabilirlik oran\u0131 testi ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Testin p de\u011feri belirli bir anlaml\u0131l\u0131k d\u00fczeyinin (\u00f6rne\u011fin 0,05) alt\u0131ndaysa, negatif binom regresyon modelinin anlaml\u0131 derecede daha iyi bir uyum sa\u011flad\u0131\u011f\u0131 sonucuna varabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, belirli bir veri k\u00fcmesi i\u00e7in Poisson regresyon modelinin mi yoksa negatif binom regresyon modelinin mi kullan\u0131lmas\u0131n\u0131n daha iyi oldu\u011funu belirlemek i\u00e7in R&#8217;de bu iki tekni\u011fin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Negatif binom regresyon ve Poisson regresyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir il\u00e7edeki bir lise beyzbol oyuncusunun okul b\u00f6l\u00fcm\u00fcne (&#8220;A&#8221;, &#8220;B&#8221; veya &#8220;C&#8221;) ve okul notuna ba\u011fl\u0131 olarak ka\u00e7 burs ald\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. \u00fcniversiteye giri\u015f s\u0131nav\u0131 (0 ile 100 aras\u0131nda \u00f6l\u00e7\u00fcl\u00fcr). ).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Negatif binom regresyon modelinin mi yoksa Poisson regresyon modelinin mi verilere daha iyi uyum sa\u011flad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullan\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: Verileri olu\u015fturun<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, \u00fczerinde \u00e7al\u0131\u015faca\u011f\u0131m\u0131z ve 1000 beyzbol oyuncusuna ili\u015fkin verileri i\u00e7eren veri k\u00fcmesini olu\u015fturur:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create dataset\n<\/span>data &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (offers = c(rep(0, 700), rep(1, 100), rep(2, 100),\n                              rep(3, 70), rep(4, 30)),\n                   division = sample(c(' <span style=\"color: #008000;\">A<\/span> ', ' <span style=\"color: #008000;\">B<\/span> ', ' <span style=\"color: #008000;\">C<\/span> '), 100, replace = <span style=\"color: #008000;\">TRUE<\/span> ),\n                   exam = c(runif(700, 60, 90), runif(100, 65, 95),\n                            runif(200, 75, 95)))\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(data)\n\n  offers division exam\n1 0 A 66.22635\n2 0 C 66.85974\n3 0 A 77.87136\n4 0 B 77.24617\n5 0 A 62.31193\n6 0 C 61.06622<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Poisson regresyon modelini ve negatif binom regresyon modelini yerle\u015ftirin<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, hem Poisson regresyon modelinin hem de negatif binom regresyon modelinin verilere nas\u0131l s\u0131\u011fd\u0131r\u0131laca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit Poisson regression model\n<\/span>p_model &lt;- glm(offers ~ division + exam, family = ' <span style=\"color: #008000;\">fish<\/span> ', data = data)\n\n<span style=\"color: #008080;\">#fit negative binomial regression model\n<\/span><span style=\"color: #993300;\">library<\/span> (MASS)\n\nnb_model &lt;- glm. <span style=\"color: #3366ff;\">nb<\/span> (offers ~ division + exam, data = data)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Art\u0131k Grafikler Olu\u015fturun<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, her iki model i\u00e7in de art\u0131k grafiklerin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#Residual plot for Poisson regression\n<\/span>p_res &lt;- <span style=\"color: #3366ff;\">resid<\/span> (p_model)\nplot(fitted(p_model), p_res, col=' <span style=\"color: #008000;\">steelblue<\/span> ', pch=16,\n     xlab=' <span style=\"color: #008000;\">Predicted Offers<\/span> ', ylab=' <span style=\"color: #008000;\">Standardized Residuals<\/span> ', main=' <span style=\"color: #008000;\">Poisson<\/span> ')\nabline(0,0)\n\n<span style=\"color: #008080;\">#Residual plot for negative binomial regression<\/span>\nnb_res &lt;- <span style=\"color: #3366ff;\">resid<\/span> (nb_model)\nplot(fitted(nb_model), nb_res, col=' <span style=\"color: #008000;\">steelblue<\/span> ', pch=16,\n     xlab=' <span style=\"color: #008000;\">Predicted Offers<\/span> ', ylab=' <span style=\"color: #008000;\">Standardized Residuals<\/span> ', main=' <span style=\"color: #008000;\">Negative Binomial<\/span> ')\nabline(0,0)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15231 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/negatifbinom1.png\" alt=\"Negatif binom ve Poisson regresyonu\" width=\"679\" height=\"327\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Grafiklerden, negatif binom regresyon modeline k\u0131yasla Poisson regresyon modelinde art\u0131klar\u0131n daha fazla yay\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz (baz\u0131 art\u0131klar\u0131n 3&#8217;\u00fcn \u00fczerine \u00e7\u0131kt\u0131\u011f\u0131n\u0131 unutmay\u0131n).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, negatif binom regresyon modelinin art\u0131klar\u0131n\u0131n daha k\u00fc\u00e7\u00fck olmas\u0131 nedeniyle muhtemelen daha uygun oldu\u011funun bir i\u015faretidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. Ad\u0131m: Olabilirlik oran\u0131 testi yap\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, iki regresyon modelinin uyumunda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in bir olabilirlik oran\u0131 testi yapabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>pchisq(2 * ( <span style=\"color: #3366ff;\">logLik<\/span> (nb_model) - <span style=\"color: #3366ff;\">logLik<\/span> (p_model)), df = 1, lower. <span style=\"color: #3366ff;\">tail<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n'log Lik.' 3.508072e-29 (df=5)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Testin p de\u011feri <strong>3,508072e-29<\/strong> olarak ortaya \u00e7\u0131k\u0131yor ve bu da 0,05&#8217;ten \u00f6nemli \u00f6l\u00e7\u00fcde d\u00fc\u015f\u00fck.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla, negatif binom regresyon modelinin Poisson regresyon modeline k\u0131yasla verilere \u00f6nemli \u00f6l\u00e7\u00fcde daha iyi uyum sa\u011flad\u0131\u011f\u0131 sonucuna varabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/negatif-1-binom-dagilimi\/\" target=\"_blank\" rel=\"noopener\">Negatif binom da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Negatif binom regresyon ve Poisson regresyon, yan\u0131t de\u011fi\u015fkeni ayr\u0131 say\u0131m sonu\u00e7lar\u0131yla temsil edildi\u011finde kullan\u0131lmas\u0131 gereken iki t\u00fcr regresyon modelidir. Ayr\u0131k say\u0131m sonu\u00e7lar\u0131n\u0131 temsil eden yan\u0131t de\u011fi\u015fkenlerinin baz\u0131 \u00f6rnekleri a\u015fa\u011f\u0131da verilmi\u015ftir: Belirli bir programdan mezun olan \u00f6\u011frenci say\u0131s\u0131 Belirli bir kav\u015faktaki trafik kazas\u0131 say\u0131s\u0131 Maratonu tamamlayan kat\u0131l\u0131mc\u0131 say\u0131s\u0131 Belirli bir ayda bir perakende ma\u011fazas\u0131ndaki iadelerin say\u0131s\u0131 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1534","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Negatif binom vs Poisson: regresyon modeli nas\u0131l se\u00e7ilir<\/title>\n<meta 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