{"id":1531,"date":"2023-07-25T23:59:19","date_gmt":"2023-07-25T23:59:19","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%af%be%e9%ad%9a\/"},"modified":"2023-07-25T23:59:19","modified_gmt":"2023-07-25T23:59:19","slug":"%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%af%be%e9%ad%9a","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%af%be%e9%ad%9a\/","title":{"rendered":"\u8ca0\u306e\u4e8c\u9805\u5bfe\u30dd\u30a2\u30bd\u30f3: \u56de\u5e30\u30e2\u30c7\u30eb\u306e\u9078\u629e\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u8ca0\u306e\u4e8c\u9805\u56de\u5e30<\/strong>\u3068<strong>\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u306f\u3001<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u5909\u6570\u306e\u8aac\u660e\u5fdc\u7b54\/\" target=\"_blank\" rel=\"noopener\">\u5fdc\u7b54\u5909\u6570\u304c<\/a>\u96e2\u6563\u30ab\u30a6\u30f3\u30c8\u7d50\u679c\u3067\u8868\u3055\u308c\u308b\u5834\u5408\u306b\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b 2 \u7a2e\u985e\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u306b\u3001\u96e2\u6563\u8a08\u6570\u7d50\u679c\u3092\u8868\u3059\u5fdc\u7b54\u5909\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u7279\u5b9a\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5352\u696d\u3057\u305f\u5b66\u751f\u306e\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\">\u3042\u308b\u4ea4\u5dee\u70b9\u3067\u306e\u4ea4\u901a\u4e8b\u6545\u4ef6\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\">\u30de\u30e9\u30bd\u30f3\u5b8c\u8d70\u8005\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\">\u5c0f\u58f2\u5e97\u306b\u304a\u3051\u308b\u7279\u5b9a\u306e\u6708\u306e\u8fd4\u54c1\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5206\u6563\u304c\u5e73\u5747\u306b\u307b\u307c\u7b49\u3057\u3044\u5834\u5408\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u4e00\u822c\u306b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u3088\u304f\u9069\u5408\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3060\u3057\u3001\u5206\u6563\u304c\u5e73\u5747\u3088\u308a\u3082\u5927\u5e45\u306b\u5927\u304d\u3044\u5834\u5408\u306f\u3001\u901a\u5e38\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u30c7\u30fc\u30bf\u3092\u3088\u308a\u3088\u304f\u9069\u5408\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3068\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u306e\u3069\u3061\u3089\u304c\u9069\u5207\u3067\u3042\u308b\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u624b\u6cd5\u304c 2 \u3064\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u6b8b\u308a\u306e\u30d7\u30ed\u30c3\u30c8<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u56de\u5e30\u30e2\u30c7\u30eb\u304b\u3089\u306e\u4e88\u6e2c\u5024\u306b\u5bfe\u3059\u308b\u6a19\u6e96\u5316\u6b8b\u5dee\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6a19\u6e96\u5316\u6b8b\u5dee\u306e\u5927\u90e8\u5206\u304c -2 \uff5e 2 \u306e\u7bc4\u56f2\u306b\u3042\u308b\u5834\u5408\u306f\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u304c\u9069\u5207\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3060\u3057\u3001\u591a\u304f\u306e\u6b8b\u5dee\u304c\u3053\u306e\u7bc4\u56f2\u5916\u306b\u3042\u308b\u5834\u5408\u306f\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u3088\u308a\u9069\u5207\u306b\u9069\u5408\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u5c24\u5ea6\u6bd4\u691c\u5b9a<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u540c\u3058\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u5f53\u3066\u306f\u3081\u3066\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u691c\u5b9a\u306e p \u5024\u304c\u7279\u5b9a\u306e\u6709\u610f\u6c34\u6e96 (0.05 \u306a\u3069) \u3092\u4e0b\u56de\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u5927\u5e45\u306b\u826f\u597d\u306a\u9069\u5408\u3092\u63d0\u4f9b\u3059\u308b\u3068\u7d50\u8ad6\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u4f8b\u306f\u3001R \u3067\u3053\u308c\u3089 2 \u3064\u306e\u624b\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3001\u7279\u5b9a\u306e\u30c7\u30fc\u30bf \u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3069\u3061\u3089\u3092\u4f7f\u7528\u3059\u308b\u65b9\u304c\u826f\u3044\u304b\u3092\u5224\u65ad\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u4f8b: \u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u3068\u30dd\u30a2\u30bd\u30f3\u56de\u5e30<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u7279\u5b9a\u306e\u90e1\u306e\u9ad8\u6821\u91ce\u7403\u9078\u624b\u304c\u5b66\u6821\u533a\u5206 (\u300cA\u300d\u3001\u300cB\u300d\u3001\u307e\u305f\u306f\u300cC\u300d) \u3068\u5b66\u5e74\u306b\u57fa\u3065\u3044\u3066\u53d7\u3051\u53d6\u3063\u305f\u5968\u5b66\u91d1\u306e\u6570\u3092\u77e5\u308a\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u5927\u5b66\u5165\u5b66\u8a66\u9a13\uff080\u304b\u3089100\u3067\u8a55\u4fa1\uff09\u3002 \uff09\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u624b\u9806\u3092\u4f7f\u7528\u3057\u3066\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3069\u3061\u3089\u304c\u30c7\u30fc\u30bf\u306b\u3088\u308a\u3088\u304f\u9069\u5408\u3059\u308b\u304b\u3092\u5224\u65ad\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 1: \u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u30011,000 \u4eba\u306e\u91ce\u7403\u9078\u624b\u306b\u95a2\u3059\u308b\u30c7\u30fc\u30bf\u3092\u542b\u3080\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/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>\u30b9\u30c6\u30c3\u30d7 2: \u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u308b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u4e21\u65b9\u3092\u30c7\u30fc\u30bf\u306b\u9069\u5408\u3055\u305b\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/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>\u30b9\u30c6\u30c3\u30d7 3: \u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001\u4e21\u65b9\u306e\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/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=\"\u8ca0\u306e\u4e8c\u9805\u56de\u5e30 vs \u30dd\u30a2\u30bd\u30f3\u56de\u5e30\" width=\"679\" height=\"327\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u30b0\u30e9\u30d5\u304b\u3089\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u306f\u6b8b\u5dee\u304c\u3055\u3089\u306b\u5e83\u304c\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059 (\u4e00\u90e8\u306e\u6b8b\u5dee\u306f 3 \u3092\u8d85\u3048\u3066\u5e83\u304c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044)\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u306f\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u6b8b\u5dee\u304c\u5c0f\u3055\u3044\u305f\u3081\u3001\u304a\u305d\u3089\u304f\u3053\u306e\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u9069\u5207\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 4: \u5c24\u5ea6\u6bd4\u691c\u5b9a\u3092\u5b9f\u884c\u3059\u308b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6700\u5f8c\u306b\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u3066\u30012 \u3064\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u9069\u5408\u306b\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3067\u304d\u307e\u3059\u3002<\/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;\">\u691c\u5b9a\u306e p \u5024\u306f<strong>3.508072e-29<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u3001\u3053\u308c\u306f 0.05 \u3088\u308a\u3082\u5927\u5e45\u306b\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3057\u305f\u304c\u3063\u3066\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u6bd4\u8f03\u3057\u3066\u30c7\u30fc\u30bf\u3078\u306e\u9069\u5408\u6027\u304c\u5927\u5e45\u306b\u512a\u308c\u3066\u3044\u308b\u3068\u7d50\u8ad6\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/ja\/\u8ca0\u306e-1-\u306e\u4e8c\u9805\u5206\u5e03\/\" target=\"_blank\" rel=\"noopener\">\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306e\u6982\u8981<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/\u9b5a\u306e\u5206\u5e03\/\" target=\"_blank\" rel=\"noopener\">\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u6982\u8981<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u3068\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u306f\u3001\u5fdc\u7b54\u5909\u6570\u304c\u96e2\u6563\u30ab\u30a6\u30f3\u30c8\u7d50\u679c\u3067\u8868\u3055\u308c\u308b\u5834\u5408\u306b\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b 2 \u7a2e\u985e\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u3059\u3002 \u4ee5\u4e0b\u306b\u3001\u96e2\u6563\u8a08\u6570\u7d50\u679c\u3092\u8868\u3059\u5fdc\u7b54\u5909\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059\u3002 \u7279\u5b9a\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5352\u696d\u3057\u305f\u5b66\u751f\u306e\u6570 \u3042\u308b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-1531","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u8ca0\u306e\u4e8c\u9805\u5bfe\u30dd\u30a2\u30bd\u30f3: \u56de\u5e30\u30e2\u30c7\u30eb\u306e\u9078\u629e\u65b9\u6cd5<\/title>\n<meta name=\"description\" content=\"\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001\u8ca0\u306e\u4e8c\u9805\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3069\u3061\u3089\u3092\u9078\u629e\u3059\u308b\u304b\u3092\u4f8b\u3092\u6319\u3052\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, 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