{"id":5034,"date":"2026-11-11T05:43:31","date_gmt":"2026-11-10T20:43:31","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=5034"},"modified":"2026-11-13T06:06:50","modified_gmt":"2026-11-12T21:06:50","slug":"item-response-theory-basics","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/item-response-theory-basics\/","title":{"rendered":"\u5408\u8a08\u70b9\u306e\u300c1\u70b9\u300d\u306f\u540c\u3058\u91cd\u3055\u3067\u306f\u306a\u3044\uff1a\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff08IRT\uff09\u306e\u57fa\u790e"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u82e5\u624b\u533b\u5e2b<\/strong>\uff1a\u3046\u3064\u75c7\u72b6\u306e\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\uff0810\u9805\u76ee\u3001\u300c\u306f\u3044\uff0f\u3044\u3044\u3048\u300d\u3067\u7b54\u3048\u308b\uff09\u3092\u4f7f\u3063\u3066\u3001\u6cbb\u7642\u524d\u5f8c\u3067\u5408\u8a08\u70b9\u3092\u6bd4\u3079\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002A\u3055\u3093\u306f3\u70b9\u304b\u30891\u70b9\u306b\u3001B\u3055\u3093\u306f10\u70b9\u304b\u30898\u70b9\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3069\u3061\u3089\u3082\u300c2\u70b9\u6539\u5584\u300d\u3067\u3044\u3044\u3067\u3059\u3088\u306d\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7d71\u8a08\u62c5\u5f53<\/strong>\uff1a\u305d\u3053\u304c\u843d\u3068\u3057\u7a74\u306a\u3093\u3060\u3002\u5408\u8a08\u70b9\u306f\u300c\u3069\u306e\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u3066\u30821\u70b9\u300d\u3068\u6570\u3048\u3066\u3044\u308b\u3002\u3067\u3082\u3001\u300c\u6700\u8fd1\u75b2\u308c\u3084\u3059\u3044\u300d\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u306e\u3068\u3001\u300c\u6b7b\u306b\u305f\u3044\u3068\u601d\u3046\u3053\u3068\u304c\u3042\u308b\u300d\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u306e\u3068\u3067\u306f\u3001\u793a\u3057\u3066\u3044\u308b\u91cd\u3055\u304c\u307e\u3063\u305f\u304f\u9055\u3046\u3088\u306d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u82e5\u624b\u533b\u5e2b<\/strong>\uff1a\u78ba\u304b\u306b\u2026\u2026\u3002\u3067\u3082\u03b1\u4fc2\u6570\u306f0.85\u3042\u3063\u3066\u3001\u4fe1\u983c\u6027\u306f\u5341\u5206\u3060\u3068\u601d\u3063\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7d71\u8a08\u62c5\u5f53<\/strong>\uff1a\u03b1\u4fc2\u6570\u306f\u3001\u9805\u76ee\u540c\u58eb\u306e\u56de\u7b54\u306e\u4e00\u8cab\u6027\u306b\u3082\u3068\u3065\u304f\u4fe1\u983c\u6027\u306e\u6307\u6a19\u3067\u3001\u5c3a\u5ea6\u5168\u4f53\u30671\u3064\u306e\u5024\u3057\u304b\u51fa\u3066\u3053\u306a\u3044\u3002\u300c\u91cd\u75c7\u306e\u4eba\u540c\u58eb\u3092\u3069\u308c\u304f\u3089\u3044\u7d30\u304b\u304f\u533a\u5225\u3067\u304d\u308b\u304b\u300d\u307e\u3067\u306f\u6559\u3048\u3066\u304f\u308c\u306a\u3044\u3093\u3060\u3002\u5b9f\u969b\u3001B\u3055\u3093\u306e\u3088\u3046\u306b\u6e80\u70b9\u8fd1\u304f\u306e\u4eba\u304c\u305f\u304f\u3055\u3093\u3044\u308b\u3068\u3001\u91cd\u75c7\u306e\u4eba\u305f\u3061\u306e\u5dee\u304c\u307b\u3068\u3093\u3069\u898b\u3048\u306a\u304f\u306a\u308b\u3002\u3044\u308f\u3086\u308b\u5929\u4e95\u52b9\u679c\u3060\u306d\u3002<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u5408\u8a08\u70b9\u306f\u4fbf\u5229\u3060\u304c\u3001\u3059\u3079\u3066\u306e\u9805\u76ee\u3092\u300c\u540c\u3058\u91cd\u3055\u306e1\u70b9\u300d\u3068\u3057\u3066\u6570\u3048\u3066\u3044\u308b\u3002\u73fe\u5b9f\u306e\u9805\u76ee\u306b\u306f\u3001<strong>\u300c\u305d\u306e\u75c7\u72b6\u304c\u51fa\u308b\u306e\u306f\u3069\u306e\u304f\u3089\u3044\u91cd\u3044\u4eba\u304b\u3089\u304b\uff08\u96e3\u3057\u3055\uff09\u300d\u3068\u3001\u300c\u305d\u306e\u9805\u76ee\u304c\u4eba\u3092\u3069\u308c\u3060\u3051\u304f\u3063\u304d\u308a\u898b\u5206\u3051\u3089\u308c\u308b\u304b\uff08\u898b\u5206\u3051\u308b\u529b\uff09\u300d<\/strong>\u306e\u9055\u3044\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u9055\u3044\u3092\u6b63\u9762\u304b\u3089\u6271\u3046\u306e\u304c\u3001<strong>\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff08Item Response Theory\uff1aIRT\uff09<\/strong>\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001IRT\u306e\u57fa\u790e\u3068\u3057\u3066\u30011PL\u30fb2PL\u30fb3PL\u30e2\u30c7\u30eb\u3001\u9805\u76ee\u7279\u6027\u66f2\u7dda\u3001\u80fd\u529b\u03b8\u3001\u8b58\u5225\u529b\u30fb\u56f0\u96e3\u5ea6\u3001\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u307e\u3067\u3092\u3001R\u306e <code>mirt<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u624b\u3092\u52d5\u304b\u3057\u306a\u304c\u3089\u7406\u89e3\u3057\u3066\u3044\u304f\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. IRT\u3068\u306f\u4f55\u304b\uff1a\u4eba\u3068\u9805\u76ee\u3092\u300c\u540c\u3058\u7269\u5dee\u3057\u300d\u306b\u4e26\u3079\u308b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">IRT\u306e\u51fa\u767a\u70b9\u306f\u3001\u76ee\u306b\u898b\u3048\u306a\u3044\u7279\u6027\uff08\u3053\u3053\u3067\u306f\u300c\u6291\u3046\u3064\u306e\u91cd\u3055\u300d\uff09\u3092\u30011\u672c\u306e\u6570\u76f4\u7dda\u3067\u8868\u3059\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u6570\u76f4\u7dda\u4e0a\u3067\u306e\u56de\u7b54\u8005\u306e\u4f4d\u7f6e\u3092 <strong>\u03b8\uff08\u30b7\u30fc\u30bf\uff09<\/strong> \u3068\u547c\u3076\u3002\u30c6\u30b9\u30c8\u306e\u4e16\u754c\u3067\u306f\u300c\u80fd\u529b\u300d\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u304c\u3001\u81e8\u5e8a\u306e\u8cea\u554f\u7968\u3067\u306f\u300c\u6291\u3046\u3064\u306e\u91cd\u3055\u300d\u300c\u8eab\u4f53\u6a5f\u80fd\u306e\u9ad8\u3055\u300d\u306a\u3069\u3001\u6e2c\u308a\u305f\u3044\u7279\u6027\u305d\u306e\u3082\u306e\u3092\u6307\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IRT\u306e\u6700\u5927\u306e\u7279\u5fb4\u306f\u3001<strong>\u56de\u7b54\u8005\uff08\u03b8\uff09\u3068\u9805\u76ee\uff08\u96e3\u3057\u3055\uff09\u3092\u3001\u540c\u3058\u6570\u76f4\u7dda\u306e\u4e0a\u306b\u4e26\u3079\u308b<\/strong>\u70b9\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8d70\u308a\u9ad8\u8df3\u3073\u3092\u30a4\u30e1\u30fc\u30b8\u3057\u3066\u307b\u3057\u3044\u3002\u9078\u624b\u306e\u8df3\u8e8d\u529b\u3082\u3001\u30d0\u30fc\u306e\u9ad8\u3055\u3082\u3001\u540c\u3058\u300c\u30bb\u30f3\u30c1\u30e1\u30fc\u30c8\u30eb\u300d\u3067\u6e2c\u308c\u308b\u3002\u3060\u304b\u3089\u3053\u305d\u3001\u300c\u8df3\u8e8d\u529b180 cm\u306e\u9078\u624b\u304c\u3001170 cm\u306e\u30d0\u30fc\u3092\u8d8a\u3048\u308b\u78ba\u7387\u306f\u4f55\uff05\u304b\u300d\u3068\u3044\u3046\u554f\u3044\u304c\u6210\u308a\u7acb\u3064\u3002IRT\u3067\u306f\u3001\u03b8 \u304c\u9078\u624b\u306e\u8df3\u8e8d\u529b\u3001\u9805\u76ee\u306e\u56f0\u96e3\u5ea6\u304c\u30d0\u30fc\u306e\u9ad8\u3055\u306b\u3042\u305f\u308b\u3002\u6291\u3046\u3064\u5c3a\u5ea6\u306a\u3089\u3001\u300c\u6291\u3046\u3064\u306e\u91cd\u3055 \u03b8 \u306e\u4eba\u304c\u3001\u3053\u306e\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u78ba\u7387\u306f\u4f55\uff05\u304b\u300d\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u308f\u3051\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u53e4\u5178\u7684\u30c6\u30b9\u30c8\u7406\u8ad6\uff08CTT\uff09\u3068IRT\u306e\u9055\u3044<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5408\u8a08\u70b9\u3084\u03b1\u4fc2\u6570\u306b\u3082\u3068\u3065\u304f\u5f93\u6765\u306e\u8003\u3048\u65b9\u3092\u3001<strong>\u53e4\u5178\u7684\u30c6\u30b9\u30c8\u7406\u8ad6\uff08Classical Test Theory\uff1aCTT\uff09<\/strong>\u3068\u547c\u3076\u3002\u4e21\u8005\u306e\u9055\u3044\u3092\u3056\u3063\u304f\u308a\u6bd4\u3079\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><\/th><th>CTT<\/th><th>IRT<\/th><\/tr><\/thead><tbody><tr><td>\u4eba\u306e\u5f97\u70b9<\/td><td>\u5408\u8a08\u70b9<\/td><td>\u03b8\uff08\u6f5c\u5728\u7279\u6027\u306e\u63a8\u5b9a\u5024\uff09<\/td><\/tr><tr><td>\u9805\u76ee\u306e\u6027\u8cea<\/td><td>\u901a\u904e\u7387\u3001\u9805\u76ee\uff0d\u5168\u4f53\u76f8\u95a2<\/td><td>\u56f0\u96e3\u5ea6 b\u3001\u8b58\u5225\u529b a \u306a\u3069<\/td><\/tr><tr><td>\u6e2c\u5b9a\u8aa4\u5dee<\/td><td>\u5168\u54e1\u306b\u5171\u901a\u306e1\u3064\u306e\u5024\uff08\u4fe1\u983c\u6027\u304b\u3089\u8a08\u7b97\uff09<\/td><td><strong>\u03b8 \u306e\u5024\u3054\u3068\u306b\u7570\u306a\u308b<\/strong><\/td><\/tr><tr><td>\u9805\u76ee\u306e\u6027\u8cea\u306e\u3001\u96c6\u56e3\u3078\u306e\u4f9d\u5b58<\/td><td>\u5927\u304d\u3044\uff08\u96c6\u56e3\u304c\u5909\u308f\u308b\u3068\u901a\u904e\u7387\u304c\u5909\u308f\u308b\uff09<\/td><td>\u30e2\u30c7\u30eb\u304c\u6210\u308a\u7acb\u3064\u7bc4\u56f2\u3067\u306f\u5c0f\u3055\u3044\uff08\u305f\u3060\u3057\u3001\u03b8 \u306e\u539f\u70b9\u3068\u5358\u4f4d\u306e\u53d6\u308a\u65b9\u306f\u5225\u9014\u6c7a\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u7279\u306b\u91cd\u8981\u306a\u306e\u306f3\u884c\u76ee\u3067\u3042\u308b\u3002CTT\u3067\u306f\u300c\u3053\u306e\u5c3a\u5ea6\u306e\u6e2c\u5b9a\u8aa4\u5dee\u306f\u25cb\u70b9\u300d\u30681\u3064\u306e\u5024\u3067\u8a9e\u308b\u304c\u3001IRT\u3067\u306f\u300c\u8efd\u75c7\u57df\u306f\u7cbe\u5bc6\u306b\u6e2c\u308c\u308b\u304c\u3001\u91cd\u75c7\u57df\u306f\u8aa4\u5dee\u304c\u5927\u304d\u3044\u300d\u3068\u3044\u3046\u3088\u3046\u306b\u3001<strong>\u03b8 \u306e\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u6e2c\u5b9a\u7cbe\u5ea6\u304c\u9055\u3046<\/strong>\u3053\u3068\u3092\u8868\u73fe\u3067\u304d\u308b\u3002\u5192\u982d\u306e\u5929\u4e95\u52b9\u679c\u306e\u60a9\u307f\u306f\u3001\u307e\u3055\u306b\u3053\u306e\u70b9\u306b\u95a2\u308f\u3063\u3066\u3044\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u9805\u76ee\u7279\u6027\u66f2\u7dda\u30682PL\u30e2\u30c7\u30eb<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2-1. \u9805\u76ee\u7279\u6027\u66f2\u7dda\uff08ICC\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6a2a\u8ef8\u306b \u03b8\u3001\u7e26\u8ef8\u306b\u300c\u305d\u306e\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u78ba\u7387\u300d\u3092\u3068\u3063\u3066\u63cf\u3044\u305f\u66f2\u7dda\u3092\u3001<strong>\u9805\u76ee\u7279\u6027\u66f2\u7dda\uff08Item Characteristic Curve\uff1aICC\uff09<\/strong>\u3068\u547c\u3076\u3002\u03b8 \u304c\u9ad8\u3044\uff08\u6291\u3046\u3064\u304c\u91cd\u3044\uff09\u4eba\u307b\u3069\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u3084\u3059\u3044\u306e\u3067\u3001\u66f2\u7dda\u306f\u53f3\u4e0a\u304c\u308a\u306eS\u5b57\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306eS\u5b57\u3092\u8868\u3059\u4ee3\u8868\u7684\u306a\u30e2\u30c7\u30eb\u304c\u3001<strong>2\u30d1\u30e9\u30e1\u30fc\u30bf\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u30e2\u30c7\u30eb\uff082PL\uff09<\/strong>\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u899a\u3048\u3066\u307b\u3057\u3044\u5f0f\u306f\u3001\u307b\u307c\u3053\u308c1\u3064\u3060\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f0f\u2460\uff082PL\u30e2\u30c7\u30eb\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_j(\\theta) = \\frac{1}{1 + \\exp{-a_j(\\theta &#8211; b_j)}}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067 $P_j(\\theta)$ \u306f\u3001\u03b8 \u306e\u4eba\u304c\u9805\u76ee $j$ \u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u78ba\u7387\u3067\u3042\u308b\u3002\u9805\u76ee\u3054\u3068\u306b2\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3064\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u6ce8\uff09\u65e5\u672c\u8a9e\u306e\u6559\u79d1\u66f8\u3067\u306f\u3001\u5f0f\u2460\u306e $a_j$ \u306e\u524d\u306b1.7\u3092\u639b\u3051\u305f\u5f62\uff08$1.7a_j(\\theta &#8211; b_j)$\uff09\u304c\u3088\u304f\u767b\u5834\u3059\u308b\u3002\u3053\u306e1.7\u306f\u300c\u5c3a\u5ea6\u5b9a\u6570 D\u300d\u3068\u547c\u3070\u308c\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u66f2\u7dda\u3092\u6b63\u898f\u5206\u5e03\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff08\u6b63\u898f\u30aa\u30fc\u30b8\u30d6\uff09\u306b\u307b\u307c\u91cd\u306d\u308b\u305f\u3081\u306e\u5024\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u4f7f\u3046 <code>mirt<\/code> \u306f1.7\u3092\u639b\u3051\u306a\u3044\u5f0f\u2460\u306e\u5f62\u3067\u63a8\u5b9a\u3059\u308b\u306e\u3067\u3001\u6559\u79d1\u66f8\u306e\u8b58\u5225\u529b\u3068\u6bd4\u3079\u308b\u3068\u304d\u306f\u3001<code>mirt<\/code> \u306e\u5024\u30921.7\u3067\u5272\u308b\u3068\u304a\u304a\u3088\u305d\u5bfe\u5fdc\u3059\u308b\u3002\u56f0\u96e3\u5ea6 b \u306f\u3069\u3061\u3089\u306e\u5f62\u3067\u3082\u5909\u308f\u3089\u306a\u3044\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u56f0\u96e3\u5ea6 $b_j$<\/strong>\uff1a\u66f2\u7dda\u306e\u300c\u4f4d\u7f6e\u300d\u3092\u6c7a\u3081\u308b\u3002\u03b8 = $b_j$ \u306e\u3068\u304d\u3001\u78ba\u7387\u304c\u3061\u3087\u3046\u30690.5\u306b\u306a\u308b\u3002\u8d70\u308a\u9ad8\u8df3\u3073\u3067\u3044\u3048\u3070\u30d0\u30fc\u306e\u9ad8\u3055\u3067\u3001\u6291\u3046\u3064\u5c3a\u5ea6\u306a\u3089\u300c\u305d\u306e\u75c7\u72b6\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u78ba\u7387\u304c\u4e94\u5206\u4e94\u5206\uff080.5\uff09\u306b\u306a\u308b\u306e\u306f\u3001\u3069\u306e\u304f\u3089\u3044\u91cd\u3044\u4eba\u304b\u300d\u3092\u8868\u3059\u3002$b_j$ \u304c\u5927\u304d\u3044\u9805\u76ee\u307b\u3069\u3001\u304b\u306a\u308a\u91cd\u75c7\u306e\u4eba\u3067\u306a\u3044\u3068\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u306b\u304f\u3044\u3002\u306a\u304a\u3001\u03b8 \u304c $b_j$ \u3088\u308a\u4f4e\u3044\u4eba\u3067\u3082\u3001\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u78ba\u7387\u306f0\u3067\u306f\u306a\u3044\u70b9\u306b\u6ce8\u610f\u3057\u305f\u3044\u3002<\/li>\n\n\n\n<li><strong>\u8b58\u5225\u529b $a_j$<\/strong>\uff1a\u66f2\u7dda\u306e\u300c\u50be\u304d\u300d\u3092\u6c7a\u3081\u308b\u3002$a_j$ \u304c\u5927\u304d\u3044\u307b\u3069\u3001\u03b8 = $b_j$ \u306e\u4ed8\u8fd1\u3067\u66f2\u7dda\u304c\u6025\u306b\u7acb\u3061\u4e0a\u304c\u308b\u3002\u3064\u307e\u308a\u3001\u30d0\u30fc\u306e\u9ad8\u3055\u4ed8\u8fd1\u306b\u3044\u308b\u4eba\u3092\u300c\u8d8a\u3048\u3089\u308c\u308b\u4eba\u300d\u3068\u300c\u8d8a\u3048\u3089\u308c\u306a\u3044\u4eba\u300d\u306b\u304f\u3063\u304d\u308a\u5206\u3051\u3089\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u56f31\u306f\u3001\u56f0\u96e3\u5ea6\u3068\u8b58\u5225\u529b\u3092\u5909\u3048\u305f\u3068\u304d\u306bICC\u304c\u3069\u3046\u5909\u308f\u308b\u304b\u3092\u793a\u3057\u305f\u3082\u306e\u3067\u3042\u308b\uff08\u56f3\u3092\u63cf\u304fR\u30b3\u30fc\u30c9\u306f\u300c6. R\u306b\u3088\u308b\u5b9f\u88c5\u300d\u306eStep 0\u306b\u8f09\u305b\u3066\u3044\u308b\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"632\" height=\"481\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-1.png\" alt=\"\" class=\"wp-image-5037\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-1.png 632w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-1-300x228.png 300w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u56f31\uff1a\u56f0\u96e3\u5ea6 b \u3068\u8b58\u5225\u529b a \u306b\u3088\u308bICC\u306e\u5909\u5316<\/strong>\uff08\u5de6\uff1ab \u3060\u3051\u3092\u5909\u3048\u308b\u3068\u66f2\u7dda\u304c\u5de6\u53f3\u306b\u5e73\u884c\u79fb\u52d5\u3059\u308b\uff0f\u53f3\uff1aa \u3060\u3051\u3092\u5909\u3048\u308b\u3068\u50be\u304d\u304c\u5909\u308f\u308b\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5de6\u56f3\u3067\u306f\u3001\u8b58\u5225\u529b\u3092 a = 1.5 \u306b\u305d\u308d\u3048\u305f\u307e\u307e\u3001\u56f0\u96e3\u5ea6\u3060\u3051\u3092 b = \u22121, 0, 1 \u3068\u5909\u3048\u3066\u3044\u308b\u30023\u672c\u306e\u66f2\u7dda\u306f\u540c\u3058\u5f62\u306e\u307e\u307e\u5de6\u53f3\u306b\u305a\u308c\u3001\u305d\u308c\u305e\u308c \u03b8 = b \u306e\u4f4d\u7f6e\u3067\u3001\u78ba\u73870.5\u306e\u7070\u8272\u306e\u7dda\u3092\u6a2a\u5207\u3063\u3066\u3044\u308b\u3002\u56f0\u96e3\u5ea6\u304c1\u4e0a\u304c\u308b\u3068\u3001\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u304c0.5\u306b\u306a\u308b \u03b8 \u304c\u3061\u3087\u3046\u30691\u3060\u3051\u53f3\uff08\u91cd\u75c7\u5074\uff09\u306b\u305a\u308c\u308b\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53f3\u56f3\u3067\u306f\u3001\u56f0\u96e3\u5ea6\u3092 b = 0 \u306b\u305d\u308d\u3048\u305f\u307e\u307e\u3001\u8b58\u5225\u529b\u3060\u3051\u3092 a = 0.5, 1.5, 3.0 \u3068\u5909\u3048\u3066\u3044\u308b\u30023\u672c\u3068\u3082 \u03b8 = 0 \u3067\u78ba\u73870.5\u3092\u901a\u308b\u70b9\u306f\u540c\u3058\u3060\u304c\u3001\u50be\u304d\u304c\u307e\u3063\u305f\u304f\u9055\u3046\u3002a = 3.0\uff08\u70b9\u7dda\uff09\u306f \u03b8 = 0 \u306e\u524d\u5f8c\u3067\u78ba\u7387\u304c\u307b\u307c0\u304b\u3089\u307b\u307c1\u3078\u4e00\u6c17\u306b\u8df3\u306d\u4e0a\u304c\u308a\u3001\u03b8 \u304c0\u3088\u308a\u5c11\u3057\u4f4e\u3044\u4eba\u3068\u5c11\u3057\u9ad8\u3044\u4eba\u3092\u3001\u306f\u3063\u304d\u308a\u5206\u3051\u3089\u308c\u308b\u3002\u4e00\u65b9\u3001a = 0.5\uff08\u5b9f\u7dda\uff09\u306f\u306a\u3060\u3089\u304b\u3067\u3001\u03b8 = 4 \u3068\u3044\u3046\u6975\u7aef\u306b\u91cd\u3044\u4eba\u3067\u3082\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u306f0.9\u306b\u5c4a\u304b\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8b58\u5225\u529b\u306e\u4f4e\u3044\u9805\u76ee\u306f\u3001\u03b8 \u304c\u4e0a\u304c\u3063\u3066\u3082\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u304c\u3086\u3063\u304f\u308a\u3068\u3057\u304b\u4e0a\u304c\u3089\u306a\u3044\u3002\u305f\u3068\u3048\u3070\u300c\u98df\u6b32\u304c\u306a\u3044\u300d\u3068\u3044\u3046\u9805\u76ee\u306f\u3001\u3046\u3064\u4ee5\u5916\u306e\u7406\u7531\uff08\u80c3\u8178\u306e\u4e0d\u8abf\u306a\u3069\uff09\u3067\u3082\u300e\u306f\u3044\u300f\u306b\u306a\u308a\u5f97\u308b\u306e\u3067\u3001\u6291\u3046\u3064\u306e\u91cd\u3055\u3092\u306f\u3063\u304d\u308a\u3068\u306f\u898b\u5206\u3051\u306b\u304f\u3044\u3001\u3068\u3044\u3046\u3053\u3068\u304c\u8d77\u3053\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u03b8 \u306f\u306a\u305c\u300c\u5e73\u57470\u3001\u6a19\u6e96\u504f\u5dee1\u300d\u306a\u306e\u304b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u591a\u304f\u306eIRT\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306f\u3001\u03b8 \u3092\u300c\u5e73\u57470\u3001\u6a19\u6e96\u504f\u5dee1\u300d\u306e\u5c3a\u5ea6\u3067\u8868\u3059\u3002\u3053\u308c\u306f\u3001\u03b8 \u306b\u3082\u3068\u3082\u3068\u6c7a\u307e\u3063\u305f\u539f\u70b9\u3084\u5358\u4f4d\u304c\u3042\u308b\u304b\u3089\u3067\u306f\u306a\u3044\u3002\u03b8 \u306f\u76ee\u306b\u898b\u3048\u306a\u3044\u91cf\u306a\u306e\u3067\u3001<strong>\u3069\u3053\u30920\u70b9\u3068\u3057\u3001\u4f55\u30921\u76ee\u76db\u308a\u3068\u3059\u308b\u304b\u306f\u4efb\u610f<\/strong>\u3067\u3042\u308b\u3002\u305d\u3053\u3067\u63a8\u5b9a\u306e\u3068\u304d\u306b\u3001\u300c\u3053\u306e\u96c6\u56e3\u306e \u03b8 \u306e\u5206\u5e03\u306f\u5e73\u57470\u3001\u5206\u65631\u300d\u3068\u6c7a\u3081\u3066\u3001\u7269\u5dee\u3057\u306e\u539f\u70b9\u3068\u76ee\u76db\u308a\u3092\u56fa\u5b9a\u3057\u3066\u3044\u308b\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6e29\u5ea6\u306b\u305f\u3068\u3048\u308b\u3068\u3001\u6442\u6c0f\u3068\u83ef\u6c0f\u306e\u3069\u3061\u3089\u3067\u6e2c\u3063\u3066\u3082\u3001\u6691\u3044\u65e5\u304c\u5bd2\u3044\u65e5\u3088\u308a\u6691\u3044\u3068\u3044\u3046\u95a2\u4fc2\u306f\u5909\u308f\u3089\u306a\u3044\u3002\u540c\u3058\u3088\u3046\u306b\u3001\u03b8 = 1.0 \u306f\u300c\u3053\u306e\u96c6\u56e3\u306e\u5e73\u5747\u3088\u308a1\u6a19\u6e96\u504f\u5dee\u3076\u3093\u91cd\u3044\u300d\u3068\u3044\u3046\u610f\u5473\u3067\u3001\u7d76\u5bfe\u7684\u306a\u91cd\u75c7\u5ea6\u306e\u57fa\u6e96\u3067\u306f\u306a\u3044\u70b9\u306b\u6ce8\u610f\u3057\u305f\u3044\u3002\u306a\u304a\u3001PROMIS\u306e\u3088\u3046\u306b\u3001\u57fa\u6e96\u3068\u306a\u308b\u96c6\u56e3\u3067\u5e73\u574750\u30fb\u6a19\u6e96\u504f\u5dee10\u306b\u5909\u63db\u3057\u305f\u30b9\u30b3\u30a2\uff08T\u30b9\u30b3\u30a2\uff09\u3092\u7528\u3044\u308b\u3053\u3068\u3082\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-2101947315\" class=\"biost- biost-entity-placement\" role=\"region\" aria-label=\"\u5e83\u544a\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">3. 1PL\u30fb2PL\u30fb3PL\u306e\u95a2\u4fc2\uff1a\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8db3\u3057\u5f15\u304d\u3057\u305f\u300c\u89aa\u621a\u300d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">2PL\u3092\u57fa\u6e96\u306b\u3059\u308b\u3068\u30011PL\u30683PL\u306f\u6b21\u306e\u3088\u3046\u306b\u6574\u7406\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1PL\uff081\u30d1\u30e9\u30e1\u30fc\u30bf\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u30e2\u30c7\u30eb\uff09<\/strong>\uff1a\u8b58\u5225\u529b $a$ \u3092<strong>\u5168\u9805\u76ee\u3067\u5171\u901a<\/strong>\u306b\u3057\u305f\u30e2\u30c7\u30eb\u3002\u9805\u76ee\u3054\u3068\u306b\u9055\u3046\u306e\u306f\u56f0\u96e3\u5ea6 $b$ \u3060\u3051\u306b\u306a\u308b\u3002ICC\u306f\u3059\u3079\u3066\u540c\u3058\u50be\u304d\u3067\u3001\u5de6\u53f3\u306e\u4f4d\u7f6e\u3060\u3051\u304c\u9055\u3046\u3002<\/li>\n\n\n\n<li><strong>2PL<\/strong>\uff1a\u8b58\u5225\u529b $a$ \u3092<strong>\u9805\u76ee\u3054\u3068\u306b<\/strong>\u63a8\u5b9a\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>3PL\uff083\u30d1\u30e9\u30e1\u30fc\u30bf\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u30e2\u30c7\u30eb\uff09<\/strong>\uff1a2PL\u306b\u3001\u66f2\u7dda\u306e\u4e0b\u9650 $c$\uff08\u5f53\u3066\u63a8\u91cf\u30d1\u30e9\u30e1\u30fc\u30bf\uff09\u3092\u52a0\u3048\u305f\u30e2\u30c7\u30eb\u3002\u03b8 \u304c\u3069\u308c\u307b\u3069\u4f4e\u304f\u3066\u3082\u3001\u78ba\u7387\u304c $c$ \u3088\u308a\u4e0b\u304c\u3089\u306a\u3044\u3002\u591a\u80a2\u9078\u629e\u5f0f\u306e\u5b66\u529b\u30c6\u30b9\u30c8\u3067\u3001\u300c4\u629e\u306a\u3089\u3001\u307e\u3063\u305f\u304f\u308f\u304b\u3089\u306a\u304f\u3066\u30824\u5206\u306e1\u304f\u3089\u3044\u306f\u5f53\u305f\u308b\u300d\u72b6\u6cc1\u3092\u8868\u3059\u305f\u3081\u306b\u8003\u3048\u3089\u308c\u305f\u30023PL\u3067\u306f\u3001\u03b8 = $b$ \u306e\u3068\u304d\u306e\u78ba\u7387\u306f0.5\u3067\u306f\u306a\u304f $(1+c)\/2$ \u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"632\" height=\"481\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-2.png\" alt=\"\" class=\"wp-image-5038\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-2.png 632w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-2-300x228.png 300w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u56f32\uff1a1PL\u30fb2PL\u30fb3PL\u306eICC\u306e\u6bd4\u8f03<\/strong>\uff081PL\uff1a\u50be\u304d\u304c\u3059\u3079\u3066\u540c\u3058\uff0f2PL\uff1a\u50be\u304d\u304c\u9805\u76ee\u3054\u3068\u306b\u9055\u3046\uff0f3PL\uff1a\u5de6\u7aef\u304c0\u307e\u3067\u4e0b\u304c\u3089\u306a\u3044\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56f32\u3067\u306f\u3001\u56f0\u96e3\u5ea6\u304c b = \u22121\uff08\u5b9f\u7dda\uff09\u30010\uff08\u7834\u7dda\uff09\u30011\uff08\u70b9\u7dda\uff09\u306e3\u9805\u76ee\u3092\u63cf\u3044\u3066\u3044\u308b\u30021PL\u3067\u306f\u8b58\u5225\u529b\u3092\u3059\u3079\u3066 a = 1.2 \u306b\u305d\u308d\u3048\u30012PL\u30683PL\u3067\u306f\u5b9f\u7dda\u30fb\u7834\u7dda\u30fb\u70b9\u7dda\u306e\u9806\u306b a = 0.6, 1.5, 3.0 \u3068\u3057\u3066\u3044\u308b\u30023PL\u306e\u4e0b\u9650\u306f c = 0.2 \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1PL\uff08\u5de6\uff09<\/strong>\uff1a3\u672c\u306e\u66f2\u7dda\u306f\u540c\u3058\u50be\u304d\u3067\u3001\u5de6\u53f3\u306e\u4f4d\u7f6e\u3060\u3051\u304c\u9055\u3046\u3002\u305d\u306e\u305f\u3081<strong>\u66f2\u7dda\u304c\u4ea4\u308f\u308b\u3053\u3068\u306f\u306a\u304f<\/strong>\u3001\u3069\u306e \u03b8 \u306e\u4eba\u306b\u3068\u3063\u3066\u3082\u300c\u5b9f\u7dda\u306e\u9805\u76ee\u304c\u4e00\u756a\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u3084\u3059\u304f\u3001\u70b9\u7dda\u306e\u9805\u76ee\u304c\u4e00\u756a\u7b54\u3048\u306b\u304f\u3044\u300d\u3068\u3044\u3046\u9806\u756a\u304c\u5909\u308f\u3089\u306a\u3044\u3002<\/li>\n\n\n\n<li><strong>2PL\uff08\u4e2d\u592e\uff09<\/strong>\uff1a\u50be\u304d\u304c\u9805\u76ee\u3054\u3068\u306b\u9055\u3046\u306e\u3067\u3001<strong>\u66f2\u7dda\u304c\u4ea4\u5dee\u3059\u308b<\/strong>\u3002\u56f0\u96e3\u5ea6\u304c\u6700\u3082\u4f4e\u3044\u5b9f\u7dda\u306e\u9805\u76ee\u306f\u3001\u03b8 \u304c\u4f4e\u3044\u4eba\u3067\u306f\u4e00\u756a\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u3084\u3059\u3044\u304c\u3001\u03b8 \u304c1.5\u3092\u8d85\u3048\u305f\u3042\u305f\u308a\u304b\u3089\u306f\u3001\u56f0\u96e3\u5ea6\u304c\u9ad8\u3044\u306f\u305a\u306e\u70b9\u7dda\u306e\u9805\u76ee\u306e\u307b\u3046\u304c\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308b\u3002\u300c\u3069\u306e\u9805\u76ee\u304c\u7b54\u3048\u3084\u3059\u3044\u304b\u300d\u306e\u9806\u756a\u304c\u3001\u03b8 \u306e\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u5165\u308c\u66ff\u308f\u308b\u306e\u3067\u3042\u308b\u30022PL\u306e\u56f0\u96e3\u5ea6\u3092\u89e3\u91c8\u3059\u308b\u3068\u304d\u306f\u3001\u300c\u78ba\u7387\u304c0.5\u306b\u306a\u308b\u4f4d\u7f6e\u300d\u3068\u3044\u3046\u5b9a\u7fa9\u306b\u7acb\u3061\u8fd4\u308b\u3053\u3068\u304c\u5927\u5207\u3060\u3002<\/li>\n\n\n\n<li><strong>3PL\uff08\u53f3\uff09<\/strong>\uff1a\u3069\u306e\u66f2\u7dda\u3082\u3001\u5de6\u7aef\u304c\u7070\u8272\u306e\u7dda\uff08c = 0.2\uff09\u3088\u308a\u4e0b\u306b\u4e0b\u304c\u3089\u306a\u3044\u3002\u03b8 \u304c\u975e\u5e38\u306b\u4f4e\u304f\u3066\u3082\u30012\u5272\u306e\u78ba\u7387\u3067\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u70b9\u7dda\u306e\u9805\u76ee\u306f \u03b8 = b = 1 \u306e\u3068\u304d\u306b\u78ba\u7387\u304c0.5\u3067\u306f\u306a\u304f\u3001$(1 + 0.2)\/2 = 0.6$ \u306b\u306a\u3063\u3066\u3044\u308b\u30023PL\u3067\u306f\u300c\u56f0\u96e3\u5ea6 = \u78ba\u73870.5\u306e\u4f4d\u7f6e\u300d\u3068\u3044\u3046\u8aad\u307f\u65b9\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u70b9\u306b\u6ce8\u610f\u3057\u305f\u3044\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u81e8\u5e8a\u306e\u8cea\u554f\u7968\uff08\u60a3\u8005\u5831\u544a\u30a2\u30a6\u30c8\u30ab\u30e0\uff1aPRO\uff09\u3067\u306f\u3001\u300c\u308f\u304b\u3089\u306a\u3044\u304b\u3089\u5f53\u3066\u305a\u3063\u307d\u3046\u3067\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u300d\u3053\u3068\u306f\u60f3\u5b9a\u3057\u306b\u304f\u3044\u3002\u305d\u306e\u305f\u3081\u3001\u4e8c\u5024\u9805\u76ee\u306e\u8cea\u554f\u7968\u3067\u306f<strong>1PL\u304b2PL\u304c\u4f7f\u308f\u308c\u308b\u306e\u304c\u4e00\u822c\u7684<\/strong>\u3067\u30013PL\u3092\u4f7f\u3046\u5834\u9762\u306f\u307e\u308c\u3067\u3042\u308b\u30023PL\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u591a\u3044\u3076\u3093\u63a8\u5b9a\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308a\u3084\u3059\u3044\u306e\u3067\u3001\u300c\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u591a\u3044\u307b\u3046\u304c\u7cbe\u5bc6\u305d\u3046\u3060\u304b\u3089\u300d\u3068\u3044\u3046\u7406\u7531\u3067\u6a5f\u68b0\u7684\u306b\u9078\u3076\u306e\u306f\u907f\u3051\u305f\u3044\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1aRasch\u30e2\u30c7\u30eb\u3068IRT\u306e1PL\u306f\u540c\u3058\u3082\u306e\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1PL\u3068\u3088\u304f\u4f3c\u305f\u30e2\u30c7\u30eb\u306b\u3001<strong>Rasch\u30e2\u30c7\u30eb<\/strong>\u304c\u3042\u308b\u3002\u6570\u5f0f\u306e\u5f62\u306f\u307b\u307c\u540c\u3058\u3067\u3001\u5b9f\u969b\u3001R\u306e <code>mirt<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u3082 <code>itemtype = \"Rasch\"<\/code> \u3068\u6307\u5b9a\u3059\u308c\u3070\u30011PL\u3068\u540c\u7b49\u306e\u30e2\u30c7\u30eb\u3092\u63a8\u5b9a\u3067\u304d\u308b\uff08\u8b58\u5225\u529b\u30921\u306b\u56fa\u5b9a\u3057\u3001\u305d\u306e\u304b\u308f\u308a\u306b \u03b8 \u306e\u5206\u6563\u3092\u63a8\u5b9a\u3059\u308b\u3002\u5168\u9805\u76ee\u306e\u8b58\u5225\u529b\u3092\u7b49\u3057\u304f\u3057\u305f2PL\u3068\u540c\u3058\u5f53\u3066\u306f\u307e\u308a\u306b\u306a\u308b\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305f\u3060\u3057\u3001\u80cc\u666f\u306b\u3042\u308b<strong>\u8003\u3048\u65b9<\/strong>\u306f\u5927\u304d\u304f\u9055\u3046\u3002IRT\u306e\u7acb\u5834\u3067\u306f\u3001\u300c\u30c7\u30fc\u30bf\u3092\u3046\u307e\u304f\u8aac\u660e\u3067\u304d\u308b\u30e2\u30c7\u30eb\u3092\u9078\u3076\u300d\u306e\u3067\u3001\u5f53\u3066\u306f\u307e\u308a\u304c\u60aa\u3051\u308c\u30702PL\u30843PL\u306b\u5207\u308a\u66ff\u3048\u308b\u3002\u4e00\u65b9\u3001Rasch\u30e2\u30c7\u30eb\u306e\u7acb\u5834\u3067\u306f\u3001\u300c\u5168\u9805\u76ee\u306e\u8b58\u5225\u529b\u304c\u7b49\u3057\u3044\u300d\u3053\u3068\u3092\u3001\u826f\u3044\u5c3a\u5ea6\u304c\u6e80\u305f\u3059\u3079\u304d\u6761\u4ef6\u3068\u8003\u3048\u308b\u3002\u305d\u306e\u305f\u3081\u3001\u30e2\u30c7\u30eb\u306b\u5408\u308f\u306a\u3044\u9805\u76ee\u306f\u3001\u5c3a\u5ea6\u304b\u3089\u5916\u3059\u30fb\u4f5c\u308a\u76f4\u3059\u5bfe\u8c61\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6d0b\u670d\u306b\u305f\u3068\u3048\u308b\u306a\u3089\u3001IRT\u306f\u300c\u4f53\u306b\u5408\u308f\u305b\u3066\u670d\u3092\u4ed5\u7acb\u3066\u76f4\u3059\u300d\u3001Rasch\u306f\u300c\u6c7a\u3081\u3089\u308c\u305f\u578b\u7d19\u306b\u4f53\u3092\u5408\u308f\u305b\u308b\uff08\u5408\u308f\u306a\u3044\u9805\u76ee\u306f\u935b\u3048\u76f4\u3059\uff09\u300d\u3068\u3044\u3046\u767a\u60f3\u3067\u3042\u308b\u3002\u3069\u3061\u3089\u304c\u6b63\u3057\u3044\u3068\u3044\u3046\u3088\u308a\u3001\u5c3a\u5ea6\u958b\u767a\u306e\u76ee\u7684\u306b\u3088\u3063\u3066\u4f7f\u3044\u5206\u3051\u3089\u308c\u3066\u3044\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u300c\u306f\u3044\uff0f\u3044\u3044\u3048\u300d\u4ee5\u5916\u306e\u8cea\u554f\u7968\u306f\u3069\u3046\u3059\u308b\u304b\uff08\u6bb5\u968e\u53cd\u5fdc\u30e2\u30c7\u30eb\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u81e8\u5e8a\u306e\u8cea\u554f\u7968\u306f\u3001\u300c\u307e\u3063\u305f\u304f\u306a\u3044\uff0f\u3068\u304d\u3069\u304d\uff0f\u3088\u304f\u3042\u308b\uff0f\u3044\u3064\u3082\u300d\u306e\u3088\u3046\u306a\u591a\u6bb5\u968e\uff08\u30ea\u30c3\u30ab\u30fc\u30c8\u5f62\u5f0f\uff09\u306e\u56de\u7b54\u304c\u591a\u3044\u3002\u3053\u306e\u5834\u5408\u306b\u3088\u304f\u4f7f\u308f\u308c\u308b\u306e\u304c\u3001<strong>\u6bb5\u968e\u53cd\u5fdc\u30e2\u30c7\u30eb\uff08Graded Response Model\uff1aGRM\uff09<\/strong>\u3067\u3042\u308b\uff08Samejima\u304c\u63d0\u6848\u3057\u305f\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GRM\u306f\u30012PL\u3092\u591a\u6bb5\u968e\u306b\u5e83\u3052\u305f\u30e2\u30c7\u30eb\u3068\u8003\u3048\u308b\u3068\u308f\u304b\u308a\u3084\u3059\u3044\u3002\u300c\u300e\u3068\u304d\u3069\u304d\u300f\u4ee5\u4e0a\u304b\u300d\u300c\u300e\u3088\u304f\u3042\u308b\u300f\u4ee5\u4e0a\u304b\u300d\u300c\u300e\u3044\u3064\u3082\u300f\u304b\u300d\u3068\u3044\u3046\u5883\u76ee\u3054\u3068\u306b2PL\u306e\u3088\u3046\u306aS\u5b57\u66f2\u7dda\u3092\u8003\u3048\u3001\u5883\u76ee\u3054\u3068\u306b\u56f0\u96e3\u5ea6\u3092\u6301\u305f\u305b\u308b\uff08\u8b58\u5225\u529b\u306f\u9805\u76ee\u3054\u3068\u306b1\u3064\uff09\u3002\u672c\u8a18\u4e8b\u3067\u5b66\u3076ICC\u30fb\u8b58\u5225\u529b\u30fb\u56f0\u96e3\u5ea6\u30fb\u60c5\u5831\u91cf\u306e\u8003\u3048\u65b9\u306f\u3001GRM\u3067\u3082\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u3002<code>mirt<\/code> \u3067\u306f <code>itemtype = \"graded\"<\/code> \u3068\u6307\u5b9a\u3059\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u60c5\u5831\u91cf\uff1a\u300c\u3069\u3053\u3092\u7cbe\u5bc6\u306b\u6e2c\u308c\u308b\u5c3a\u5ea6\u304b\u300d\u304c\u898b\u3048\u308b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4-1. \u9805\u76ee\u60c5\u5831\u91cf\u3068\u30c6\u30b9\u30c8\u60c5\u5831\u91cf<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">IRT\u306e\u3082\u30461\u3064\u306e\u67f1\u304c\u3001<strong>\u60c5\u5831\u91cf\uff08information\uff09<\/strong>\u3067\u3042\u308b\u3002\u9805\u76ee\u60c5\u5831\u91cf\u306f\u3001\u300c\u305d\u306e\u9805\u76ee\u304c\u3001\u03b8 \u306e\u3069\u306e\u3042\u305f\u308a\u306e\u4eba\u3092\u533a\u5225\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u304b\u300d\u3092\u8868\u3059\u66f2\u7dda\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2PL\u306e\u9805\u76ee\u60c5\u5831\u91cf\u306f\u3001<strong>\u03b8 = $b_j$\uff08\u56f0\u96e3\u5ea6\uff09\u306e\u4ed8\u8fd1\u3067\u6700\u5927\u306b\u306a\u308a\u3001\u305d\u306e\u9ad8\u3055\u306f\u8b58\u5225\u529b $a_j$ \u304c\u5927\u304d\u3044\u307b\u3069\u9ad8\u304f\u306a\u308b<\/strong>\u3002\u3064\u307e\u308a\u3001\u56f0\u96e3\u5ea6\u306f\u300c\u3069\u3053\u306b\u30d4\u30f3\u30c8\u304c\u5408\u3046\u304b\u300d\u3001\u8b58\u5225\u529b\u306f\u300c\u3069\u308c\u3060\u3051\u304f\u3063\u304d\u308a\u898b\u3048\u308b\u304b\u300d\u3092\u6c7a\u3081\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u9805\u76ee\u306e\u60c5\u5831\u91cf\u3092\u8db3\u3057\u5408\u308f\u305b\u305f\u3082\u306e\u304c\u3001<strong>\u30c6\u30b9\u30c8\u60c5\u5831\u91cf $I(\\theta)$<\/strong> \u3067\u3042\u308b\u3002\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u304b\u3089\u306f\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\u306e\u6a19\u6e96\u8aa4\u5dee\uff08SE\uff09\u304c\u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f0f\u2461\uff08\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$SE(\\theta) \\approx \\frac{1}{\\sqrt{I(\\theta)}}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u60c5\u5831\u91cf\u304c\u591a\u3044 \u03b8 \u306e\u7bc4\u56f2\u307b\u3069\u3001\u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\u3001\u6e2c\u5b9a\u304c\u7cbe\u5bc6\u306b\u306a\u308b\u3002\u3053\u308c\u304c\u3001\u30b3\u30e9\u30e0\u3067\u8ff0\u3079\u305f\u300cIRT\u3067\u306f \u03b8 \u306e\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u6e2c\u5b9a\u7cbe\u5ea6\u304c\u9055\u3046\u300d\u3053\u3068\u306e\u6b63\u4f53\u3067\u3042\u308b\u3002\uff08\u6b63\u78ba\u306b\u306f\u3001\u3053\u306e\u95a2\u4fc2\u306f\u60c5\u5831\u91cf\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u3068\u304d\u306e\u8fd1\u4f3c\u3068\u3057\u3066\u6210\u308a\u7acb\u3064\u3002\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"632\" height=\"481\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-4.png\" alt=\"\" class=\"wp-image-5040\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-4.png 632w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-4-300x228.png 300w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u56f33\uff1a\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u66f2\u7dda\uff08\u9752\u306e\u5b9f\u7dda\u3001\u5de6\u306e\u76ee\u76db\u308a\uff09\u3068\u6a19\u6e96\u8aa4\u5dee\u66f2\u7dda\uff08\u8d64\u306e\u7834\u7dda\u3001\u53f3\u306e\u76ee\u76db\u308a\uff09<\/strong>\uff08\u300c6. R\u306b\u3088\u308b\u5b9f\u88c5\u300d\u306eStep 5\u3067\u3001\u7591\u4f3c\u30c7\u30fc\u30bf\u306b2PL\u3092\u5f53\u3066\u306f\u3081\u305f\u7d50\u679c\u304b\u3089\u63cf\u3044\u305f\u3082\u306e\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9752\u306e\u60c5\u5831\u91cf\u66f2\u7dda\u306f\u3001\u03b8 = \u22121.17 \u3067\u5c71\u306e\u9802\u4e0a\uff08\u60c5\u5831\u91cf3.75\uff09\u3092\u8fce\u3048\u3001\u305d\u3053\u304b\u3089\u96e2\u308c\u308b\u307b\u3069\u4f4e\u304f\u306a\u308b\u3002\u8d64\u306e\u6a19\u6e96\u8aa4\u5dee\u66f2\u7dda\u306f\u3001\u3061\u3087\u3046\u3069\u305d\u306e\u9006\u306e\u5f62\u3067\u3001\u5c71\u306e\u9802\u4e0a\u4ed8\u8fd1\u3067\u6700\u3082\u5c0f\u3055\u304f\uff08\u7d040.52\uff09\u3001\u5c71\u304b\u3089\u96e2\u308c\u308b\u307b\u3069\u5927\u304d\u304f\u306a\u308b\u3002\u5f0f\u2461\u306e\u3068\u304a\u308a\u3001\u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\u306f\u8868\u88cf\u4e00\u4f53\u306e\u95a2\u4fc2\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ce8\u76ee\u3057\u3066\u307b\u3057\u3044\u306e\u306f\u3001\u5c71\u304c\u5de6\u53f3\u5bfe\u79f0\u306e\u4f4d\u7f6e\u3067\u306f\u306a\u304f\u3001\u03b8 \u306e\u4f4e\u3044\u5074\uff08\u8efd\u75c7\u57df\uff09\u306b\u5bc4\u3063\u3066\u3044\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u03b8 \u304c2\u3092\u8d85\u3048\u308b\u91cd\u75c7\u57df\u3067\u306f\u60c5\u5831\u91cf\u304c0.5\u3092\u4e0b\u56de\u308a\u3001\u6a19\u6e96\u8aa4\u5dee\u306f\u6025\u6fc0\u306b\u5927\u304d\u304f\u306a\u308b\u3002\u03b8 = 4 \u3067\u306f\u3001\u6a19\u6e96\u8aa4\u5dee\u304c4.8\u306b\u307e\u3067\u9054\u3057\u3066\u3044\u308b\uff08\u6570\u5024\u306f <code>testinfo()<\/code> \u3067\u78ba\u8a8d\u3057\u305f\uff09\u3002\u03b8 \u306e\u6a19\u6e96\u504f\u5dee\u304c1\u3067\u3042\u308b\u3053\u3068\u3092\u8003\u3048\u308b\u3068\u3001\u3053\u308c\u306f\u300c\u91cd\u75c7\u57df\u306e\u4eba\u306b\u3064\u3044\u3066\u306f\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\u304c\u307b\u3068\u3093\u3069\u5f53\u3066\u306b\u306a\u3089\u306a\u3044\u300d\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4-2. \u30ab\u30e1\u30e9\u306e\u30d4\u30f3\u30c8\u3067\u8003\u3048\u308b\u5929\u4e95\u52b9\u679c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u306e\u66f2\u7dda\u306f\u3001\u30ab\u30e1\u30e9\u306e\u30d4\u30f3\u30c8\u306b\u4f3c\u3066\u3044\u308b\u3002\u30d4\u30f3\u30c8\u304c\u5408\u3063\u3066\u3044\u308b\u8ddd\u96e2\u306e\u88ab\u5199\u4f53\u306f\u304f\u3063\u304d\u308a\u5199\u308b\u304c\u3001\u30d4\u30f3\u30c8\u304b\u3089\u5916\u308c\u305f\u624b\u524d\u3084\u5965\u306f\u307c\u3084\u3051\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5192\u982d\u306e\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\u3067\u3001\u8efd\u3044\u75c7\u72b6\u306e\u9805\u76ee\uff08\u56f0\u96e3\u5ea6\u304c\u4f4e\u3044\u9805\u76ee\uff09\u3070\u304b\u308a\u3060\u3063\u305f\u3068\u3057\u3088\u3046\u3002\u3059\u308b\u3068\u60c5\u5831\u91cf\u306e\u5c71\u306f\u3001\u03b8 \u306e\u4f4e\u3044\u5074\uff08\u8efd\u75c7\u57df\uff09\u306b\u3067\u304d\u308b\u3002\u8efd\u75c7\u306e\u4eba\u540c\u58eb\u306e\u9055\u3044\u306f\u304f\u3063\u304d\u308a\u898b\u3048\u308b\u304c\u3001\u91cd\u75c7\u57df\u306f\u30d4\u30f3\u30c8\u306e\u5916\u306b\u306a\u308a\u3001\u91cd\u75c7\u306e\u4eba\u306f\u307f\u3093\u306a\u300c\u307b\u307c\u5168\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u300d\u3068\u7b54\u3048\u3066\u5408\u8a08\u70b9\u304c\u6e80\u70b9\u4ed8\u8fd1\u306b\u96c6\u307e\u308b\u3002<strong>\u3053\u308c\u304c\u5929\u4e95\u52b9\u679c\u3092\u3001\u60c5\u5831\u91cf\u306e\u8a00\u8449\u3067\u8a00\u3044\u76f4\u3057\u305f\u3082\u306e<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u898b\u65b9\u306f\u81e8\u5e8a\u7684\u306b\u3068\u3066\u3082\u5f79\u306b\u7acb\u3064\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u9805\u76ee\u9078\u3073\u30fb\u77ed\u7e2e\u7248\u306e\u4f5c\u6210<\/strong>\uff1a\u60c5\u5831\u91cf\u306e\u5c11\u306a\u3044\u9805\u76ee\u3092\u5916\u3057\u3066\u3082\u3001\u6e2c\u308a\u305f\u3044\u7bc4\u56f2\u306e\u7cbe\u5ea6\u304c\u307b\u3068\u3093\u3069\u843d\u3061\u306a\u3044\u306a\u3089\u3001\u9805\u76ee\u6570\u3092\u6e1b\u3089\u3057\u3066\u56de\u7b54\u8005\u306e\u8ca0\u62c5\u3092\u8efd\u304f\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5c3a\u5ea6\u306e\u5f31\u70b9\u306e\u767a\u898b<\/strong>\uff1a\u91cd\u75c7\u57df\u306e\u60c5\u5831\u91cf\u304c\u8db3\u308a\u306a\u3051\u308c\u3070\u3001\u300c\u91cd\u75c7\u306e\u4eba\u3067\u306a\u3044\u3068\u300e\u306f\u3044\u300f\u3068\u8a00\u308f\u306a\u3044\u9805\u76ee\u300d\u3092\u8ffd\u52a0\u3059\u308c\u3070\u3088\u3044\u3001\u3068\u6539\u5584\u306e\u65b9\u5411\u304c\u308f\u304b\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9069\u5fdc\u578b\u30c6\u30b9\u30c8\uff08CAT\uff09<\/strong>\uff1a\u56de\u7b54\u306b\u5fdc\u3058\u3066\u3001\u305d\u306e\u4eba\u306e \u03b8 \u4ed8\u8fd1\u3067\u60c5\u5831\u91cf\u304c\u6700\u3082\u5927\u304d\u3044\u9805\u76ee\u3092\u6b21\u3005\u306b\u51fa\u984c\u3059\u308b\u65b9\u6cd5\u3067\u3042\u308b\u3002\u7c73\u56fdNIH\u306e<strong>PROMIS\uff08Patient-Reported Outcomes Measurement Information System\uff09<\/strong>\u3067\u306f\u3001IRT\u3067\u8f03\u6b63\u3057\u305f\u9805\u76ee\u30d0\u30f3\u30af\u3068CAT\u3092\u4f7f\u3044\u3001\u5c11\u306a\u3044\u9805\u76ee\u6570\u3067\u75c7\u72b6\u3084QOL\u3092\u6e2c\u5b9a\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u3066\u3044\u308b\uff08Bevans et al., 2014\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u6b63\u653b\u6cd5\uff1aIRT\u5206\u6790\u306e\u6a19\u6e96\u7684\u306a\u6d41\u308c\u3068\u524d\u63d0<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">5-1. IRT\u306e\u524d\u63d0<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u6271\u3046\u4e00\u6b21\u5143IRT\u306b\u306f\u3001\u6b21\u306e\u524d\u63d0\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e00\u6b21\u5143\u6027<\/strong>\uff1a\u3059\u3079\u3066\u306e\u9805\u76ee\u304c\u30011\u3064\u306e\u6f5c\u5728\u7279\u6027\uff08\u03b8\uff09\u3092\u6e2c\u3063\u3066\u3044\u308b\u3053\u3068\u3002<\/li>\n\n\n\n<li><strong>\u5c40\u6240\u72ec\u7acb\u6027<\/strong>\uff1a\u03b8 \u304c\u540c\u3058\u4eba\u306e\u4e2d\u3067\u306f\u3001\u9805\u76ee\u540c\u58eb\u306e\u56de\u7b54\u304c\u4e92\u3044\u306b\u72ec\u7acb\u3067\u3042\u308b\u3053\u3068\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u9805\u76ee\u9593\u306e\u76f8\u95a2\u306f \u03b8 \u3060\u3051\u3067\u8aac\u660e\u3067\u304d\u308b\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u305f\u3068\u3048\u3070\u300c\u7720\u308c\u306a\u3044\u300d\u3068\u300c\u591c\u4e2d\u306b\u76ee\u304c\u899a\u3081\u308b\u300d\u306e\u3088\u3046\u306b\u3001\u5185\u5bb9\u304c\u307b\u307c\u91cd\u306a\u308b\u9805\u76ee\u304c\u3042\u308b\u3068\u3001\u03b8 \u4ee5\u5916\u306e\u7406\u7531\u3067\u56de\u7b54\u304c\u305d\u308d\u3044\u3001\u3053\u306e\u524d\u63d0\u304c\u5d29\u308c\u3084\u3059\u3044\u3002<\/li>\n\n\n\n<li><strong>\u5358\u8abf\u6027<\/strong>\uff1a\u03b8 \u304c\u9ad8\u3044\u307b\u3069\u3001\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u304c\u4e0a\u304c\u308b\uff08\u4e0b\u304c\u3089\u306a\u3044\uff09\u3053\u3068\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">IRT\u3092\u4f7f\u3048\u3070\u4e00\u6b21\u5143\u6027\u306e\u78ba\u8a8d\u304c\u4e0d\u8981\u306b\u306a\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u3080\u3057\u308d\u3001<strong>IRT\u306f\u4e00\u6b21\u5143\u6027\u3092\u300c\u524d\u63d0\u3068\u3057\u3066\u300d\u7d44\u307f\u7acb\u3066\u3089\u308c\u305f\u30e2\u30c7\u30eb<\/strong>\u3067\u3042\u308b\u3002\u524d\u63d0\u304c\u5d29\u308c\u3066\u3044\u308c\u3070\u3001\u51fa\u3066\u304f\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u89e3\u91c8\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5-2. \u5206\u6790\u306e\u6d41\u308c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8cea\u554f\u7968\u306e\u958b\u767a\u30fb\u8a55\u4fa1\u306bIRT\u3092\u4f7f\u3046\u624b\u9806\u306f\u3001Edelen &amp; Reeve\uff082007\uff09\u3084PROMIS\u306e\u89e3\u6790\u8a08\u753b\uff08Reeve et al., 2007\uff09\u306b\u6574\u7406\u3055\u308c\u3066\u3044\u308b\u3002\u57fa\u672c\u5f62\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8a18\u8ff0\u7d71\u8a08\u3068\u524d\u63d0\u306e\u78ba\u8a8d<\/strong>\uff1a\u5404\u9805\u76ee\u306e\u56de\u7b54\u5206\u5e03\u3092\u78ba\u8a8d\u3057\u3001\u4e00\u6b21\u5143\u6027\u3092\u56e0\u5b50\u5206\u6790\u306a\u3069\u3067\u78ba\u304b\u3081\u308b\u3002\u5c40\u6240\u72ec\u7acb\u6027\u306e\u9055\u53cd\u304c\u306a\u3044\u304b\u3082\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u3081\u3068\u9078\u629e<\/strong>\uff1a1PL\u30682PL\u3092\u5f53\u3066\u306f\u3081\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u3084AIC\u30fbBIC\u3067\u6bd4\u8f03\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9069\u5408\u5ea6\u306e\u78ba\u8a8d<\/strong>\uff1a\u30e2\u30c7\u30eb\u5168\u4f53\u306e\u9069\u5408\u5ea6\uff08M2\u7d71\u8a08\u91cf\u306a\u3069\uff09\u3068\u3001\u9805\u76ee\u3054\u3068\u306e\u9069\u5408\u5ea6\uff08S-X\u00b2 \u7d71\u8a08\u91cf\u306a\u3069\uff09\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf\u3068ICC\u30fb\u60c5\u5831\u91cf\u306e\u78ba\u8a8d<\/strong>\uff1a\u8b58\u5225\u529b\u304c\u6975\u7aef\u306b\u4f4e\u3044\u9805\u76ee\u3001\u56f0\u96e3\u5ea6\u304c\u504f\u3063\u3066\u3044\u308b\u9805\u76ee\u304c\u306a\u3044\u304b\u3092\u898b\u308b\u3002<\/li>\n\n\n\n<li><strong>\u03b8 \u306e\u63a8\u5b9a<\/strong>\uff1a\u56de\u7b54\u8005\u3054\u3068\u306b \u03b8 \u3092\u63a8\u5b9a\u3059\u308b\uff08EAP\u63a8\u5b9a\u306a\u3069\uff09\u3002<\/li>\n<\/ol>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u3069\u308c\u304f\u3089\u3044\u5fc5\u8981\u304b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IRT\u3001\u7279\u306b2PL\u4ee5\u4e0a\u306e\u30e2\u30c7\u30eb\u3067\u306f\u3001\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5b89\u5b9a\u3057\u3066\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u3042\u308b\u7a0b\u5ea6\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u300c2PL\u306a\u3089\u6570\u767e\u4f8b\u300d\u304c\u3088\u304f\u6319\u3052\u3089\u308c\u308b\u76ee\u5b89\u3060\u304c\u3001\u5fc5\u8981\u306a\u4eba\u6570\u306f\u9805\u76ee\u6570\u3001\u56de\u7b54\u306e\u5206\u5e03\u306e\u504f\u308a\u3001\u3069\u308c\u304f\u3089\u3044\u306e\u7cbe\u5ea6\u3092\u6c42\u3081\u308b\u304b\u306b\u3088\u3063\u3066\u5909\u308f\u308a\u3001\u4e00\u5f8b\u306e\u6b63\u89e3\u306f\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305f\u3068\u3048\u3070\u3001\u307b\u3068\u3093\u3069\u5168\u54e1\u304c\u300e\u3044\u3044\u3048\u300f\u3068\u7b54\u3048\u308b\u9805\u76ee\uff08\u56f0\u96e3\u5ea6\u304c\u6975\u7aef\u306b\u9ad8\u3044\u9805\u76ee\uff09\u306f\u3001\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u305f\u5c11\u6570\u306e\u4eba\u306e\u60c5\u5831\u3060\u3051\u3067\u66f2\u7dda\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u3001\u63a8\u5b9a\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308a\u3084\u3059\u3044\u3002\u5c11\u306a\u3044\u30b5\u30f3\u30d7\u30eb\u30672PL\u30843PL\u3092\u5f53\u3066\u306f\u3081\u3001\u3082\u3063\u3068\u3082\u3089\u3057\u3044\u6570\u5024\u304c\u51fa\u3066\u3082\u3001\u6a19\u6e96\u8aa4\u5dee\u304c\u5927\u304d\u3051\u308c\u3070\u4fe1\u983c\u3067\u304d\u306a\u3044\u3001\u3068\u3044\u3046\u70b9\u3092\u899a\u3048\u3066\u304a\u304d\u305f\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">6. R\u306b\u3088\u308b\u5b9f\u88c5\uff08mirt\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001R\u306e <code>mirt<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\uff08Chalmers, 2012\uff09\u3092\u4f7f\u3063\u3066\u3001IRT\u5206\u6790\u306e\u6d41\u308c\u3092\u4f53\u9a13\u3059\u308b\u3002<code>mirt<\/code> \u306f\u591a\u6b21\u5143IRT\u306b\u3082\u5bfe\u5fdc\u3057\u305f\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u3001\u672c\u8a18\u4e8b\u306e\u4e00\u6b21\u5143\u30e2\u30c7\u30eb\u306f\u305d\u306e\u57fa\u672c\u5f62\u306b\u3042\u305f\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 0\uff1a\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u6e96\u5099\u3068\u3001\u6982\u5ff5\u56f3\uff08\u56f31\u30fb\u56f32\uff09\u306e\u63cf\u753b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># install.packages(c(\"mirt\", \"latticeExtra\"))  # \u521d\u56de\u306e\u307f\nlibrary(mirt)\n# latticeExtra \u306f\u3001Step 5 \u306e plot(type = \"infoSE\") \u3067\n# \u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\u30922\u8ef8\u3067\u91cd\u306d\u3066\u63cf\u304f\u3068\u304d\u306b\u4f7f\u308f\u308c\u308b\uff08library() \u3067\u306e\u8aad\u307f\u8fbc\u307f\u306f\u4e0d\u8981\uff09\n\n# --- \u56f31\uff1ab \u3068 a \u306b\u3088\u308bICC\u306e\u5909\u5316\uff08\u6982\u5ff5\u56f3\uff09 ---\ntheta &lt;- seq(-4, 4, length.out = 200)\np2pl  &lt;- function(theta, a, b, c = 0) c + (1 - c) \/ (1 + exp(-a * (theta - b)))\n\npar(mfrow = c(1, 2))\n# \u5de6\uff1ab \u3060\u3051\u3092\u5909\u3048\u308b\uff08a = 1.5 \u3067\u56fa\u5b9a\uff09\nplot(theta, p2pl(theta, a = 1.5, b = -1), type = \"l\", lwd = 2, ylim = c(0, 1),\n     xlab = expression(theta), ylab = \"P(Yes)\", main = \"Varying difficulty (b)\")\nlines(theta, p2pl(theta, a = 1.5, b = 0), lwd = 2, lty = 2)\nlines(theta, p2pl(theta, a = 1.5, b = 1), lwd = 2, lty = 3)\nabline(h = 0.5, col = \"gray\")\nlegend(\"topleft\", legend = c(\"b = -1\", \"b = 0\", \"b = 1\"), lty = 1:3, lwd = 2, bty = \"n\")\n\n# \u53f3\uff1aa \u3060\u3051\u3092\u5909\u3048\u308b\uff08b = 0 \u3067\u56fa\u5b9a\uff09\nplot(theta, p2pl(theta, a = 0.5, b = 0), type = \"l\", lwd = 2, ylim = c(0, 1),\n     xlab = expression(theta), ylab = \"P(Yes)\", main = \"Varying discrimination (a)\")\nlines(theta, p2pl(theta, a = 1.5, b = 0), lwd = 2, lty = 2)\nlines(theta, p2pl(theta, a = 3.0, b = 0), lwd = 2, lty = 3)\nabline(h = 0.5, col = \"gray\")\nlegend(\"topleft\", legend = c(\"a = 0.5\", \"a = 1.5\", \"a = 3.0\"), lty = 1:3, lwd = 2, bty = \"n\")\npar(mfrow = c(1, 1))\n\n# --- \u56f32\uff1a1PL\u30fb2PL\u30fb3PL\u306e\u6bd4\u8f03\uff08\u6982\u5ff5\u56f3\uff09 ---\npar(mfrow = c(1, 3))\nbs &lt;- c(-1, 0, 1)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"1PL\")\nfor (k in 1:3) lines(theta, p2pl(theta, a = 1.2, b = bs&#91;k]), lwd = 2, lty = k)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"2PL\")\nas &lt;- c(0.6, 1.5, 3.0)\nfor (k in 1:3) lines(theta, p2pl(theta, a = as&#91;k], b = bs&#91;k]), lwd = 2, lty = k)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"3PL\")\nfor (k in 1:3) lines(theta, p2pl(theta, a = as&#91;k], b = bs&#91;k], c = 0.2), lwd = 2, lty = k)\nabline(h = 0.2, col = \"gray\")\npar(mfrow = c(1, 1))<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>p2pl()<\/code> \u306f\u5f0f\u2460\u3092\u305d\u306e\u307e\u307eR\u306e\u95a2\u6570\u306b\u3057\u305f\u3082\u306e\u3067\u3001<code>c<\/code> \u30920\u306b\u3059\u308c\u30702PL\u30010\u3088\u308a\u5927\u304d\u304f\u3059\u308c\u30703PL\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u751f\u6210<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3046\u3064\u75c7\u72b6\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\uff0810\u9805\u76ee\u3001\u4e8c\u5024\uff09\u3092\u60f3\u5b9a\u3057\u305f\u7591\u4f3c\u30c7\u30fc\u30bf\u3092\u4f5c\u308b\u3002\u30dd\u30a4\u30f3\u30c8\u306f\u3001<strong>\u5168\u54e1\u306e \u03b8\uff08\u6291\u3046\u3064\u306e\u91cd\u3055\uff09\u3092\u307e\u305a\u751f\u6210\u3057\u3001\u305d\u306e \u03b8 \u304b\u3089\u5404\u9805\u76ee\u306e\u56de\u7b54\u3092\u4f5c\u308b<\/strong>\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u3046\u3059\u308b\u3053\u3068\u3067\u3001\u300c\u5171\u901a\u306e\u6f5c\u5728\u7279\u6027\u304c\u9805\u76ee\u9593\u306e\u76f8\u95a2\u3092\u751f\u3080\u300d\u3068\u3044\u3046IRT\u306e\u69cb\u9020\u3092\u3001\u30c7\u30fc\u30bf\u306b\u7d44\u307f\u8fbc\u3081\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305f\u3001\u5192\u982d\u306e\u60a9\u307f\u3092\u518d\u73fe\u3059\u308b\u305f\u3081\u3001<strong>\u56f0\u96e3\u5ea6\u306e\u4f4e\u3044\uff08\u8efd\u3044\u75c7\u72b6\u306e\uff09\u9805\u76ee\u3092\u591a\u3081\u306b\u3001\u91cd\u3044\u75c7\u72b6\u306e\u9805\u76ee\u3092\u5c11\u306a\u3081\u306b<\/strong>\u8a2d\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>set.seed(2026)\nN &lt;- 1000   # \u56de\u7b54\u8005\u6570\nJ &lt;- 10     # \u9805\u76ee\u6570\n\n# \u771f\u306e\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u8efd\u3044\u75c7\u72b6\u306e\u9805\u76ee\u304c\u591a\u3044\u8a2d\u8a08\uff09\ntrue_a &lt;- c(1.2, 1.5, 0.8, 1.8, 1.0, 2.0, 1.4, 0.7, 2.2, 1.6)\ntrue_b &lt;- c(-2.4, -2.0, -1.8, -1.5, -1.3, -1.1, -0.8, -0.6, -0.3, 0.4)\n\n# \u771f\u306e \u03b8\uff08\u6291\u3046\u3064\u306e\u91cd\u3055\uff09\uff1a\u6a19\u6e96\u6b63\u898f\u5206\u5e03\ntrue_theta &lt;- rnorm(N, mean = 0, sd = 1)\n\n# \u5f0f\u2460\u306b\u5f93\u3063\u3066\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3057\u3001\u56de\u7b54\uff081 = \u306f\u3044, 0 = \u3044\u3044\u3048\uff09\u3092\u751f\u6210\nP &lt;- 1 \/ (1 + exp(-sweep(outer(true_theta, true_b, \"-\"), 2, true_a, \"*\")))\ndat &lt;- matrix(rbinom(N * J, size = 1, prob = P), nrow = N, ncol = J)\ncolnames(dat) &lt;- paste0(\"Q\", 1:J)\n\n# \u9805\u76ee\u3054\u3068\u306e\u300e\u306f\u3044\u300f\u306e\u5272\u5408\u3068\u3001\u5408\u8a08\u70b9\u306e\u5206\u5e03\nround(colMeans(dat), 2)\ntable(rowSums(dat))<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>outer(true_theta, true_b, \"-\")<\/code> \u3067\u300c\u03b8 \u2212 b\u300d\u3092\u5168\u54e1\u00d7\u5168\u9805\u76ee\u3076\u3093\u8a08\u7b97\u3057\u3001<code>sweep()<\/code> \u3067\u9805\u76ee\u3054\u3068\u306e\u8b58\u5225\u529b a \u3092\u639b\u3051\u3066\u3044\u308b\u3002\u6700\u5f8c\u306e <code>table(rowSums(dat))<\/code> \u3067\u3001\u5408\u8a08\u70b9\u304c\u6e80\u70b9\uff0810\u70b9\uff09\u4ed8\u8fd1\u306b\u4eba\u304c\u96c6\u307e\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u307b\u3057\u3044\u3002\u3053\u308c\u304c\u5929\u4e95\u52b9\u679c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2\uff1a1PL\u30682PL\u3092\u5f53\u3066\u306f\u3081\u3066\u6bd4\u8f03\u3059\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># 1PL\uff08Rasch\u30e2\u30c7\u30eb\uff1a\u8b58\u5225\u529b\u3092\u5171\u901a\u306b\u3057\u305f\u30e2\u30c7\u30eb\uff09\nfit_1pl &lt;- mirt(dat, model = 1, itemtype = \"Rasch\", verbose = FALSE)\n\n# 2PL\uff08\u8b58\u5225\u529b\u3092\u9805\u76ee\u3054\u3068\u306b\u63a8\u5b9a\uff09\nfit_2pl &lt;- mirt(dat, model = 1, itemtype = \"2PL\", verbose = FALSE)\n\n# \u5c24\u5ea6\u6bd4\u691c\u5b9a\u3068\u60c5\u5831\u91cf\u898f\u6e96\u306b\u3088\u308b\u6bd4\u8f03\nanova(fit_1pl, fit_2pl)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>model = 1<\/code> \u306f\u300c\u56e0\u5b50\uff08\u6f5c\u5728\u7279\u6027\uff09\u304c1\u3064\u300d\u3001\u3064\u307e\u308a\u4e00\u6b21\u5143\u30e2\u30c7\u30eb\u3067\u3042\u308b\u3053\u3068\u3092\u6307\u5b9a\u3057\u3066\u3044\u308b\u3002\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> <code>            AIC    SABIC       HQ      BIC    logLik      X2 df p\nfit_1pl 9567.833 9586.882 9588.351 9621.818 -4772.916             \nfit_2pl 9480.412 9515.046 9517.718 9578.567 -4720.206 105.421  9 0<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">AIC\u30fbBIC\u306f\u3044\u305a\u308c\u30822PL\u306e\u307b\u3046\u304c\u5c0f\u3055\u304f\uff08AIC\uff1a9480.4 vs. 9567.8\u3001BIC\uff1a9578.6 vs. 9621.8\uff09\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u3082 \u03c7\u00b2 = 105.4\u3001\u81ea\u7531\u5ea69\u3067\u3001P\u5024\u306f\u8868\u793a\u4e0a0\uff08P &lt; 0.001\uff09\u3068\u306a\u3063\u305f\u3002\u81ea\u7531\u5ea69\u306f\u30012PL\u304c1PL\u3088\u308a\u63a8\u5b9a\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570\u306e\u5dee\u3067\u3042\u308b\uff082PL\u306f\u8b58\u5225\u529b10\u500b\uff0b\u56f0\u96e3\u5ea610\u500b\uff1d20\u500b\u3001Rasch\u30e2\u30c7\u30eb\u306f\u56f0\u96e3\u5ea610\u500b\uff0b\u03b8 \u306e\u5206\u65631\u500b\uff1d11\u500b\uff09\u3002\u8b58\u5225\u529b\u304c\u9805\u76ee\u3054\u3068\u306b\u9055\u3046\u3088\u3046\u306b\u4f5c\u3063\u305f\u30c7\u30fc\u30bf\u306a\u306e\u3067\u30012PL\u304c\u9078\u3070\u308c\u308b\u306e\u306f\u671f\u5f85\u3069\u304a\u308a\u306e\u7d50\u679c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u304a\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u306eP\u5024\u306f\u300c1PL\u3067\u5341\u5206\u300d\u3068\u3044\u3046\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306e\u3082\u306e\u3067\u3042\u308a\u3001P\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\u300c2PL\u3068\u306e\u5dee\u304c\u5927\u304d\u3044\u300d\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u3044\u70b9\u306b\u6ce8\u610f\u3057\u305f\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3\uff1a\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u8b58\u5225\u529b\u30fb\u56f0\u96e3\u5ea6\uff09\u3092\u78ba\u8a8d\u3059\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># IRT\u306e\u901a\u5e38\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\uff08a, b\uff09\u3067\u8868\u793a\nest &lt;- coef(fit_2pl, IRTpars = TRUE, simplify = TRUE)\nround(est$items&#91;, c(\"a\", \"b\")], 2)\n\n# \u771f\u5024\u3068\u306e\u6bd4\u8f03\nround(cbind(true_a, est_a = est$items&#91;, \"a\"],\n            true_b, est_b = est$items&#91;, \"b\"]), 2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>mirt<\/code> \u306f\u5185\u90e8\u3067\u306f\u300c\u50be\u304d a1 \u3068\u5207\u7247 d\u300d\u306e\u5f62\uff08$a\\theta + d$\uff09\u3067\u63a8\u5b9a\u3057\u3066\u3044\u308b\u3002<code>IRTpars = TRUE<\/code> \u3092\u6307\u5b9a\u3059\u308b\u3068\u3001\u672c\u8a18\u4e8b\u306e\u5f0f\u2460\u3068\u540c\u3058\u300ca \u3068 b\u300d\u306e\u5f62\u306b\u5909\u63db\u3057\u3066\u8868\u793a\u3057\u3066\u304f\u308c\u308b\u30022\u3064\u306e\u95a2\u4fc2\u306f $b = -d\/a$ \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u771f\u5024\u3068\u306e\u6bd4\u8f03\u306e\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> <code>   true_a est_a true_b est_b\nQ1     1.2  1.28   -2.4 -2.37\nQ2     1.5  1.74   -2.0 -1.98\nQ3     0.8  0.68   -1.8 -2.10\nQ4     1.8  1.64   -1.5 -1.63\nQ5     1.0  0.81   -1.3 -1.61\nQ6     2.0  1.87   -1.1 -1.11\nQ7     1.4  1.46   -0.8 -0.81\nQ8     0.7  0.72   -0.6 -0.70\nQ9     2.2  1.82   -0.3 -0.36\nQ10    1.6  1.53    0.4  0.39<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u63a8\u5b9a\u5024\u306f\u3001\u304a\u304a\u3080\u306d\u771f\u5024\u306e\u8fd1\u304f\u306b\u623b\u3063\u3066\u304d\u3066\u3044\u308b\u3002\u8b58\u5225\u529b\u306f0.68\u301c1.87\u3001\u56f0\u96e3\u5ea6\u306f\u22122.37\u301c0.39\u306e\u7bc4\u56f2\u3067\u3001\u300c\u8efd\u3044\u75c7\u72b6\u306e\u9805\u76ee\u304c\u591a\u304f\u3001\u91cd\u3044\u75c7\u72b6\u306e\u9805\u76ee\uff08Q10\uff09\u304c\u5c11\u306a\u3044\u300d\u3068\u3044\u3046\u8a2d\u8a08\u3069\u304a\u308a\u306e\u59ff\u304c\u518d\u73fe\u3055\u308c\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d30\u304b\u304f\u898b\u308b\u3068\u3001\u56f0\u96e3\u5ea6\u306e\u305a\u308c\u304c\u5927\u304d\u3044\u306e\u306f Q3\uff08\u771f\u5024 \u22121.8 \u2192 \u63a8\u5b9a \u22122.10\uff09\u3068 Q5\uff08\u22121.3 \u2192 \u22121.61\uff09\u3067\u3001\u3069\u3061\u3089\u3082\u8b58\u5225\u529b\u306e\u4f4e\u3044\u9805\u76ee\u3067\u3042\u308b\u3002\u8b58\u5225\u529b\u304c\u4f4e\u3044\u9805\u76ee\u306fICC\u304c\u306a\u3060\u3089\u304b\u306a\u306e\u3067\u3001\u300c\u78ba\u7387\u304c0.5\u306b\u306a\u308b\u4f4d\u7f6e\u300d\u3092\u30d4\u30f3\u30dd\u30a4\u30f3\u30c8\u3067\u6c7a\u3081\u306b\u304f\u304f\u3001\u56f0\u96e3\u5ea6\u306e\u63a8\u5b9a\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308a\u3084\u3059\u3044\u3002\u307e\u305f\u3001\u8b58\u5225\u529b\u306e\u63a8\u5b9a\u5024\u306b\u3082\u3001Q9\uff082.2 \u2192 1.82\uff09\u306e\u3088\u3046\u306b\u771f\u5024\u304b\u30890.4\u307b\u3069\u305a\u308c\u308b\u9805\u76ee\u304c\u3042\u308b\u3002N = 1000 \u3067\u3082\u3053\u306e\u7a0b\u5ea6\u306e\u8aa4\u5dee\u306f\u51fa\u308b\u3001\u3068\u3044\u3046\u611f\u899a\u3092\u6301\u3063\u3066\u304a\u304f\u3068\u3088\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4\uff1a\u9069\u5408\u5ea6\u3092\u78ba\u8a8d\u3059\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \u9805\u76ee\u3054\u3068\u306e\u9069\u5408\u5ea6\uff08S-X2\u7d71\u8a08\u91cf\uff09\nitemfit(fit_2pl)\n\n# \u30e2\u30c7\u30eb\u5168\u4f53\u306e\u9069\u5408\u5ea6\uff08M2\u7d71\u8a08\u91cf\u3001RMSEA\u3001CFI \u306a\u3069\uff09\nM2(fit_2pl)\n\n# \u5c40\u6240\u72ec\u7acb\u6027\u306e\u78ba\u8a8d\uff08Yen \u306e Q3\uff1a\u6b8b\u5dee\u3069\u3046\u3057\u306e\u76f8\u95a2\uff09\nQ3 &lt;- residuals(fit_2pl, type = \"Q3\")<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>itemfit()<\/code> \u306f\u3001\u65e2\u5b9a\u3067\u9805\u76ee\u3054\u3068\u306e S-X\u00b2 \u7d71\u8a08\u91cf\u3068RMSEA\u3001P\u5024\u3092\u51fa\u3059\u3002\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> <code>  item   S_X2 df.S_X2 RMSEA.S_X2 p.S_X2\n1    Q1  3.081       7      0.000  0.877\n2    Q2  4.880       7      0.000  0.675\n3    Q3  7.275       7      0.006  0.401\n4    Q4 10.119       6      0.026  0.120\n5    Q5  9.227       7      0.018  0.237\n6    Q6  2.370       6      0.000  0.883\n7    Q7  4.049       6      0.000  0.670\n8    Q8  6.246       6      0.006  0.396\n9    Q9  7.984       5      0.024  0.157\n10  Q10  4.697       4      0.013  0.320<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u3059\u3079\u3066\u306e\u9805\u76ee\u3067P\u5024\u306f0.05\u3092\u4e0a\u56de\u308a\uff08\u6700\u5c0f\u306f Q4 \u306e0.120\uff09\u3001RMSEA\u30820.03\u672a\u6e80\u3067\u3042\u3063\u305f\u3002\u30e2\u30c7\u30eb\u306b\u5927\u304d\u304f\u5408\u308f\u306a\u3044\u9805\u76ee\u306f\u898b\u5f53\u305f\u3089\u306a\u3044\u3002\u306a\u304a\u3001\u9805\u76ee\u6570\u304c\u591a\u3044\u3068\u591a\u91cd\u6bd4\u8f03\u306e\u554f\u984c\u304c\u751f\u3058\u308b\u306e\u3067\u3001\u5b9f\u30c7\u30fc\u30bf\u3067\u306f\u3001P\u5024\u3060\u3051\u3067\u6a5f\u68b0\u7684\u306b\u9805\u76ee\u3092\u524a\u9664\u305b\u305a\u3001ICC\u306e\u5f62\u3084\u9805\u76ee\u306e\u5185\u5bb9\u3068\u3042\u308f\u305b\u3066\u5224\u65ad\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>M2()<\/code> \u306e\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> <code>         M2 df     p RMSEA RMSEA_5 RMSEA_95 SRMSR   TLI CFI\nstats 26.956 35 0.833     0       0    0.014 0.021 1.006   1<\/code><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">M2 = 26.96\uff08\u81ea\u7531\u5ea635\u3001P = 0.83\uff09\u3001RMSEA = 0\uff0890\uff05\u4fe1\u983c\u533a\u9593 0\u301c0.014\uff09\u3001SRMSR = 0.021\u3001CFI = 1 \u3068\u3001\u30e2\u30c7\u30eb\u5168\u4f53\u306e\u5f53\u3066\u306f\u307e\u308a\u3082\u826f\u597d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305f\u3060\u3057\u3001\u3053\u308c\u306f<strong>2PL\u30e2\u30c7\u30eb\u305d\u306e\u3082\u306e\u304b\u3089\u751f\u6210\u3057\u305f\u7591\u4f3c\u30c7\u30fc\u30bf<\/strong>\u306a\u306e\u3067\u3001\u5f53\u3066\u306f\u307e\u308a\u304c\u826f\u3044\u306e\u306f\u5f53\u7136\u306e\u7d50\u679c\u3067\u3042\u308b\u3002\u5b9f\u30c7\u30fc\u30bf\u3067\u306f\u3001\u3053\u3053\u307e\u3067\u304d\u308c\u3044\u306a\u5024\u306b\u306a\u308b\u3053\u3068\u306f\u307e\u305a\u306a\u3044\u3002\u4e00\u6b21\u5143\u6027\u3084\u5c40\u6240\u72ec\u7acb\u6027\u304c\u5d29\u308c\u3066\u3044\u308c\u3070\u3001\u9069\u5408\u5ea6\u306f\u60aa\u5316\u3059\u308b\u3002\u305d\u306e\u3068\u304d\u306b\u691c\u8a0e\u3059\u308b\u306e\u304c\u3001\u672c\u8a18\u4e8b\u306e\u6700\u5f8c\u3067\u7d39\u4ecb\u3059\u308b\u591a\u6b21\u5143IRT\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u5f8c\u306e <code>residuals(fit_2pl, type = \"Q3\")<\/code> \u306f\u30015\u7ae0\u3067\u8aac\u660e\u3057\u305f<strong>\u5c40\u6240\u72ec\u7acb\u6027<\/strong>\u306e\u78ba\u8a8d\u3067\u3042\u308b\u3002Yen \u306e <strong>Q3<\/strong> \u306f\u3001\u300c\u30e2\u30c7\u30eb\u3067\u8aac\u660e\u3057\u304d\u308c\u306a\u304b\u3063\u305f\u6b8b\u308a\uff08\u6b8b\u5dee\uff09\u300d\u3069\u3046\u3057\u306e\u76f8\u95a2\u3092\u3001\u9805\u76ee\u306e\u30da\u30a2\u3054\u3068\u306b\u8a08\u7b97\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u03b8 \u3067\u8aac\u660e\u3057\u304d\u308c\u306a\u3044\u5171\u901a\u306e\u7406\u7531\uff08\u5185\u5bb9\u306e\u91cd\u8907\u306a\u3069\uff09\u3067\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u9805\u76ee\u306e\u30da\u30a2\u304c\u3042\u308b\u3068\u3001\u305d\u306e\u30da\u30a2\u306e Q3 \u304c\u9ad8\u304f\u306a\u308b\u3002\u5b9f\u884c\u3059\u308b\u3068\u3001\u8981\u7d04\u7d71\u8a08\u91cf\u306810\u00d710\u306e\u884c\u5217\u304c\u8868\u793a\u3055\u308c\u308b\uff08<code>Q3 &lt;-<\/code> \u3067\u53d7\u3051\u53d6\u3063\u3066\u3044\u308b\u306e\u306f\u3001\u8868\u793a\u304c\u4e8c\u91cd\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u305f\u3081\u3067\u3042\u308b\uff09\u3002\u4eca\u56de\u306e\u8981\u7d04\u7d71\u8a08\u91cf\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Q3 summary statistics:\n   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n -0.241  -0.099  -0.072  -0.077  -0.046   0.023<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Q3 \u306f\u3001\u5c40\u6240\u72ec\u7acb\u6027\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u3066\u3082\u5e73\u5747\u304c\u3084\u3084\u30de\u30a4\u30ca\u30b9\u306b\u504f\u308b\u6027\u8cea\u304c\u3042\u308b\uff08\u9805\u76ee\u6570\u304c\u5c11\u306a\u3044\u307b\u3069\u504f\u308a\u304c\u5927\u304d\u3044\uff09\u3002\u305d\u306e\u305f\u3081\u3001Q3 \u306e\u5024\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u304f\u3001\u300c\u5e73\u5747\u3088\u308a\u3069\u308c\u3060\u3051\u9ad8\u3044\u304b\u300d\u3092\u898b\u308b\u306e\u304c\u3088\u3044\u3068\u3055\u308c\u308b\u3002Christensen \u3089\uff082017\uff09\u306f\u3001\u4e00\u5f8b\u306e\u57fa\u6e96\u5024\u306f\u306a\u3044\u3068\u3057\u305f\u3046\u3048\u3067\u3001\u5e73\u5747\u3088\u308a0.2\u7a0b\u5ea6\u4ee5\u4e0a\u9ad8\u3044\u30da\u30a2\u3092\u5c40\u6240\u4f9d\u5b58\u306e\u5019\u88dc\u3068\u3059\u308b\u76ee\u5b89\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u4eca\u56de\u306f\u6700\u5927\u50240.023\u304c\u5e73\u5747\uff08\u22120.077\uff09\u3088\u308a0.10\u9ad8\u3044\u3060\u3051\u3067\u3001\u5c40\u6240\u72ec\u7acb\u6027\u3092\u7591\u308f\u305b\u308b\u30da\u30a2\u306f\u898b\u5f53\u305f\u3089\u306a\u304b\u3063\u305f\u3002\u30e2\u30c7\u30eb\u304b\u3089\u751f\u6210\u3057\u305f\u30c7\u30fc\u30bf\u306a\u306e\u3067\u3001\u3053\u308c\u3082\u671f\u5f85\u3069\u304a\u308a\u306e\u7d50\u679c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5\uff1aICC\u3068\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u3092\u63cf\u304f<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5168\u9805\u76ee\u306eICC\uff08\u9805\u76ee\u7279\u6027\u66f2\u7dda\uff09\nplot(fit_2pl, type = \"trace\")\n\n# \u7279\u5b9a\u306e\u9805\u76ee\u306eICC\u3068\u9805\u76ee\u60c5\u5831\u91cf\uff08\u4f8b\uff1aQ9\uff09\nitemplot(fit_2pl, item = 9, type = \"trace\")\nitemplot(fit_2pl, item = 9, type = \"info\")\n\n# \u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\uff08\u56f33\uff09\nplot(fit_2pl, type = \"infoSE\", theta_lim = c(-4, 4))<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>type = \"infoSE\"<\/code> \u306f\u3001\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\u30921\u679a\u306b\u91cd\u306d\u3066\u63cf\u304f\uff08\u3053\u306e\u3068\u304d <code>latticeExtra<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u304c\u5fc5\u8981\u306b\u306a\u308b\uff09\u3002<code>theta_lim<\/code> \u306f\u6a2a\u8ef8\u306e\u7bc4\u56f2\u3067\u3001\u65e2\u5b9a\u306f \u22126\u301c6 \u3067\u3042\u308b\u3002\u4e21\u7aef\u3067\u306f\u6a19\u6e96\u8aa4\u5dee\u304c\u975e\u5e38\u306b\u5927\u304d\u304f\u306a\u3063\u3066\u53f3\u306e\u76ee\u76db\u308a\u304c\u5f15\u304d\u4f38\u3070\u3055\u308c\u3001\u30b0\u30e9\u30d5\u304c\u8aad\u307f\u306b\u304f\u304f\u306a\u308b\u306e\u3067\u3001\u3053\u3053\u3067\u306f \u22124\u301c4 \u306b\u7d5e\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fa\u529b\u304c4\u7ae0\u306e\u56f33\u3067\u3042\u308b\u3002\u4eca\u56de\u306e\u30c7\u30fc\u30bf\u3067\u306f\u56f0\u96e3\u5ea6\u306e\u4f4e\u3044\u9805\u76ee\u304c\u591a\u3044\u305f\u3081\u3001<strong>\u60c5\u5831\u91cf\u306e\u5c71\u306f \u03b8 = \u22121.2 \u4ed8\u8fd1\uff08\u8efd\u75c7\u57df\uff09\u306b\u5bc4\u308a\u3001\u03b8 \u306e\u9ad8\u3044\u5074\uff08\u91cd\u75c7\u57df\uff09\u3067\u306f\u6a19\u6e96\u8aa4\u5dee\u304c\u6025\u6fc0\u306b\u5927\u304d\u304f\u306a\u3063\u305f<\/strong>\u3002\u3053\u308c\u304c\u3001\u30ab\u30e1\u30e9\u306e\u30d4\u30f3\u30c8\u306e\u4f8b\u3048\u3067\u8aac\u660e\u3057\u305f\u5929\u4e95\u52b9\u679c\u306e\u59ff\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u60c5\u5831\u91cf\u306e\u6570\u5024\u305d\u306e\u3082\u306e\u3092\u898b\u305f\u3044\u5834\u5408\u306f\u3001<code>testinfo()<\/code> \u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>theta_grid &lt;- matrix(seq(-3, 3, by = 1))\ninfo &lt;- testinfo(fit_2pl, Theta = theta_grid)\nround(data.frame(theta = theta_grid&#91;, 1], info = info, SE = 1 \/ sqrt(info)), 2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u5f8c\u306e\u5217\u304c\u3001\u5f0f\u2461\u306e $1\/\\sqrt{I(\\theta)}$ \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6\uff1a\u03b8 \u3092\u63a8\u5b9a\u3057\u3001\u5408\u8a08\u70b9\u3068\u6bd4\u3079\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \u03b8 \u306e\u63a8\u5b9a\uff08EAP\u63a8\u5b9a\uff09\ntheta_hat &lt;- fscores(fit_2pl, method = \"EAP\")\n\n# \u5408\u8a08\u70b9\u3068 \u03b8 \u306e\u95a2\u4fc2\nsum_score &lt;- rowSums(dat)\nplot(jitter(sum_score, amount = 0.2), theta_hat&#91;, 1],\n     xlab = \"Sum score\", ylab = expression(hat(theta)),\n     main = expression(paste(\"Sum score vs. estimated \", theta)), pch = 16, col = rgb(0, 0, 0, 0.3))\n\n# \u5408\u8a08\u70b9\u3054\u3068\u306e \u03b8 \u306e\u7bc4\u56f2\nround(t(sapply(split(theta_hat&#91;, 1], sum_score),\n               function(x) c(min = min(x), max = max(x)))), 2)\n\n# \u5408\u8a08\u70b9\u3054\u3068\u306e \u03b8 \u306e\u5e73\u5747\nround(tapply(theta_hat&#91;, 1], sum_score, mean), 2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>split()<\/code> \u3092\u4f7f\u3063\u305f\u884c\u3067\u306f\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\u3092\u5408\u8a08\u70b9\u3054\u3068\u306b\u5206\u3051\u3001\u305d\u308c\u305e\u308c\u306e\u6700\u5c0f\u5024\u3068\u6700\u5927\u5024\u3092\u8868\u306b\u3057\u3066\u3044\u308b\u3002\u6700\u5f8c\u306e\u884c\u306f\u3001\u5408\u8a08\u70b9\u3054\u3068\u306e \u03b8 \u306e\u5e73\u5747\u3067\u3042\u308b\uff08\u56f34\u306e3\u3064\u76ee\u306e\u8aad\u307f\u53d6\u308a\u3067\u4f7f\u3046\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"632\" height=\"481\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-5.png\" alt=\"\" class=\"wp-image-5041\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-5.png 632w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/11\/image-5-300x228.png 300w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u56f34\uff1a\u5408\u8a08\u70b9\u3068 \u03b8 \u306e\u63a8\u5b9a\u5024\u306e\u95a2\u4fc2<\/strong>\uff08\u6a2a\u8ef8\u306e\u70b9\u306f\u3001\u91cd\u306a\u308a\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u5de6\u53f3\u306b\u5c11\u3057\u305a\u3089\u3057\u3066\u3044\u308b\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56f34\u304b\u3089\u30013\u3064\u306e\u3053\u3068\u304c\u8aad\u307f\u53d6\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\u3064\u76ee\u306f\u3001<strong>\u540c\u3058\u5408\u8a08\u70b9\u3067\u3082\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\u306b\u5e45\u304c\u3042\u308b<\/strong>\u3053\u3068\u3067\u3042\u308b\u3002\u305f\u3068\u3048\u3070\u5408\u8a08\u70b96\u70b9\u306e\u4eba\u305f\u3061\u306f\u3001\u03b8 \u304c\u304a\u3088\u305d \u22120.9\u301c\u22120.2 \u306e\u7bc4\u56f2\u306b\u6563\u3089\u3070\u3063\u3066\u3044\u308b\u30022PL\u3067\u306f\u3001\u8b58\u5225\u529b\u306e\u9ad8\u3044\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u308b\u307b\u3046\u304c \u03b8 \u306e\u63a8\u5b9a\u5024\u306b\u5f37\u304f\u52b9\u304f\u305f\u3081\u3001\u540c\u30586\u70b9\u3067\u3082\u3001\u3069\u306e\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u3068\u7b54\u3048\u305f\u304b\u306b\u3088\u3063\u3066 \u03b8 \u304c\u5909\u308f\u308b\u306e\u3067\u3042\u308b\u3002\u5408\u8a08\u70b99\u70b9\u306e\u5217\u304c\u6570\u500b\u306e\u304b\u305f\u307e\u308a\u306b\u5206\u304b\u308c\u3066\u3044\u308b\u306e\u306f\u3001\u300c\u3069\u306e1\u9805\u76ee\u306b\u300e\u3044\u3044\u3048\u300f\u3068\u7b54\u3048\u305f\u304b\u300d\u306e\u9055\u3044\u304c\u305d\u306e\u307e\u307e\u8868\u308c\u3066\u3044\u308b\u305f\u3081\u3060\u3002\uff081PL\u3067\u306f\u3001\u5408\u8a08\u70b9\u304c\u540c\u3058\u306a\u3089 \u03b8 \u306e\u63a8\u5b9a\u5024\u3082\u540c\u3058\u306b\u306a\u308b\u3002\u3053\u308c\u30821PL\u30682PL\u306e\u9055\u3044\u306e1\u3064\u3067\u3042\u308b\u3002\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2\u3064\u76ee\u306f\u3001<strong>\u5408\u8a08\u70b910\u70b9\uff08\u6e80\u70b9\uff09\u306e\u4eba\u306f\u3001\u5168\u54e1\u304c\u540c\u3058 \u03b8\uff08\u7d041.1\uff09\u306b\u306a\u3063\u3066\u3044\u308b<\/strong>\u3053\u3068\u3067\u3042\u308b\u3002\u6e80\u70b9\u306e\u4eba\u306f\u300c\u5168\u9805\u76ee\u306b\u300e\u306f\u3044\u300f\u300d\u3068\u3044\u3046\u540c\u3058\u56de\u7b54\u30d1\u30bf\u30fc\u30f3\u306a\u306e\u3067\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\u30821\u3064\u306b\u6c7a\u307e\u308b\u3002\u3057\u304b\u3057\u3001\u56f33\u3067\u898b\u305f\u3068\u304a\u308a\u3001\u3053\u306e\u5c3a\u5ea6\u306f\u91cd\u75c7\u57df\u306e\u60c5\u5831\u91cf\u304c\u4e4f\u3057\u3044\u3002\u771f\u306e \u03b8 \u304c1.5\u306e\u4eba\u30823.0\u306e\u4eba\u3082\u3001\u3053\u306e\u5c3a\u5ea6\u3067\u306f\u300c\u6e80\u70b9\u300d\u3068\u3057\u304b\u8a18\u9332\u3055\u308c\u305a\u3001\u533a\u5225\u3067\u304d\u306a\u3044\u3002\u3053\u308c\u304c\u5929\u4e95\u52b9\u679c\u306e\u6b63\u4f53\u3067\u3042\u308b\u3002\u7279\u306b\u771f\u306e \u03b8 \u304c\u975e\u5e38\u306b\u9ad8\u3044\u4eba\u3067\u306f\u3001\u03b8 \u306e\u63a8\u5b9a\u5024\uff08\u7d041.1\uff09\u304c\u5b9f\u969b\u306e\u91cd\u75c7\u5ea6\u3092\u904e\u5c0f\u8a55\u4fa1\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u70b9\u306b\u6ce8\u610f\u3057\u305f\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3\u3064\u76ee\u306f\u3001<strong>\u5408\u8a08\u70b91\u70b9\u3042\u305f\u308a\u306e \u03b8 \u306e\u4e0a\u304c\u308a\u5e45\u304c\u4e00\u5b9a\u3067\u306f\u306a\u3044<\/strong>\u3053\u3068\u3067\u3042\u308b\u3002\u5408\u8a08\u70b9\u3054\u3068\u306b \u03b8 \u306e\u63a8\u5b9a\u5024\u306e\u5e73\u5747\u3092\u6c42\u3081\u308b\u3068\uff08<code>tapply(theta_hat[, 1], sum_score, mean)<\/code>\uff09\u30011\u70b9\u304b\u30898\u70b9\u307e\u3067\u306f\u30011\u70b9\u4e0a\u304c\u308b\u3054\u3068\u306b \u03b8 \u304c0.28\u301c0.39\u305a\u3064\u4e0a\u304c\u3063\u3066\u3044\u305f\u3002\u3068\u3053\u308d\u304c\u30018\u70b9\u21929\u70b9\u30019\u70b9\u219210\u70b9\u3067\u306f\u3001\u4e0a\u304c\u308a\u5e45\u304c\u3069\u3061\u3089\u3082\u7d040.50\u306b\u5e83\u304c\u3063\u3066\u3044\u305f\u3002\u9ad8\u5f97\u70b9\u5074\u306e1\u70b9\u306f\u3001\u4f4e\u5f97\u70b9\u5074\u306e1\u70b9\u3088\u308a\u3082\u3001\u03b8 \u306e\u5dee\u3068\u3057\u3066\u5927\u304d\u3044\u306e\u3067\u3042\u308b\u3002\u5408\u8a08\u70b9\u306e\u300c1\u70b9\u300d\u306e\u91cd\u3055\u304c\u3001\u5c3a\u5ea6\u306e\u3069\u3053\u306b\u3044\u308b\u304b\u306b\u3088\u3063\u3066\u9055\u3046\u3053\u3068\u304c\u3001\u3053\u3053\u304b\u3089\u3082\u8aad\u307f\u53d6\u308c\u308b\u3002\u5192\u982d\u306e\u300c3\u70b9\u21921\u70b9\u306810\u70b9\u21928\u70b9\u306f\u540c\u30582\u70b9\u306e\u6539\u5584\u304b\uff1f\u300d\u3068\u3044\u3046\u554f\u3044\u3078\u306e\u7b54\u3048\u306f\u3001\u300c\u540c\u3058\u3068\u306f\u9650\u3089\u306a\u3044\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">7. \u8ad6\u6587\u3067\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306f\u8a18\u8ff0\u4f8b\u3067\u3042\u308b\u3002Results\u306e\u6570\u5024\u306f<strong>\u672c\u8a18\u4e8b\u306e\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u89e3\u6790\u7d50\u679c<\/strong>\uff086\u7ae0\u306e\u51fa\u529b\uff09\u306b\u3082\u3068\u3065\u304f\u3082\u306e\u306a\u306e\u3067\u3001\u5b9f\u969b\u306e\u89e3\u6790\u7d50\u679c\u306b\u7f6e\u304d\u63db\u3048\u3066\u4f7f\u3063\u3066\u307b\u3057\u3044\u3002\u306a\u304a\u3001Methods\u306b\u3042\u308b\u4e00\u6b21\u5143\u6027\u306e\u78ba\u8a8d\uff08\u63a2\u7d22\u7684\u56e0\u5b50\u5206\u6790\uff09\u306f\u30016\u7ae0\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306b\u306f\u542b\u3081\u3066\u3044\u306a\u3044\u3002\u5b9f\u30c7\u30fc\u30bf\u3067\u306f\u5fc5\u305a\u5b9f\u65bd\u3057\u3066\u307b\u3057\u3044\u3002\u4e00\u6b21\u5143\u6027\u306e\u78ba\u8a8d\u3068\u3001\u305d\u308c\u304c\u5d29\u308c\u305f\u3068\u304d\u306e\u5bfe\u51e6\u306f\u3001\u591a\u6b21\u5143IRT\u306e\u8a18\u4e8b\u3067\u6271\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Methods<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">We applied item response theory (IRT) to evaluate the psychometric properties of the 10-item depressive symptom checklist. Unidimensionality was first examined using exploratory factor analysis of the tetrachoric correlation matrix. We then fitted the one-parameter logistic (Rasch) model and the two-parameter logistic (2PL) model, and compared them using the likelihood ratio test, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC). Model fit was assessed using the M2 statistic and the root mean square error of approximation (RMSEA), and item fit was assessed using the S-X2 statistic. Local independence was examined using Yen&#8217;s Q3 statistic. Item parameters were estimated by marginal maximum likelihood, and individual latent trait scores (\u03b8) were estimated using the expected a posteriori (EAP) method. All analyses were conducted using the mirt package (version X.X) in R (version X.X.X).<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u65e5\u672c\u8a9e\u8a33\uff0910\u9805\u76ee\u306e\u6291\u3046\u3064\u75c7\u72b6\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\u306e\u5fc3\u7406\u6e2c\u5b9a\u5b66\u7684\u7279\u6027\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u3001\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff08IRT\uff09\u3092\u9069\u7528\u3057\u305f\u3002\u307e\u305a\u3001\u30c6\u30c8\u30e9\u30b3\u30ea\u30c3\u30af\u76f8\u95a2\u884c\u5217\u306b\u3082\u3068\u3065\u304f\u63a2\u7d22\u7684\u56e0\u5b50\u5206\u6790\u306b\u3088\u308a\u4e00\u6b21\u5143\u6027\u3092\u691c\u8a0e\u3057\u305f\u3002\u6b21\u306b\u30011\u30d1\u30e9\u30e1\u30fc\u30bf\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\uff08Rasch\uff09\u30e2\u30c7\u30eb\u30682\u30d1\u30e9\u30e1\u30fc\u30bf\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\uff082PL\uff09\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a\u3001\u8d64\u6c60\u60c5\u5831\u91cf\u898f\u6e96\uff08AIC\uff09\u3001\u30d9\u30a4\u30ba\u60c5\u5831\u91cf\u898f\u6e96\uff08BIC\uff09\u306b\u3088\u308a\u6bd4\u8f03\u3057\u305f\u3002\u30e2\u30c7\u30eb\u306e\u9069\u5408\u5ea6\u306fM2\u7d71\u8a08\u91cf\u3068\u8fd1\u4f3c\u8aa4\u5dee\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\uff08RMSEA\uff09\u3067\u3001\u9805\u76ee\u306e\u9069\u5408\u5ea6\u306fS-X\u00b2 \u7d71\u8a08\u91cf\u3067\u8a55\u4fa1\u3057\u305f\u3002\u5c40\u6240\u72ec\u7acb\u6027\u306fYen\u306eQ3\u7d71\u8a08\u91cf\u3067\u691c\u8a0e\u3057\u305f\u3002\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u5468\u8fba\u6700\u5c24\u6cd5\u3067\u63a8\u5b9a\u3057\u3001\u500b\u4eba\u306e\u6f5c\u5728\u7279\u6027\u5024\uff08\u03b8\uff09\u306fEAP\u6cd5\u3067\u63a8\u5b9a\u3057\u305f\u3002\u89e3\u6790\u306b\u306fR\uff08\u30d0\u30fc\u30b8\u30e7\u30f3X.X.X\uff09\u306emirt\u30d1\u30c3\u30b1\u30fc\u30b8\uff08\u30d0\u30fc\u30b8\u30e7\u30f3X.X\uff09\u3092\u7528\u3044\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Results<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The 2PL model showed better fit than the Rasch model (AIC, 9480.4 vs. 9567.8; BIC, 9578.6 vs. 9621.8; likelihood ratio test, \u03c72 = 105.4, df = 9, P &lt; 0.001). The overall fit of the 2PL model was good (M2 = 26.96, df = 35, P = 0.83; RMSEA = 0.000 [90% CI, 0.000\u20130.014]; SRMSR = 0.021; CFI = 1.00), and no item showed significant misfit according to the S-X2 statistic (all P &gt; 0.10). No item pair showed evidence of local dependence (Yen&#8217;s Q3: maximum, 0.02; mean, \u22120.08). Item discrimination parameters ranged from 0.68 to 1.87, and item difficulty parameters ranged from \u22122.37 to 0.39. The test information function peaked at around \u03b8 = \u22121.2, indicating that the checklist measured mild to moderate depressive symptoms most precisely, whereas measurement precision was lower at the severe end of the latent trait.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u65e5\u672c\u8a9e\u8a33\uff092PL\u30e2\u30c7\u30eb\u306f\u3001Rasch\u30e2\u30c7\u30eb\u3088\u308a\u826f\u597d\u306a\u5f53\u3066\u306f\u307e\u308a\u3092\u793a\u3057\u305f\uff08AIC\uff1a9480.4 vs. 9567.8\u3001BIC\uff1a9578.6 vs. 9621.8\u3001\u5c24\u5ea6\u6bd4\u691c\u5b9a \u03c7\u00b2 = 105.4\u3001\u81ea\u7531\u5ea69\u3001P &lt; 0.001\uff09\u30022PL\u30e2\u30c7\u30eb\u306e\u5168\u4f53\u7684\u306a\u9069\u5408\u5ea6\u306f\u826f\u597d\u3067\u3042\u308a\uff08M2 = 26.96\u3001\u81ea\u7531\u5ea635\u3001P = 0.83\u3001RMSEA = 0.000\uff3b90\uff05\u4fe1\u983c\u533a\u9593 0.000\u301c0.014\uff3d\u3001SRMSR = 0.021\u3001CFI = 1.00\uff09\u3001S-X\u00b2 \u7d71\u8a08\u91cf\u3067\u6709\u610f\u306a\u4e0d\u9069\u5408\u3092\u793a\u3057\u305f\u9805\u76ee\u306f\u306a\u304b\u3063\u305f\uff08\u3059\u3079\u3066 P &gt; 0.10\uff09\u3002\u5c40\u6240\u4f9d\u5b58\u3092\u793a\u3059\u9805\u76ee\u30da\u30a2\u3082\u8a8d\u3081\u3089\u308c\u306a\u304b\u3063\u305f\uff08Yen \u306e Q3\uff1a\u6700\u5927\u50240.02\u3001\u5e73\u5747\u5024\u22120.08\uff09\u3002\u9805\u76ee\u306e\u8b58\u5225\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f0.68\u301c1.87\u3001\u56f0\u96e3\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u22122.37\u301c0.39\u306e\u7bc4\u56f2\u3067\u3042\u3063\u305f\u3002\u30c6\u30b9\u30c8\u60c5\u5831\u91cf\u306f \u03b8 = \u22121.2 \u4ed8\u8fd1\u3067\u6700\u5927\u3068\u306a\u308a\u3001\u672c\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\u306f\u8efd\u5ea6\u301c\u4e2d\u7b49\u5ea6\u306e\u6291\u3046\u3064\u75c7\u72b6\u3092\u6700\u3082\u7cbe\u5bc6\u306b\u6e2c\u5b9a\u3059\u308b\u4e00\u65b9\u3001\u6f5c\u5728\u7279\u6027\u306e\u91cd\u75c7\u5074\u3067\u306f\u6e2c\u5b9a\u7cbe\u5ea6\u304c\u4f4e\u3044\u3053\u3068\u304c\u793a\u3055\u308c\u305f\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">8. \u307e\u3068\u3081<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5408\u8a08\u70b9\u306f\u3001\u3059\u3079\u3066\u306e\u9805\u76ee\u3092\u300c\u540c\u3058\u91cd\u3055\u306e1\u70b9\u300d\u3068\u3057\u3066\u6570\u3048\u3066\u3044\u308b\u3002IRT\u306f\u3001\u9805\u76ee\u3054\u3068\u306e<strong>\u56f0\u96e3\u5ea6 b<\/strong>\uff08\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u304c\u4e94\u5206\u4e94\u5206\u306b\u306a\u308b\u306e\u306f\u3001\u3069\u306e\u304f\u3089\u3044\u91cd\u3044\u4eba\u304b\uff09\u3068<strong>\u8b58\u5225\u529b a<\/strong>\uff08\u3069\u308c\u3060\u3051\u304f\u3063\u304d\u308a\u898b\u5206\u3051\u3089\u308c\u308b\u304b\uff09\u3092\u8003\u616e\u3057\u3066\u3001\u6f5c\u5728\u7279\u6027 <strong>\u03b8<\/strong> \u3092\u63a8\u5b9a\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9805\u76ee\u7279\u6027\u66f2\u7dda\uff08ICC\uff09<\/strong>\u306f\u3001\u03b8 \u3054\u3068\u306e\u300e\u306f\u3044\u300f\u306e\u78ba\u7387\u3092\u8868\u3059S\u5b57\u66f2\u7dda\u3067\u3001b \u304c\u4f4d\u7f6e\u3001a \u304c\u50be\u304d\u3092\u6c7a\u3081\u308b\u3002<\/li>\n\n\n\n<li><strong>1PL<\/strong>\u306f\u8b58\u5225\u529b\u3092\u5171\u901a\u3001<strong>2PL<\/strong>\u306f\u9805\u76ee\u3054\u3068\u3001<strong>3PL<\/strong>\u306f\u5f53\u3066\u63a8\u91cf\u306e\u4e0b\u9650 c \u3092\u52a0\u3048\u305f\u30e2\u30c7\u30eb\u3002\u81e8\u5e8a\u306e\u4e8c\u5024\u9805\u76ee\u306e\u8cea\u554f\u7968\u3067\u306f\u30011PL\u304b2PL\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30c6\u30b9\u30c8\u60c5\u5831\u91cf<\/strong>\u306f\u300c\u5c3a\u5ea6\u304c\u3069\u306e \u03b8 \u306e\u7bc4\u56f2\u3092\u7cbe\u5bc6\u306b\u6e2c\u308c\u308b\u304b\u300d\u3092\u793a\u3057\u3001$SE(\\theta) \\approx 1\/\\sqrt{I(\\theta)}$ \u3067\u6e2c\u5b9a\u8aa4\u5dee\u306b\u76f4\u7d50\u3059\u308b\u3002\u5929\u4e95\u52b9\u679c\u30fb\u5e8a\u52b9\u679c\u306f\u3001\u60c5\u5831\u91cf\u306e\u5c71\u304c\u504f\u3063\u3066\u3044\u308b\u72b6\u614b\u3068\u8a00\u3044\u63db\u3048\u3089\u308c\u308b\u3002<\/li>\n\n\n\n<li>IRT\u306f<strong>\u4e00\u6b21\u5143\u6027\u30fb\u5c40\u6240\u72ec\u7acb\u6027<\/strong>\u3092\u524d\u63d0\u3068\u3059\u308b\u3002\u524d\u63d0\u306e\u78ba\u8a8d\u3092\u7701\u7565\u3057\u3066\u306f\u3044\u3051\u306a\u3044\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u9805\u76ee\u304c\u300c1\u3064\u306e\u7279\u6027\u300d\u3092\u6e2c\u3063\u3066\u3044\u308b\u4e00\u6b21\u5143IRT\u3092\u6271\u3063\u305f\u3002\u3057\u304b\u3057\u5b9f\u969b\u306e\u8cea\u554f\u7968\u3067\u306f\u3001\u300c\u6291\u3046\u3064\u300d\u3068\u300c\u4e0d\u5b89\u300d\u306e\u3088\u3046\u306b\u3001\u8907\u6570\u306e\u7279\u6027\u304c\u6df7\u3056\u3063\u3066\u3044\u308b\u3053\u3068\u3082\u591a\u3044\u3002\u4e00\u6b21\u5143\u6027\u306e\u524d\u63d0\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u5834\u5408\u306b\u4f7f\u3046\u306e\u304c\u3001<strong>\u591a\u6b21\u5143\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff08MIRT\uff09<\/strong>\u3067\u3042\u308b\u3002\u7d9a\u304d\u306f<a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/multidimensional-irt-questionnaire-mirt-r\/\">\u591a\u6b21\u5143\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\u306e\u8a18\u4e8b<\/a>\u3067\u89e3\u8aac\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># ============================================\n# \u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff08IRT\uff09\u306e\u57fa\u790e\uff1amirt\u306b\u3088\u308b2PL\u5206\u6790\n# ============================================\n# install.packages(c(\"mirt\", \"latticeExtra\"))  # \u521d\u56de\u306e\u307f\nlibrary(mirt)\n# latticeExtra \u306f\u3001Step 5 \u306e plot(type = \"infoSE\") \u3067\n# \u60c5\u5831\u91cf\u3068\u6a19\u6e96\u8aa4\u5dee\u30922\u8ef8\u3067\u91cd\u306d\u3066\u63cf\u304f\u3068\u304d\u306b\u4f7f\u308f\u308c\u308b\uff08library() \u3067\u306e\u8aad\u307f\u8fbc\u307f\u306f\u4e0d\u8981\uff09\n\n# ---- Step 0\uff1a\u6982\u5ff5\u56f3\uff08\u56f31\u30fb\u56f32\uff09 ----\ntheta &lt;- seq(-4, 4, length.out = 200)\np2pl  &lt;- function(theta, a, b, c = 0) c + (1 - c) \/ (1 + exp(-a * (theta - b)))\n\npar(mfrow = c(1, 2))\nplot(theta, p2pl(theta, a = 1.5, b = -1), type = \"l\", lwd = 2, ylim = c(0, 1),\n     xlab = expression(theta), ylab = \"P(Yes)\", main = \"Varying difficulty (b)\")\nlines(theta, p2pl(theta, a = 1.5, b = 0), lwd = 2, lty = 2)\nlines(theta, p2pl(theta, a = 1.5, b = 1), lwd = 2, lty = 3)\nabline(h = 0.5, col = \"gray\")\nlegend(\"topleft\", legend = c(\"b = -1\", \"b = 0\", \"b = 1\"), lty = 1:3, lwd = 2, bty = \"n\")\nplot(theta, p2pl(theta, a = 0.5, b = 0), type = \"l\", lwd = 2, ylim = c(0, 1),\n     xlab = expression(theta), ylab = \"P(Yes)\", main = \"Varying discrimination (a)\")\nlines(theta, p2pl(theta, a = 1.5, b = 0), lwd = 2, lty = 2)\nlines(theta, p2pl(theta, a = 3.0, b = 0), lwd = 2, lty = 3)\nabline(h = 0.5, col = \"gray\")\nlegend(\"topleft\", legend = c(\"a = 0.5\", \"a = 1.5\", \"a = 3.0\"), lty = 1:3, lwd = 2, bty = \"n\")\npar(mfrow = c(1, 1))\n\npar(mfrow = c(1, 3))\nbs &lt;- c(-1, 0, 1)\nas &lt;- c(0.6, 1.5, 3.0)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"1PL\")\nfor (k in 1:3) lines(theta, p2pl(theta, a = 1.2, b = bs&#91;k]), lwd = 2, lty = k)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"2PL\")\nfor (k in 1:3) lines(theta, p2pl(theta, a = as&#91;k], b = bs&#91;k]), lwd = 2, lty = k)\nplot(NA, xlim = c(-4, 4), ylim = c(0, 1), xlab = expression(theta), ylab = \"P(Yes)\", main = \"3PL\")\nfor (k in 1:3) lines(theta, p2pl(theta, a = as&#91;k], b = bs&#91;k], c = 0.2), lwd = 2, lty = k)\nabline(h = 0.2, col = \"gray\")\npar(mfrow = c(1, 1))\n\n# ---- Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u751f\u6210 ----\nset.seed(2026)\nN &lt;- 1000\nJ &lt;- 10\ntrue_a &lt;- c(1.2, 1.5, 0.8, 1.8, 1.0, 2.0, 1.4, 0.7, 2.2, 1.6)\ntrue_b &lt;- c(-2.4, -2.0, -1.8, -1.5, -1.3, -1.1, -0.8, -0.6, -0.3, 0.4)\ntrue_theta &lt;- rnorm(N, mean = 0, sd = 1)\nP &lt;- 1 \/ (1 + exp(-sweep(outer(true_theta, true_b, \"-\"), 2, true_a, \"*\")))\ndat &lt;- matrix(rbinom(N * J, size = 1, prob = P), nrow = N, ncol = J)\ncolnames(dat) &lt;- paste0(\"Q\", 1:J)\nround(colMeans(dat), 2)\ntable(rowSums(dat))\n\n# ---- Step 2\uff1a1PL\u30682PL\u306e\u6bd4\u8f03 ----\nfit_1pl &lt;- mirt(dat, model = 1, itemtype = \"Rasch\", verbose = FALSE)\nfit_2pl &lt;- mirt(dat, model = 1, itemtype = \"2PL\", verbose = FALSE)\nanova(fit_1pl, fit_2pl)\n\n# ---- Step 3\uff1a\u9805\u76ee\u30d1\u30e9\u30e1\u30fc\u30bf ----\nest &lt;- coef(fit_2pl, IRTpars = TRUE, simplify = TRUE)\nround(est$items&#91;, c(\"a\", \"b\")], 2)\nround(cbind(true_a, est_a = est$items&#91;, \"a\"],\n            true_b, est_b = est$items&#91;, \"b\"]), 2)\n\n# ---- Step 4\uff1a\u9069\u5408\u5ea6 ----\nitemfit(fit_2pl)\nM2(fit_2pl)\nQ3 &lt;- residuals(fit_2pl, type = \"Q3\")\n\n# ---- Step 5\uff1aICC\u3068\u30c6\u30b9\u30c8\u60c5\u5831\u91cf ----\nplot(fit_2pl, type = \"trace\")\nitemplot(fit_2pl, item = 9, type = \"trace\")\nitemplot(fit_2pl, item = 9, type = \"info\")\nplot(fit_2pl, type = \"infoSE\", theta_lim = c(-4, 4))\ntheta_grid &lt;- matrix(seq(-3, 3, by = 1))\ninfo &lt;- testinfo(fit_2pl, Theta = theta_grid)\nround(data.frame(theta = theta_grid&#91;, 1], info = info, SE = 1 \/ sqrt(info)), 2)\n\n# ---- Step 6\uff1a\u03b8 \u306e\u63a8\u5b9a\u3068\u5408\u8a08\u70b9\u3068\u306e\u6bd4\u8f03 ----\ntheta_hat &lt;- fscores(fit_2pl, method = \"EAP\")\nsum_score &lt;- rowSums(dat)\nplot(jitter(sum_score, amount = 0.2), theta_hat&#91;, 1],\n     xlab = \"Sum score\", ylab = expression(hat(theta)),\n     main = expression(paste(\"Sum score vs. estimated \", theta)), pch = 16, col = rgb(0, 0, 0, 0.3))\nround(t(sapply(split(theta_hat&#91;, 1], sum_score),\n               function(x) c(min = min(x), max = max(x)))), 2)\nround(tapply(theta_hat&#91;, 1], sum_score, mean), 2)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Reeve BB, Hays RD, Bjorner JB, et al. Psychometric evaluation and calibration of health-related quality of life item banks: plans for the Patient-Reported Outcomes Measurement Information System (PROMIS). <em>Medical Care<\/em>. 2007;45(5 Suppl 1):S22\u2013S31. <a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/17443115\/\">https:\/\/pubmed.ncbi.nlm.nih.gov\/17443115\/<\/a><\/li>\n\n\n\n<li>Edelen MO, Reeve BB. Applying item response theory (IRT) modeling to questionnaire development, evaluation, and refinement. <em>Quality of Life Research<\/em>. 2007;16(Suppl 1):5\u201318. <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s11136-007-9198-0\">doi:10.1007\/s11136-007-9198-0<\/a><\/li>\n\n\n\n<li>Bevans M, Ross A, Cella D. Patient-Reported Outcomes Measurement Information System (PROMIS): efficient, standardized tools to measure self-reported health and quality of life. <em>Nursing Outlook<\/em>. 2014;62(5):339\u2013345. <a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC4179871\/\">https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC4179871\/<\/a><\/li>\n\n\n\n<li>Christensen KB, Makransky G, Horton M. Critical values for Yen&#8217;s Q3: identification of local dependence in the Rasch model using residual correlations. <em>Applied Psychological Measurement<\/em>. 2017;41(3):178\u2013194. <a href=\"https:\/\/journals.sagepub.com\/doi\/10.1177\/0146621616677520\">doi:10.1177\/0146621616677520<\/a><\/li>\n\n\n\n<li>Chalmers RP. mirt: A multidimensional item response theory package for the R environment. <em>Journal of Statistical Software<\/em>. 2012;48(6):1\u201329. <a href=\"https:\/\/www.jstatsoft.org\/article\/view\/v048i06\">doi:10.18637\/jss.v048.i06<\/a><\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u52a0\u85e4\u5065\u592a\u90ce\u30fb\u5c71\u7530\u525b\u53f2\u30fb\u5ddd\u7aef\u4e00\u5149\u300eR\u306b\u3088\u308b\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\u300f\u30aa\u30fc\u30e0\u793e\uff082014\uff09<br><a href=\"https:\/\/link.amazon\/B0cJ8V09d\">https:\/\/www.amazon.co.jp\/dp\/4274050173<\/a>\n<ul class=\"wp-block-list\">\n<li>R\u3067\u5b9f\u969b\u306b\u624b\u3092\u52d5\u304b\u3057\u306a\u304c\u3089IRT\u3092\u5b66\u3079\u308b\u4e00\u518a\u3002\u672c\u8a18\u4e8b\u306e\u6b21\u306b\u8aad\u3080\u672c\u3068\u3057\u3066\u304a\u3059\u3059\u3081\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u8c4a\u7530\u79c0\u6a39\u300e\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\uff3b\u5165\u9580\u7de8\uff3d\uff08\u7b2c2\u7248\uff09\u300f\u671d\u5009\u66f8\u5e97\uff082012\uff09<br><a href=\"https:\/\/link.amazon\/B0gdCTYR0\">https:\/\/www.amazon.co.jp\/dp\/4254127952<\/a>\n<ul class=\"wp-block-list\">\n<li>\u65e5\u672c\u8a9e\u3067IRT\u3092\u5b66\u3076\u5b9a\u756a\u306e\u6559\u79d1\u66f8\u3002\u5168\u7de8\u3067R\u306b\u3088\u308b\u5b9f\u7fd2\u304c\u3067\u304d\u308b\u3002\u5c3a\u5ea6\u5b9a\u6570 D = 1.7 \u3092\u542b\u3080\u5f0f\u306e\u5f62\u306f\u3053\u306e\u672c\u3067\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u9ad8\u6a4b\u4fe1\u300eIRT\u9805\u76ee\u53cd\u5fdc\u7406\u8ad6\u5165\u9580\uff1a\u7d71\u8a08\u5b66\u306e\u57fa\u790e\u304b\u3089\u5b66\u3076\u826f\u8cea\u306a\u30c6\u30b9\u30c8\u306e\u4f5c\u308a\u65b9\u300f\u30aa\u30fc\u30e0\u793e<br><a href=\"https:\/\/link.amazon\/B00VkcwcT\">https:\/\/www.amazon.co.jp\/dp\/4274227685<\/a>\n<ul class=\"wp-block-list\">\n<li>\u526f\u984c\u306e\u3068\u304a\u308a\u3001\u7d71\u8a08\u5b66\u306e\u57fa\u790e\u304b\u3089IRT\u3092\u5b66\u3079\u308b\u5165\u9580\u66f8\u3002\u6570\u5f0f\u306b\u4e0d\u5b89\u304c\u3042\u308b\u8aad\u8005\u306f\u3001\u3053\u3061\u3089\u304b\u3089\u8aad\u3080\u3068\u3088\u3044\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u82e5\u624b\u533b\u5e2b\uff1a\u3046\u3064\u75c7\u72b6\u306e\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8\uff0810\u9805\u76ee\u3001\u300c\u306f\u3044\uff0f\u3044\u3044\u3048\u300d\u3067\u7b54\u3048\u308b\uff09\u3092\u4f7f\u3063\u3066\u3001\u6cbb\u7642\u524d\u5f8c\u3067\u5408\u8a08\u70b9\u3092\u6bd4\u3079\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002A\u3055\u3093\u306f3\u70b9\u304b\u30891\u70b9\u306b\u3001B\u3055\u3093\u306f10\u70b9\u304b\u30898\u70b9\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3069\u3061\u3089\u3082\u300c2\u70b9\u6539\u5584\u300d\u3067\u3044\u3044\u3067\u3059\u3088\u306d\uff1f [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[157],"tags":[],"class_list":["post-5034","post","type-post","status-publish","format-standard","hentry","category-157"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/5034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=5034"}],"version-history":[{"count":12,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/5034\/revisions"}],"predecessor-version":[{"id":5077,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/5034\/revisions\/5077"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=5034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=5034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=5034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}