{"id":39,"date":"2024-04-12T21:04:56","date_gmt":"2024-04-12T12:04:56","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/difference-among-goodness-of-fit-indices-for-linear-regression\/"},"modified":"2024-08-26T07:41:32","modified_gmt":"2024-08-25T22:41:32","slug":"difference-among-goodness-of-fit-indices-for-linear-regression","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/difference-among-goodness-of-fit-indices-for-linear-regression\/","title":{"rendered":"\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3055\u306b\u95a2\u3059\u308b\u3044\u304f\u3064\u304b\u306e\u6307\u6a19\u306e\u9055\u3044\u3068\u4f7f\u3044\u5206\u3051"},"content":{"rendered":"\n

\u91cd\u56de\u5e30\u5206\u6790\uff08\u4ee5\u4e0b\u3001\u7dda\u5f62\u56de\u5e30\u3082\u540c\u7fa9\uff09\u306b\u306f\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3055\u306e\u6307\u6a19\u3068\u3057\u3066\u3044\u304f\u3064\u304b\u3042\u308b\u304c\u3001\u305d\u308c\u3089\u306e\u9055\u3044\u3068\u4f7f\u3044\u5206\u3051\u306f\u3069\u3046\u3057\u305f\u3089\u3088\u3044\u306e\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u81ea\u7531\u5ea6\u8abf\u6574\u6e08\u307f\u6c7a\u5b9a\u4fc2\u6570\u306e\u7279\u5fb4<\/h2>\n\n\n\n

\u8aac\u660e\u7387\u3068\u3082\u8a00\u308f\u308c\u308b\u6c7a\u5b9a\u4fc2\u6570\u306e\u8aac\u660e\u5909\u6570\u306e\u500b\u6570\u3092\u8003\u616e\u3057\u305f\u30d0\u30fc\u30b8\u30e7\u30f3<\/p>\n\n\n\n

0 \u304b\u3089 1 \u306e\u9593\u306e\u5024\u3092\u53d6\u308a\u30011 \u306b\u8fd1\u3065\u304f\u307b\u3069\u5f53\u3066\u306f\u307e\u308a\u304c\u3088\u3044\u3068\u3044\u3046\u6307\u6a19\u306b\u306a\u308b<\/p>\n\n\n\n

\u7d76\u5bfe\u8a55\u4fa1\u304c\u53ef\u80fd<\/p>\n\n\n\n

\u6c7a\u5b9a\u4fc2\u6570\u306e\u5927\u304d\u3055\u306b\u3064\u3044\u3066\u306f\u3001\u904e\u53bb\u8a18\u4e8b\u53c2\u7167<\/p>\n\n\n

\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\t\u6c7a\u5b9a\u4fc2\u6570\u306e\u76ee\u5b89 \u2015 \u6c7a\u5b9a\u4fc2\u6570 R 2 \u4e57\u5024\u306f\u3044\u304f\u3064\u306a\u3089\u3088\u3044\u304b\uff1f<\/a>\n\t\t\t\t\t\t\u91cd\u56de\u5e30\u5206\u6790\u306e\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3055\u3092\u793a\u3059\u6c7a\u5b9a\u4fc2\u6570\u3002 \u6c7a\u5b9a\u4fc2\u6570\u306fR2\u4e57\u5024\u3068\u3082\u3044\u3046\u3002 \u6c7a\u5b9a\u4fc2\u6570\u306e\u76ee\u5b89\u306f\u3042\u308b\u306e\u3060\u308d\u3046\u304b\uff1f \u30bc\u30ed\u304b\u3089\uff11\u306e\u7bc4\u56f2\u3092\u3068\u308b\u308f\u3051\u3060\u304c\u3001\u3044\u304f\u3064\u306a\u3089\u826f\u3044\u306e\u304b\uff1f…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n
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\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\t\u6c7a\u5b9a\u4fc2\u6570\u304c\u5c0f\u3055\u3044\u5834\u5408\u306e\u8003\u3048\u65b9<\/a>\n\t\t\t\t\t\t\u91cd\u56de\u5e30\u5206\u6790\u306e\u8a55\u4fa1\u6307\u6a19\u306e\u4e00\u3064\u3001\u6c7a\u5b9a\u4fc2\u6570\u304c\u5c0f\u3055\u3044\u3068\u304d\u306b\u3001\u3069\u3046\u8003\u3048\u305f\u3089\u3088\u3044\u304b \u3069\u306e\u304f\u3089\u3044\u306e\u6570\u5024\u3067\u3042\u3063\u305f\u3089\u3001\u5927\u4e08\u592b\u306a\u306e\u3060\u308d\u3046\u304b \u6c7a\u5b9a\u4fc2\u6570\u304c\u3069\u306e\u304f\u3089\u3044\u3067\u3042\u308c\u3070\u610f\u5473\u304c\u3042\u308b…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n

Mallows Cp \u898f\u6e96\u3001AIC\u3001BIC \u306e\u7279\u5fb4<\/h2>\n\n\n\n

\u3053\u308c\u3089\u306f\u3001\u30e2\u30c7\u30eb\u304b\u3089\u6570\u5024\u304c\u8a08\u7b97\u3055\u308c\u308b\u304c\u3001\u305d\u306e\u6570\u5024\u81ea\u4f53\u3067\u5224\u65ad\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044<\/p>\n\n\n\n

\u305d\u306e\u4ed6\u306e\u5909\u6570\u30bb\u30c3\u30c8\u30e2\u30c7\u30eb\u3068\u76f8\u5bfe\u7684\u306b\u6bd4\u8f03\u3057\u3066\u5224\u65ad\u3059\u308b<\/p>\n\n\n\n

\u6570\u5024\u304c\u5c0f\u3055\u3044\u30e2\u30c7\u30eb\u307b\u3069\u3001\u5f53\u3066\u306f\u307e\u308a\u304c\u826f\u3044\u30e2\u30c7\u30eb\u3068\u5224\u65ad\u3059\u308b<\/p>\n\n\n\n

\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>\r\n

\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>

AIC \u3068 Mallows Cp \u898f\u6e96\u306e\u9055\u3044<\/h2>\n\n\n\n

\u8aac\u660e\u5909\u6570\u306e\u6570\u3067\u7f70\u5247\u3092\u8a2d\u3051\u3066\u3044\u308b\u70b9\u304c\u4f3c\u901a\u3063\u3066\u3044\u308b<\/p>\n\n\n\n

\u7dda\u5f62\u56de\u5e30\u3067\u3042\u308c\u3070\u3001\u540c\u69d8\u306e\u6307\u6a19\u3068\u8003\u3048\u3089\u308c\u308b<\/p>\n\n\n\n

\n

\u50be\u5411\u304b\u3089\u306f\u5909\u6570\u9078\u629e\u306e\u3055\u308c\u3084\u3059\u3055\u306f HQC> (AI C \u2252Malllows\u2032s Cp) > BI C H Q C > (A I C \u2252 Malllows \u2032 s C p) > B I C \u3067\u3059\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u51fa\u5178\uff1a\u30b9\u30c6\u30c3\u30d7\u30ef\u30a4\u30ba\u6cd5\u306b\u304a\u3051\u308bAIC\/BIC\/Mallows’s CP\u306e\u6bd4\u8f03 – Engineering Skills<\/a><\/p>\n\n\n\n

\n

\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306b\u5bfe\u3057\u3066\u306fAIC\u3068Cp\u306e\u6700\u5c0f\u5316\u306f\u307b\u307c\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u3082\u77e5\u3089\u308c\u3066\u3044\u308b<\/p>\n<\/blockquote>\n\n\n\n

\u51fa\u5178\uff1ahttps:\/\/www.ieice.org\/publications\/conference-FIT-DVDs\/FIT2014\/data\/pdf\/A-006.pdf<\/a><\/p>\n\n\n\n

AIC\uff08\u8d64\u6c60\u60c5\u5831\u91cf\u898f\u6e96\uff09\u3068 BIC\uff08\u30d9\u30a4\u30ba\u60c5\u5831\u91cf\u898f\u6e96\uff09\u306e\u7279\u5fb4\u3068\u9055\u3044<\/h2>\n\n\n\n

AIC \u3068 BIC \u306f\u3001\u7dda\u5f62\u56de\u5e30\uff08\u91cd\u56de\u5e30\uff09\u3060\u3051\u3067\u306a\u304f\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u3001Cox \u56de\u5e30\u306b\u4f7f\u3048\u308b<\/p>\n\n\n\n

\n

\u3053\u308c\u306b\u3064\u3044\u3066\u306f\uff0c\u6700\u521d\u306b\u6319\u3052\u305f\u8d64\u6c60\uff081996\uff09\u8ad6\u6587\u304c\uff0c\u6700\u5f8c\u306e\u90e8\u5206\u3067\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7d50\u8ad6\u3057\u3066\u3044\u308b\u3053\u3068\u3068\u3082\u7b26\u5408\u3059\u308b\u3002<\/p>\n\n\n\n

BIC \u306f\uff0c\u6709\u610f\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\uff0c\u305d\u3046\u3067\u306a\u3044\u3082\u306e\u3068\u304c\uff0c\u5bb9\u6613\u306b\u8b58\u5225\u3067\u304d\u308b\u72b6\u6cc1\u306b\u5bfe\u5fdc\u3059\u308b\u30e2\u30c7\u30eb\u304b\u3089\u5f97\u3089\u308c\uff0c\u3053\u308c\u306b\u5bfe\u3057\u3066AIC\u306f\uff0c\u6709\u610f\u6027\u304c\u3088\u3046\u3084\u304f\u8a8d\u3081\u3089\u308c\u308b\u7a0b\u5ea6\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u53d6\u308a\u6271\u3044\u306b\u6ce8\u76ee\u3057\uff0c\u8aa4\u5dee\u306e\u5f71\u97ff\u306b\u57cb\u6ca1\u3057\u305d\u3046\u306b\u306a\u308b\u3068\u3053\u308d\u307e\u3067\u30e2\u30c7\u30eb\u5316\u306e\u53ef\u80fd\u6027\u3092\u8ffd\u53ca<\/p>\n\n\n\n

\u53c2\u7167\uff1a\u8d64\u6c60\u5f18\u6b21 (1996) AIC \u3068 MDL \u3068 BIC (p. 378)<\/p>\n\n\n\n

\u5f97\u3089\u308c\u305f\u30c7\u30fc\u30bf\u306e\u7d71\u8a08\u89e3\u6790\u306e\u5b9f\u8df5\u7684\u306a\u5834\u9762\u3067\uff0c AIC \u3068 BIC \u306e\u3069\u3061\u3089\u3092\u4f7f\u3046\u304b\u8ff7\u3046\u3068\u304d\u306e\u6307\u91dd\u306b\u3082\u306a\u308a\u3046\u308b\u8d64\u6c60\u306e\u8aac\u660e\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u51fa\u5178\uff1aAIC \u3068 BIC\uff0c\u305d\u306e\u7279\u5fb4\u3092\u6bd4\u8f03<\/a><\/p>\n\n\n\n

\n

AIC\u3068\u6bd4\u8f03\u3059\u308b\u3068,\u30e2\u30c7\u30eb\u306e\u8907\u96d1\u3055\u3078\u306e\u7f70\u5247\u9805\u304c\u7570\u306a\u308b.\u3059\u306a\u308f\u3061, AIC\u306f2(d+2)\u3067,BIC\u306f(d+2)logn\u3067\u3042\u308b.\u3053\u308c\u3089\u306e\u9055\u3044\u304b\u3089\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u77e5\u3089\u308c\u3066\u3044\u308b.BIC\u306f\u771f\u306e\u30e2\u30c7\u30eb\u306e\u9078\u629e\u306b\u5bfe\u3059\u308b\u4e00\u81f4\u6027\u3092\u6301\u3064.\u4e00\u65b9,AIC\u306f\u305d\u306e\u6027\u8cea\u3092\u6301\u305f\u306a\u3044.\u3057\u304b\u3057,AIC\u306f\u4e88\u6e2c\u8aa4\u5dee\u3092\u6700\u5c0f\u306b\u3059\u308b\u30e2\u30c7\u30eb\u3092\u9078\u629e\u3059\u308b\u304c,BIC\u306f\u305d\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u305f\u306a\u3044.<\/p>\n<\/blockquote>\n\n\n\n

\u51fa\u5178\uff1ahttps:\/\/mcm-www.jwu.ac.jp\/~konno\/pdf\/chuo2023_ch1_0504.pdf<\/a><\/p>\n\n\n\n

\u3053\u3061\u3089\u306e\u904e\u53bb\u8a18\u4e8b\u3082\u3001\u53c2\u8003\u306b\u306a\u308c\u3070<\/p>\n\n\n

\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tAIC\u3068BIC\u306e\u9055\u3044\u306f\u4f55\u304b\uff1f\u7d71\u8a08\u89e3\u6790\u3067\u306e\u7279\u5fb4\u6bd4\u8f03<\/a>\n\t\t\t\t\t\t\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u306e\u6307\u6a19\u3067\u3042\u308b\u3001AIC\u3068BIC\u3002 \u9055\u3044\u306f\u4f55\u304b\uff1f AIC\u3084BIC\u3068\u306f\u4f55\u304b\uff1f AIC\u306f\u3001Akaike’s Information Criterion \u8d64\u6c60\u60c5\u5831\u91cf\u898f\u6e96\u306e\u982d\u6587\u5b57\u8a9e\u3001BIC\u306f\u3001Bayesia…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n

\u4f7f\u3044\u5206\u3051<\/h2>\n\n\n\n
\u6307\u6a19<\/th>\u9069\u7528\u30e2\u30c7\u30eb<\/th>\u89e3\u91c8\u306e\u4ed5\u65b9<\/th>\u4f7f\u7528\u60f3\u5b9a\u5834\u9762<\/th><\/tr><\/thead>
\u81ea\u7531\u5ea6\u8abf\u6574\u6e08\u307f\u6c7a\u5b9a\u4fc2\u6570<\/td>\u7dda\u5f62\u56de\u5e30<\/td>1 \u306b\u8fd1\u3044\u307b\u3069\u5f53\u3066\u306f\u307e\u308a\u304c\u826f\u3044\u30e2\u30c7\u30eb\uff08\u7d76\u5bfe\u8a55\u4fa1\uff09<\/td>\u91cd\u56de\u5e30\u5206\u6790\u306e\u30e2\u30c7\u30eb\u8a55\u4fa1<\/td><\/tr>
Mallows Cp \u898f\u6e96<\/td>\u7dda\u5f62\u56de\u5e30<\/td>\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u5c0f\u3055\u3044\u307b\u3046\u304c\u826f\u3044\uff08\u76f8\u5bfe\u8a55\u4fa1\uff09<\/td>\u91cd\u56de\u5e30\u5206\u6790\u306e\u5909\u6570\u9078\u629e\u306e\u53c2\u8003<\/td><\/tr>
AIC<\/td>\u7dda\u5f62\u56de\u5e30\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30fbCox \u56de\u5e30<\/td>\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u5c0f\u3055\u3044\u307b\u3046\u304c\u826f\u3044\uff08\u76f8\u5bfe\u8a55\u4fa1\uff09<\/td>\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5909\u6570\u9078\u629e\u306e\u53c2\u8003\uff08\u306a\u308b\u3079\u304f\u5909\u6570\u3092\u6b8b\u3057\u305f\u3044\uff09<\/td><\/tr>
BIC<\/td>\u7dda\u5f62\u56de\u5e30\u30fb\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30fbCox \u56de\u5e30<\/td>\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u5c0f\u3055\u3044\u307b\u3046\u304c\u826f\u3044\uff08\u76f8\u5bfe\u8a55\u4fa1\uff09<\/td>\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5909\u6570\u9078\u629e\u306e\u53c2\u8003\uff08\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\u306b\u3057\u305f\u3044\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u307e\u3068\u3081<\/h2>\n\n\n\n

\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u3001\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3055\u306e\u6307\u6a19\u3092 4 \u3064\u3042\u3052\u3001\u9055\u3044\u3068\u4f7f\u3044\u5206\u3051\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u305f<\/p>\n\n\n\n

\u30e2\u30c7\u30eb\u305d\u306e\u3082\u306e\u306e\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3057\u3042\u3057\u306f\u3001\u7d76\u5bfe\u7684\u306a\u8a55\u4fa1\u304c\u3067\u304d\u308b\u81ea\u7531\u5ea6\u8abf\u6574\u6e08\u307f\u6c7a\u5b9a\u4fc2\u6570\u304c\u826f\u3044\u3068\u601d\u3046<\/p>\n\n\n\n

\u3044\u304f\u3064\u304b\u306e\u30e2\u30c7\u30eb\u3092\u6bd4\u8f03\u3057\u3066\u3001\u76f8\u5bfe\u7684\u306b\u5f53\u3066\u306f\u307e\u308a\u306e\u826f\u3044\u30e2\u30c7\u30eb\u3092\u898b\u6975\u3081\u308b\u306b\u306f\u3001\u91cd\u56de\u5e30\u3060\u3051\u3067\u306a\u304f\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30fbCox \u56de\u5e30\u306b\u3082\u4f7f\u3048\u3066\u3001\u306a\u308b\u3079\u304f\u5909\u6570\u3092\u6b8b\u3057\u3066\u3001\u6700\u5927\u9650\u4ea4\u7d61\u56e0\u5b50\u8abf\u6574\u3092\u3057\u3088\u3046\u3068\u3059\u308b AIC \u304c\u826f\u3044\u3068\u601d\u3046<\/p>\n\n\n\n

\u4f55\u3089\u304b\u53c2\u8003\u306b\u306a\u308c\u3070\u5e78\u3044<\/p>\n\n\n\n

\u53c2\u8003\u6587\u732e\u30fb\u30b5\u30a4\u30c8<\/h2>\n\n\n\n

\u7dda\u578b\u56de\u5e30\u306b\u304a\u3051\u308b\u5404\u7a2e\u5f53\u3066\u306f\u307e\u308a\u6307\u6a19\u306e\u6570\u5f0f\u8aac\u660e
https:\/\/mcm-www.jwu.ac.jp\/~konno\/pdf\/chuo2023_ch1_0504.pdf<\/a><\/p>\n\n\n\n

Mallows \u306e Cp \u898f\u6e96\u306b\u3088\u308b\u56de\u5e30\u5f0f\u306e\u5909\u6570\u9078\u629e
https:\/\/www.ieice.org\/publications\/conference-FIT-DVDs\/FIT2014\/data\/pdf\/A-006.pdf<\/a><\/p>\n\n\n\n

AIC \u3068 BIC \u306e\u7279\u5fb4\u6bd4\u8f03
https:\/\/biolab.sakura.ne.jp\/aic-and-bic.html<\/a><\/p>\n\n\n\n

\u985e\u4f3c\u306e\u904e\u53bb\u8a18\u4e8b<\/h2>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tAIC\u3068BIC\u306e\u9055\u3044\u306f\u4f55\u304b\uff1f\u7d71\u8a08\u89e3\u6790\u3067\u306e\u7279\u5fb4\u6bd4\u8f03<\/a>\n\t\t\t\t\t\t\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u306e\u6307\u6a19\u3067\u3042\u308b\u3001AIC\u3068BIC\u3002 \u9055\u3044\u306f\u4f55\u304b\uff1f AIC\u3084BIC\u3068\u306f\u4f55\u304b\uff1f AIC\u306f\u3001Akaike’s Information Criterion \u8d64\u6c60\u60c5\u5831\u91cf\u898f\u6e96\u306e\u982d\u6587\u5b57\u8a9e\u3001BIC\u306f\u3001Bayesia…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n","protected":false},"excerpt":{"rendered":"

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