{"id":4122,"date":"2025-07-05T21:43:24","date_gmt":"2025-07-05T12:43:24","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4122"},"modified":"2025-07-05T21:43:25","modified_gmt":"2025-07-05T12:43:25","slug":"full-information-maximum-likelihood-missing-data-handling","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/full-information-maximum-likelihood-missing-data-handling\/","title":{"rendered":"Full Information Maximum Likelihood (FIML) \u306b\u3088\u308b\u6b20\u640d\u30c7\u30fc\u30bf\u51e6\u7406\uff1a\u6982\u8981\u3068R\u3067\u306e\u5b9f\u8df5"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u30c7\u30fc\u30bf\u5206\u6790\u3092\u884c\u3046\u969b\u3001<strong>\u6b20\u640d\u30c7\u30fc\u30bf<\/strong>\u306f\u907f\u3051\u3066\u901a\u308c\u306a\u3044\u8ab2\u984c\u306e\u4e00\u3064\u3067\u3042\u308b\u3002\u5358\u7d14\u306a\u6b20\u640d\u51e6\u7406\u65b9\u6cd5\u3067\u306f\u60c5\u5831\u304c\u5931\u308f\u308c\u305f\u308a\u3001\u7d50\u679c\u306b\u504f\u308a\u304c\u751f\u3058\u305f\u308a\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u305d\u3053\u3067\u6ce8\u76ee\u3055\u308c\u308b\u306e\u304c\u3001<strong>Full Information Maximum Likelihood\uff08FIML\uff09<\/strong>\u3067\u3042\u308b\u3002FIML\u306f\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u3092\u7d71\u8a08\u7684\u306b\u6700\u3082\u9069\u5207\u306b\u6271\u3046\u65b9\u6cd5\u306e\u4e00\u3064\u3068\u3057\u3066\u3001\u7279\u306b\u69cb\u9020\u65b9\u7a0b\u5f0f\u30e2\u30c7\u30ea\u30f3\u30b0\uff08SEM\uff09\u306a\u3069\u306e\u591a\u5909\u91cf\u89e3\u6790\u3067\u5e83\u304f\u5229\u7528\u3055\u308c\u3066\u3044\u308b\u3002\u672c\u30d6\u30ed\u30b0\u8a18\u4e8b\u3067\u306f\u3001FIML\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u304b\u3089\u3001\u5177\u4f53\u7684\u306a\u9069\u7528\u4f8b\u3001\u3055\u3089\u306b\u306f\u7d71\u8a08\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2R\u3092\u7528\u3044\u305f\u8a08\u7b97\u4f8b\u307e\u3067\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">FIML\u306e\u6982\u8981<\/h2>\n\n\n\n<p>FIML\u306f\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u3092\u542b\u3080\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u5168\u4f53\u304b\u3089\u3001\u30e2\u30c7\u30eb\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b<strong>\u6700\u5c24\u63a8\u5b9a<\/strong>\u306e\u4e00\u7a2e\u3067\u3042\u308b\u3002\u5f93\u6765\u306e\u6b20\u640d\u51e6\u7406\u65b9\u6cd5\uff08\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u3084\u5e73\u5747\u5024\u88dc\u5b8c\u306a\u3069\uff09\u3068\u306f\u7570\u306a\u308a\u3001FIML\u306f\u89b3\u6e2c\u3055\u308c\u305f\u3059\u3079\u3066\u306e\u60c5\u5831\uff08\u5b8c\u5168\u306a\u89b3\u6e2c\u30c7\u30fc\u30bf\u3068\u90e8\u5206\u7684\u306b\u6b20\u640d\u3057\u305f\u89b3\u6e2c\u30c7\u30fc\u30bf\uff09\u3092\u6700\u5927\u9650\u306b\u6d3b\u7528\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u5c24\u5ea6\u95a2\u6570\u306e\u6700\u5927\u5316<\/strong>: FIML\u306f\u3001\u30c7\u30fc\u30bf\u304c\u7279\u5b9a\u306e\u30e2\u30c7\u30eb\u304b\u3089\u751f\u6210\u3055\u308c\u308b\u78ba\u7387\uff08\u5c24\u5ea6\uff09\u3092\u6700\u5927\u5316\u3059\u308b\u3088\u3046\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u3002\u6b20\u640d\u30c7\u30fc\u30bf\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3067\u3082\u3001\u89b3\u6e2c\u3055\u308c\u3066\u3044\u308b\u90e8\u5206\u306e\u5c24\u5ea6\u3092\u8003\u616e\u3057\u3066\u5168\u4f53\u306e\u5c24\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u306e\u4eee\u5b9a<\/strong>: \u591a\u304f\u306e\u5834\u5408\u3001FIML\u306f\u30c7\u30fc\u30bf\u304c\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u306e\u4eee\u5b9a\u306e\u3082\u3068\u3067\u3001\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\u30d1\u30bf\u30fc\u30f3\u3054\u3068\u306b\u5c24\u5ea6\u3092\u8a08\u7b97\u3057\u3001\u305d\u308c\u3089\u3092\u5408\u8a08\u3057\u3066\u5168\u4f53\u306e\u5c24\u5ea6\u3068\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u60c5\u5831\u640d\u5931\u306e\u6700\u5c0f\u5316<\/strong>: \u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u306e\u3088\u3046\u306b\u6b20\u640d\u3092\u542b\u3080\u30b1\u30fc\u30b9\u3092\u4e38\u3054\u3068\u524a\u9664\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u89b3\u6e2c\u3055\u308c\u305f\u60c5\u5831\u3092\u5168\u3066\u5229\u7528\u3059\u308b\u305f\u3081\u3001\u7d71\u8a08\u7684\u52b9\u7387\u6027\u304c\u9ad8\u304f\u3001\u63a8\u5b9a\u91cf\u306e\u30d0\u30a4\u30a2\u30b9\u304c\u5c11\u306a\u3044\u3068\u3044\u3046\u5229\u70b9\u304c\u3042\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<p>FIML\u306f\u3001\u7279\u306b\u6b20\u640d\u304c\u30e9\u30f3\u30c0\u30e0\u306b\u767a\u751f\u3057\u3066\u3044\u308b\u5834\u5408\uff08<strong>MAR: Missing At Random<\/strong>\uff09\u306b\u6709\u52b9\u3067\u3042\u308b\u3068\u3055\u308c\u3066\u3044\u308b\u3002MAR\u3068\u306f\u3001\u6b20\u640d\u306e\u6709\u7121\u304c\u3001\u30e2\u30c7\u30eb\u306b\u542b\u307e\u308c\u308b\u4ed6\u306e\u89b3\u6e2c\u3055\u308c\u305f\u5909\u6570\u306b\u4f9d\u5b58\u3059\u308b\u304c\u3001\u6b20\u640d\u3057\u3066\u3044\u308b\u5024\u305d\u306e\u3082\u306e\u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044\u72b6\u614b\u3092\u6307\u3059\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001FIML\u304c\u3069\u306e\u3088\u3046\u306b\u9069\u7528\u3055\u308c\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u7c21\u5358\u306a\u4f8b\u3092\u8003\u3048\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<p><strong>\u4f8b\uff1a\u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u95a2\u4fc2<\/strong><\/p>\n\n\n\n<p>\u3042\u308b\u5b66\u6821\u306e\u751f\u5f92\u306b\u3064\u3044\u3066\u3001\u300c\u6570\u5b66\u306e\u70b9\u6570\u300d\u300c\u56fd\u8a9e\u306e\u70b9\u6570\u300d\u300c\u52c9\u5f37\u6642\u9593\u300d\u306e3\u3064\u306e\u5909\u6570\u3092\u8abf\u67fb\u3057\u305f\u3068\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u4e00\u90e8\u306e\u751f\u5f92\u3067\u300c\u6570\u5b66\u306e\u70b9\u6570\u300d\u304c\u6b20\u640d\u3057\u3066\u3044\u305f\u308a\u3001\u300c\u56fd\u8a9e\u306e\u70b9\u6570\u300d\u304c\u6b20\u640d\u3057\u3066\u3044\u305f\u308a\u3059\u308b\u30c7\u30fc\u30bf\u304c\u5f97\u3089\u308c\u305f\u3002<\/p>\n\n\n\n<p><strong>\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u4f8b:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td>\u751f\u5f92ID<\/td><td>\u6570\u5b66\u306e\u70b9\u6570<\/td><td>\u56fd\u8a9e\u306e\u70b9\u6570<\/td><td>\u52c9\u5f37\u6642\u9593<\/td><\/tr><\/thead><tbody><tr><td>1<\/td><td>80<\/td><td>75<\/td><td>10<\/td><\/tr><tr><td>2<\/td><td>90<\/td><td>\u6b20\u640d<\/td><td>12<\/td><\/tr><tr><td>3<\/td><td>\u6b20\u640d<\/td><td>85<\/td><td>8<\/td><\/tr><tr><td>4<\/td><td>70<\/td><td>60<\/td><td>7<\/td><\/tr><tr><td>5<\/td><td>85<\/td><td>80<\/td><td>11<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u3053\u306e\u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u3001\u300c\u52c9\u5f37\u6642\u9593\u304c\u6570\u5b66\u306e\u70b9\u6570\u3068\u56fd\u8a9e\u306e\u70b9\u6570\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u300d\u3092\u5206\u6790\u3059\u308b\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3057\u305f\u3044\u3068\u3059\u308b\u3002\u3082\u3057<strong>\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664<\/strong>\u3092\u884c\u3046\u3068\u3001\u751f\u5f922\u30683\u306e\u30c7\u30fc\u30bf\u306f\u5206\u6790\u304b\u3089\u9664\u5916\u3055\u308c\u3066\u3057\u307e\u3044\u3001\u8cb4\u91cd\u306a\u60c5\u5831\u304c\u5931\u308f\u308c\u308b\u3002<strong>\u5e73\u5747\u5024\u88dc\u5b8c<\/strong>\u3067\u306f\u3001\u6b20\u640d\u5024\u306b\u4eba\u70ba\u7684\u306a\u5024\u3092\u4ee3\u5165\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u3001\u6a19\u6e96\u8aa4\u5dee\u304c\u904e\u5c0f\u8a55\u4fa1\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>FIML\u3092\u7528\u3044\u308b\u3068\u3001\u6b20\u640d\u30d1\u30bf\u30fc\u30f3\u3054\u3068\u306b\u7570\u306a\u308b\u5c24\u5ea6\u95a2\u6570\u3092\u9069\u7528\u3057\u3001\u3059\u3079\u3066\u306e\u89b3\u6e2c\u30c7\u30fc\u30bf\u3092\u5206\u6790\u306b\u542b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4f8b\u3048\u3070\u3001\u751f\u5f922\u306e\u30c7\u30fc\u30bf\u3067\u306f\u300c\u56fd\u8a9e\u306e\u70b9\u6570\u300d\u304c\u6b20\u640d\u3057\u3066\u3044\u308b\u304c\u3001\u300c\u6570\u5b66\u306e\u70b9\u6570\u300d\u3068\u300c\u52c9\u5f37\u6642\u9593\u300d\u306e\u30c7\u30fc\u30bf\u306f\u5229\u7528\u3067\u304d\u308b\u3002FIML\u306f\u3053\u308c\u3089\u306e\u5229\u7528\u53ef\u80fd\u306a\u60c5\u5831\u3092\u6700\u5927\u9650\u306b\u6d3b\u7528\u3057\u3066\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-2337153148\" class=\"biost- biost-entity-placement\"><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\">\u5177\u4f53\u4f8b\u306e R \u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>R\u3067FIML\u3092\u5b9f\u88c5\u3059\u308b\u969b\u306b\u306f\u3001<strong><code>lavaan<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8<\/strong>\u304c\u975e\u5e38\u306b\u4fbf\u5229\u3067\u3042\u308b\u3002<code>lavaan<\/code>\u306f\u69cb\u9020\u65b9\u7a0b\u5f0f\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u305f\u3081\u306e\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u3042\u308b\u304c\u3001FIML\u306b\u3088\u308b\u6b20\u640d\u30c7\u30fc\u30bf\u51e6\u7406\u3092\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3057\u3001\u4e00\u90e8\u306b\u6b20\u640d\u5024\u3092\u5c0e\u5165\u3059\u308b\u3002<\/p>\n\n\n\n<p><strong>R \u30b9\u30af\u30ea\u30d7\u30c8\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb (\u307e\u3060\u306e\u5834\u5408)\n# install.packages(\"lavaan\")\n# install.packages(\"mice\") # \u6b20\u640d\u4f5c\u6210\u306e\u305f\u3081\u306b\u4f7f\u7528\n\n# \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u8aad\u307f\u8fbc\u307f\nlibrary(lavaan)\nlibrary(mice)\n\n# \u30b7\u30fc\u30c9\u3092\u8a2d\u5b9a\u3057\u3066\u518d\u73fe\u6027\u3092\u78ba\u4fdd\nset.seed(123)\n\n# \u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u751f\u6210\nn_obs &lt;- 100\nstudy_time &lt;- round(rnorm(n_obs, mean = 10, sd = 2))\nmath_score &lt;- round(50 + 3 * study_time + rnorm(n_obs, mean = 0, sd = 5))\njapanese_score &lt;- round(40 + 2.5 * study_time + rnorm(n_obs, mean = 0, sd = 4))\n\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306e\u4f5c\u6210\ndf &lt;- data.frame(study_time, math_score, japanese_score)\n\n# \u610f\u56f3\u7684\u306b\u6b20\u640d\u3092\u4f5c\u6210 (\u30e9\u30f3\u30c0\u30e0\u306b\u6b20\u640d\u3055\u305b\u308b\u5834\u5408)\n# \u6570\u5b66\u306e\u70b9\u6570\u306e\u7d0410%\u3092\u6b20\u640d\u3055\u305b\u308b\ndf$math_score&#91;sample(1:n_obs, size = round(n_obs * 0.1))] &lt;- NA\n# \u56fd\u8a9e\u306e\u70b9\u6570\u306e\u7d0415%\u3092\u6b20\u640d\u3055\u305b\u308b\ndf$japanese_score&#91;sample(1:n_obs, size = round(n_obs * 0.15))] &lt;- NA\n\n# \u6b20\u640d\u30c7\u30fc\u30bf\u306e\u78ba\u8a8d\nsummary(df)\n\n# \u30e2\u30c7\u30eb\u306e\u5b9a\u7fa9 (\u52c9\u5f37\u6642\u9593\u304c\u6570\u5b66\u3068\u56fd\u8a9e\u306e\u70b9\u6570\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u56de\u5e30\u30e2\u30c7\u30eb)\nmodel &lt;- '\n  math_score ~ study_time\n  japanese_score ~ study_time\n'\n\n# FIML\u3092\u7528\u3044\u305f\u30e2\u30c7\u30eb\u306e\u63a8\u5b9a\n# missing = \"fiml\" \u3092\u6307\u5b9a\u3059\u308b\u3053\u3068\u3067FIML\u304c\u9069\u7528\u3055\u308c\u308b\nfit_fiml &lt;- sem(model, data = df, missing = \"fiml\")\n\n# \u7d50\u679c\u306e\u8981\u7d04\nsummary(fit_fiml, standardized = TRUE)\n\n# \u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u306e\u5834\u5408\u3068\u6bd4\u8f03\nfit_listwise &lt;- sem(model, data = df, missing = \"listwise\")\nsummary(fit_listwise, standardized = TRUE)\n<\/code><\/pre>\n\n\n\n<p><strong>\u30b3\u30fc\u30c9\u306e\u8aac\u660e:<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong><code>library(lavaan)<\/code><\/strong>: <code>lavaan<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u8aad\u307f\u8fbc\u3080\u3002<\/li>\n\n\n\n<li><strong>\u30c7\u30fc\u30bf\u751f\u6210\u3068\u6b20\u640d\u4f5c\u6210<\/strong>: <code>rnorm()<\/code>\u95a2\u6570\u3067\u6b63\u898f\u4e71\u6570\u3092\u751f\u6210\u3057\u3001\u67b6\u7a7a\u306e\u300c\u52c9\u5f37\u6642\u9593\u300d\u300c\u6570\u5b66\u306e\u70b9\u6570\u300d\u300c\u56fd\u8a9e\u306e\u70b9\u6570\u300d\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b\u3002\u305d\u306e\u5f8c\u3001<code>sample()<\/code>\u95a2\u6570\u3092\u4f7f\u3063\u3066\u30e9\u30f3\u30c0\u30e0\u306b<code>NA<\/code>\uff08\u6b20\u640d\u5024\uff09\u3092\u633f\u5165\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30e2\u30c7\u30eb\u5b9a\u7fa9<\/strong>: <code>model<\/code>\u5909\u6570\u306b\u3001SEM\u306e\u30e2\u30c7\u30eb\u69cb\u6587\u3092\u6587\u5b57\u5217\u3067\u5b9a\u7fa9\u3059\u308b\u3002\u3053\u3053\u3067\u306f\u3001\u300c<code>math_score<\/code>\u304c<code>study_time<\/code>\u306b\u3088\u3063\u3066\u4e88\u6e2c\u3055\u308c\u308b\u300d\u300c<code>japanese_score<\/code>\u304c<code>study_time<\/code>\u306b\u3088\u3063\u3066\u4e88\u6e2c\u3055\u308c\u308b\u300d\u3068\u3044\u3046\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u6307\u5b9a\u3057\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li><strong>FIML\u306b\u3088\u308b\u63a8\u5b9a<\/strong>: <code>sem()<\/code>\u95a2\u6570\u3092\u7528\u3044\u3066\u30e2\u30c7\u30eb\u3092\u63a8\u5b9a\u3059\u308b\u3002<code>data = df<\/code>\u3067\u4f5c\u6210\u3057\u305f\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u3092\u6307\u5b9a\u3057\u3001<strong><code>missing = \"fiml\"<\/code><\/strong> \u3092\u6307\u5b9a\u3059\u308b\u3053\u3068\u304cFIML\u3092\u9069\u7528\u3059\u308b\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7d50\u679c\u306e\u8981\u7d04<\/strong>: <code>summary()<\/code>\u95a2\u6570\u3067\u63a8\u5b9a\u7d50\u679c\u3092\u8868\u793a\u3059\u308b\u3002<code>standardized = TRUE<\/code>\u3092\u6307\u5b9a\u3059\u308b\u3068\u3001\u6a19\u6e96\u5316\u3055\u308c\u305f\u63a8\u5b9a\u5024\u3082\u8868\u793a\u3055\u308c\u3001\u7570\u306a\u308b\u5909\u6570\u306e\u5f71\u97ff\u5ea6\u3092\u6bd4\u8f03\u3057\u3084\u3059\u304f\u306a\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u3068\u306e\u6bd4\u8f03<\/strong>: \u53c2\u8003\u306b\u3001<code>missing = \"listwise\"<\/code>\u3092\u6307\u5b9a\u3057\u3066\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u3092\u884c\u3063\u305f\u5834\u5408\u306e\u63a8\u5b9a\u7d50\u679c\u3082\u793a\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001FIML\u3068\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u306e\u7d50\u679c\u306e\u9055\u3044\u3092\u6bd4\u8f03\u3067\u304d\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8<\/h2>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # \u7d50\u679c\u306e\u8981\u7d04\n> summary(fit_fiml, standardized = TRUE)\nlavaan 0.6-19 ended normally after 27 iterations\n\n  Estimator                                         ML\n  Optimization method                           NLMINB\n  Number of model parameters                         7\n\n  Number of observations                           100\n  Number of missing patterns                         4\n\nModel Test User Model:\n                                                      \n  Test statistic                                 0.000\n  Degrees of freedom                                 0\n\nParameter Estimates:\n\n  Standard errors                             Standard\n  Information                                 Observed\n  Observed information based on                Hessian\n\nRegressions:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n  math_score ~                                                          \n    study_time        2.857    0.277   10.298    0.000    2.857    0.732\n  japanese_score ~                                                      \n    study_time        2.439    0.256    9.512    0.000    2.439    0.753\n\nCovariances:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n .math_score ~~                                                         \n   .japanese_score    1.082    2.067    0.523    0.601    1.082    0.059\n\nIntercepts:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n   .math_score       51.017    2.883   17.695    0.000   51.017    7.259\n   .japanese_score   41.025    2.687   15.267    0.000   41.025    7.035\n\nVariances:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n   .math_score       22.900    3.414    6.707    0.000   22.900    0.464\n   .japanese_score   14.702    2.255    6.521    0.000   14.702    0.432\n\n> # \u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u306e\u5834\u5408\u3068\u6bd4\u8f03\n> fit_listwise &lt;- sem(model, data = df, missing = \"listwise\")\n> summary(fit_listwise, standardized = TRUE)\nlavaan 0.6-19 ended normally after 9 iterations\n\n  Estimator                                         ML\n  Optimization method                           NLMINB\n  Number of model parameters                         5\n\n                                                  Used       Total\n  Number of observations                            76         100\n\nModel Test User Model:\n                                                      \n  Test statistic                                 0.000\n  Degrees of freedom                                 0\n\nParameter Estimates:\n\n  Standard errors                             Standard\n  Information                                 Expected\n  Information saturated (h1) model          Structured\n\nRegressions:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n  math_score ~                                                          \n    study_time        2.823    0.358    7.893    0.000    2.823    0.671\n  japanese_score ~                                                      \n    study_time        2.570    0.265    9.684    0.000    2.570    0.743\n\nCovariances:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n .math_score ~~                                                         \n   .japanese_score    1.131    2.142    0.528    0.597    1.131    0.061\n\nVariances:\n                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all\n   .math_score       25.113    4.074    6.164    0.000   25.113    0.550\n   .japanese_score   13.836    2.244    6.164    0.000   13.836    0.448\n\n> <\/code><\/pre>\n\n\n\n<p><code>summary(fit_fiml)<\/code>\u306e\u51fa\u529b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u60c5\u5831\u304c\u542b\u307e\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><code>Estimates<\/code><\/strong>: \u5404\u30d1\u30b9\uff08\u95a2\u4fc2\u6027\uff09\u306e\u63a8\u5b9a\u5024\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001<code>math_score ~ study_time<\/code>\u306e\u884c\u306b\u306f\u3001\u52c9\u5f37\u6642\u9593\u304c\u6570\u5b66\u306e\u70b9\u6570\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u306e\u4fc2\u6570\uff08\u56de\u5e30\u4fc2\u6570\uff09\u304c\u8868\u793a\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong><code>Std. Err<\/code><\/strong>: \u63a8\u5b9a\u5024\u306e\u6a19\u6e96\u8aa4\u5dee\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong><code>z-value<\/code><\/strong>: \u63a8\u5b9a\u5024\u3092\u6a19\u6e96\u8aa4\u5dee\u3067\u5272\u3063\u305fZ\u5024\u3067\u3001\u4fc2\u6570\u306e\u7d71\u8a08\u7684\u6709\u610f\u6027\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong><code>P(>|z|)<\/code><\/strong>: Z\u5024\u306b\u5bfe\u5fdc\u3059\u308bp\u5024\u3067\u3042\u308b\u3002\u4e00\u822c\u7684\u306b\u3001p\u5024\u304c0.05\u672a\u6e80\u3067\u3042\u308c\u3070\u3001\u305d\u306e\u95a2\u4fc2\u6027\u306f\u7d71\u8a08\u7684\u306b\u6709\u610f\u3067\u3042\u308b\u3068\u5224\u65ad\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong><code>Std.all<\/code><\/strong>: \u5168\u3066\u3092\u6a19\u6e96\u5316\u3057\u305f\u63a8\u5b9a\u5024\u3067\u3042\u308b\u3002\u7570\u306a\u308b\u5c3a\u5ea6\u3092\u6301\u3064\u5909\u6570\u9593\u306e\u5f71\u97ff\u5ea6\u3092\u6bd4\u8f03\u3059\u308b\u969b\u306b\u6709\u7528\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>FIML\u306b\u3088\u308b\u7d50\u679c\u306f\u3001\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u306b\u3088\u308b\u7d50\u679c\u3068\u6bd4\u8f03\u3057\u3066\u3001\u3088\u308a\u591a\u304f\u306e\u30c7\u30fc\u30bf\u304c\u5229\u7528\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u63a8\u5b9a\u91cf\u306e\u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\u306a\u308b\u50be\u5411\u304c\u3042\u308b\uff08\u4f8b\uff1a0.277 (FIML) vs. 0.358 (listwise) in Std.Err of math_score ~ study_time in Regressions\uff09\u3002\u3053\u308c\u306f\u3001FIML\u304c\u3088\u308a\u52b9\u7387\u7684\u306a\u63a8\u5b9a\u3092\u884c\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u5506\u3059\u308b\u3002\u307e\u305f\u3001\u6b20\u640d\u304c\u30e9\u30f3\u30c0\u30e0\u306a\u5834\u5408\u306b\u306f\u3001FIML\u306b\u3088\u308b\u63a8\u5b9a\u5024\u306f\u30ea\u30b9\u30c8\u30ef\u30a4\u30ba\u524a\u9664\u3088\u308a\u3082\u771f\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u306b\u8fd1\u3044\u3068\u671f\u5f85\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001R\u306e\u51fa\u529b\u3067<code>study_time<\/code>\u304b\u3089<code>math_score<\/code>\u3078\u306e\u30d1\u30b9\u306e\u63a8\u5b9a\u5024\u304c\u6b63\u3067\u3042\u308a\u3001p\u5024\u304c\u5341\u5206\u306b\u5c0f\u3055\u3044\u306e\u3067\u3001\u300c\u52c9\u5f37\u6642\u9593\u304c\u9577\u3044\u307b\u3069\u6570\u5b66\u306e\u70b9\u6570\u304c\u9ad8\u304f\u306a\u308b\u50be\u5411\u304c\u3042\u308b\u300d\u3068\u3044\u3046\u7d50\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002FIML\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u304c\u5b58\u5728\u3057\u3066\u3082\u3001\u3053\u306e\u7d50\u8ad6\u306e\u4fe1\u983c\u6027\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\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\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>Full Information Maximum Likelihood\uff08FIML\uff09\u306f\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u304c\u5b58\u5728\u3059\u308b\u72b6\u6cc1\u3067\u3001\u7d71\u8a08\u7684\u306b\u52b9\u7387\u7684\u3067\u30d0\u30a4\u30a2\u30b9\u306e\u5c11\u306a\u3044\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u3092\u53ef\u80fd\u306b\u3059\u308b\u5f37\u529b\u306a\u624b\u6cd5\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u69cb\u9020\u65b9\u7a0b\u5f0f\u30e2\u30c7\u30ea\u30f3\u30b0\u306a\u3069\u306e\u591a\u5909\u91cf\u89e3\u6790\u306b\u304a\u3044\u3066\u3001\u305d\u306e\u771f\u4fa1\u3092\u767a\u63ee\u3059\u308b\u3002<\/p>\n\n\n\n<p>FIML\u306f\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u3092\u542b\u3080\u3059\u3079\u3066\u306e\u89b3\u6e2c\u60c5\u5831\u3092\u6700\u5927\u9650\u306b\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u60c5\u5831\u306e\u640d\u5931\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u3001\u3088\u308a\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u5206\u6790\u7d50\u679c\u3092\u3082\u305f\u3089\u3059\u3002R\u306e<code>lavaan<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3048\u3070\u3001\u7c21\u5358\u306bFIML\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u8907\u96d1\u306a\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u5206\u6790\u3092\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u306b\u7169\u308f\u3055\u308c\u308b\u3053\u3068\u306a\u304f\u5b9f\u884c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u5206\u6790\u306e\u73fe\u5834\u3067\u6b20\u640d\u30c7\u30fc\u30bf\u306b\u76f4\u9762\u3057\u305f\u969b\u306b\u306f\u3001FIML\u306e\u9069\u7528\u3092\u305c\u3072\u691c\u8a0e\u3057\u3066\u307b\u3057\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30c7\u30fc\u30bf\u5206\u6790\u3092\u884c\u3046\u969b\u3001\u6b20\u640d\u30c7\u30fc\u30bf\u306f\u907f\u3051\u3066\u901a\u308c\u306a\u3044\u8ab2\u984c\u306e\u4e00\u3064\u3067\u3042\u308b\u3002\u5358\u7d14\u306a\u6b20\u640d\u51e6\u7406\u65b9\u6cd5\u3067\u306f\u60c5\u5831\u304c\u5931\u308f\u308c\u305f\u308a\u3001\u7d50\u679c\u306b\u504f\u308a\u304c\u751f\u3058\u305f\u308a\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u305d\u3053\u3067\u6ce8\u76ee\u3055\u308c\u308b\u306e\u304c\u3001Full Information Maximum Lik [&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_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}},"categories":[75,149],"tags":[],"class_list":["post-4122","post","type-post","status-publish","format-standard","hentry","category-sem","category-149"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4122","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=4122"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4122\/revisions"}],"predecessor-version":[{"id":4124,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4122\/revisions\/4124"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}