{"id":767,"date":"2026-01-08T17:15:42","date_gmt":"2026-01-08T08:15:42","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/?page_id=767"},"modified":"2026-01-08T17:24:24","modified_gmt":"2026-01-08T08:24:24","slug":"mmrm","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/r\/3pecification\/mmrm\/","title":{"rendered":"\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30ebANOVA"},"content":{"rendered":"<h1 style=\"background: #F7F7F7;padding: 10px\"><span style=\"color: #3366ff\">\u25a0 <span style=\"color: #000000\">\u53cd\u5fa9\u6e2c\u5b9a\u306e\u6df7\u5408\u52b9\u679c\u30e2\u30c7\u30eb<span style=\"font-size: 18pt\"><strong>\uff08Mixed-effects Models for Repeated Measures\uff1bMMRM\uff09<\/strong><\/span><\/span><\/span><\/h1>\n<p><a href=\"https:\/\/www.jstage.jst.go.jp\/article\/jappstat\/46\/2\/46_53\/_pdf\/-char\/ja\" target=\"_blank\" rel=\"noopener\">MMRM<\/a>\u306f\u7dda\u5f62\u6df7\u5408\u52b9\u679c\u30e2\u30c7\u30eb\uff08Linear Mixed Effects Model\uff1bLMM\uff09\u3068\u3082\u547c\u3070\u308c\u307e\u3059\uff0e\u30c7\u30fc\u30bf\u306f\uff0c\u53cd\u5fa9\u6e2c\u5b9a\u306b\u3088\u308bANOVA\uff08Repeated measures ANOVA\uff1brep-ANOVA\uff09\u3068\u540c\u3058\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>rep-ANOVA\u306f\u533b\u5b66\u306e\u5206\u91ce\u306b\u9650\u3089\u305a\u9577\u5e74\u4f7f\u308f\u308c\u3066\u304d\u3066\u3044\u308b\u306e\u3067\uff0c\u898b\u6163\u308c\u305f\u7d71\u8a08\u624b\u6cd5\u3067\u3059\uff0e\u3057\u304b\u3057\uff0c\u540c\u3058\u3082\u306e\u3092\u691c\u5b9a\u3059\u308b\u305f\u3081\u306b\uff0c\u306a\u305c\u9055\u3046\u624b\u6cd5\u304c\u5b58\u5728\u3059\u308b\u306e\u304b\u3068\u3044\u3046\u7591\u554f\u3092\u6301\u3064\u4eba\u3082\u591a\u3044\u3068\u601d\u3044\u307e\u3059\uff0e\u305d\u306e\u7406\u7531\u306b\u306fMMRM\u304c\uff0c\u69d8\u3005\u306a\u5229\u70b9\u304c\u3042\u308b\u305f\u3081\u3067\u3059\uff0e<\/p>\n<p>&nbsp;<\/p>\n<h1 style=\"background: #F7F7F7;padding: 10px\"><span style=\"color: #3366ff\">\u25a0 <span style=\"color: #000000\">MMRM\u306e\u7279\u5fb4<\/span><\/span><\/h1>\n<p>rep-ANOVA\u3068\u6bd4\u8f03\u3057\u305fMMRM\u306e\u30e1\u30ea\u30c3\u30c8\u306f\u4ee5\u4e0b\u306e\u70b9\u3067\u3059\uff0e<\/p>\n<p><span style=\"color: #ff0000\"><strong>\u25cf \u691c\u5b9a\u306e\u305f\u3081\u306e\u524d\u63d0\u6761\u4ef6\u304c\u5c11\u306a\u3044<\/strong><\/span><\/p>\n<p>rep-ANOVA\u3067\u306f\uff0c\u5f93\u5c5e\u5909\u6570\u306e\u5206\u6563\u5171\u5206\u6563\u884c\u5217\u304c\u7403\u5f62\u3067\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u306b\u3059\u308b\u306e\u3067\uff0c\u4e8b\u524d\u306b<span class=\"gs_cit_txt\" data-sups=\"1,2,3\" data-hover-id=\"1\"><span class=\"gs_tkn\"><a href=\"http:\/\/www.chino-asymmetry.com\/anova\/chapter2\/sec2-1-2.html\" target=\"_blank\" rel=\"noopener\">Mauchly\u306e\u7403\u5f62\u6027\u691c\u5b9a<\/a>\uff08one-way\u306e\u3068\u304d\uff09\u3082\u3057\u304f\u306f<a href=\"http:\/\/www.chino-asymmetry.com\/anova\/chapter2\/sec2-1-4.html\" target=\"_blank\" rel=\"noopener\">Mendoza\u306e\u591a\u6a19\u672c\u7403\u5f62\u691c\u5b9a<\/a>\uff08multi-way\u306e\u3068\u304d\uff09\u306b\u3088\u308a\u7403\u5f62\u6027\u304c\u5426\u5b9a\u3055\u308c\u305f\u3068\u304d\u306f\uff0cGreenhouse-Geisser\u306e\u30a4\u30d7\u30b7\u30ed\u30f3\u4fee\u6b63\u306a\u3069\u3067\u81ea\u7531\u5ea6\u88dc\u6b63\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\uff0e\u904e\u53bb\u306b\u306f\u300c\u305d\u3093\u306a\u9762\u5012\u306a\u3053\u3068\u3057\u306a\u304f\u3066\u3082\u3088\u3044\u300d\u3068\u3044\u3046\u610f\u898b\u3082\u805e\u304d\u307e\u3057\u305f\u304c\uff0c\u3053\u308c\u306f\u898b\u9003\u305b\u306a\u3044\u554f\u984c\u3067\u3059\uff0e \u2192\u3000<a href=\"http:\/\/www.chino-asymmetry.com\/anova\/bias.html\" target=\"_blank\" rel=\"noopener\">\u53c2\u7167<\/a><\/span><\/span><\/p>\n<p>rep-ANOVA\u3067\u306f\uff0c\u524d\u63d0\u6761\u4ef6\u306e\u78ba\u8a8d\u306e\u305f\u3081\u306b\u691c\u5b9a\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3084\uff0c\u7403\u5f62\u6027\u304c\u5426\u5b9a\u3055\u308c\u305f\u3068\u304d\u306b\u81ea\u7531\u5ea6\u3092\u4fee\u6b63\u3059\u308b\u306a\u3069\u306e\u624b\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u51fa\u3066\u304f\u308b\u306e\u3067\uff08\u3053\u306e\u6b63\u8aa4\u306b\u3064\u3044\u3066\u306f\u65ad\u8a00\u3057\u307e\u305b\u3093\u304c\uff09\uff0c\u306a\u308b\u3079\u304f\u3059\u3063\u304d\u308a\u691c\u5b9a\u3092\u9032\u3081\u305f\u65b9\u304c\u3088\u3044\u3068\u8003\u3048\u307e\u3059\uff0e<\/p>\n<p align=\"left\"><span style=\"color: #ff0000\"><strong>\u25cf \u6b20\u640d\u5024\u306b\u5bfe\u3057\u3066\u67d4\u8edf<\/strong><\/span><\/p>\n<p>\u3000\u6b20\u640d\u5024\u304c\u3042\u3063\u3066\u3082\uff0c\u89e3\u6790\u3067\u304d\u308b\u3068\u3044\u3046\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff0e\u305f\u3060\u3057\uff0cMissing At Random\uff08MAR\uff09\u3068\u3044\u3046\u6761\u4ef6\u304c\u5fc5\u8981\u3067\u3059\uff0e<\/p>\n<p align=\"left\"><span style=\"color: #ff0000\"><strong>\u25cf \u53cd\u5fa9\u6e2c\u5b9a\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u6700\u3082\u9069\u5207\u306a\u89e3\u6790\u624b\u6cd5\u3067\u3042\u308b<\/strong><\/span><\/p>\n<p>\u3000\u53cd\u5fa9\u6e2c\u5b9a\u30c7\u30fc\u30bf\u306f\uff0c\u56fa\u5b9a\u8981\u56e0\u3068\u5909\u91cf\u8981\u56e0\u306e\u7d44\u307f\u5408\u308f\u305b\uff08\u3086\u3048\u306b\u6df7\u5408\u30e2\u30c7\u30eb\u3068\u547c\u3070\u308c\u308b\uff09\u3067\u3059\uff0erep-ANOVA\u306f\u4e71\u584a\u6cd5\u306b\u57fa\u3065\u304f\u624b\u6cd5\u306a\u306e\u3067\uff0c\u9069\u7528\u3055\u308c\u308b\u30c7\u30fc\u30bf\u306f\u5f62\u5f0f\u3053\u305d\u53cd\u5fa9\u6e2c\u5b9a\u30c7\u30fc\u30bf\u3067\u3059\u304c\uff0c\u56fa\u5b9a\u56e0\u5b50\u306e\u5168\u3066\u306e\u6c34\u6e96\u306b\u5909\u91cf\u56e0\u5b50\u306e\u5168\u3066\u306e\u6c34\u6e96\u304c\u542b\u307e\u308c\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\uff08\u3053\u308c\u304c\u6b20\u640d\u3092\u8a31\u3055\u306a\u3044\u539f\u56e0\u3067\u3059\uff09\uff0eMMRM\u304c\u6700\u3082\u9069\u3057\u305f\u624b\u6cd5\u3067\u3059\uff0e<\/p>\n<p>&nbsp;<\/p>\n<h1 style=\"background: #F7F7F7;padding: 10px\"><span style=\"color: #3366ff\">\u25a0 <span style=\"color: #000000\">\u6539\u5909R\u30b3\u30de\u30f3\u30c0\u30fc\u306b\u3088\u308bMMRM<\/span><\/span><\/h1>\n<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/r\/1mrcom\/\" target=\"_blank\" rel=\"noopener\">\u6539\u5909R\u30b3\u30de\u30f3\u30c0\u30fc<\/a>\u3067\u306f\uff0c\u56fa\u5b9a\u8981\u56e0\u304c1\u3064\u306eMMRM\uff0c\u5171\u5909\u91cf\u3092\u542b\u3080\u56fa\u5b9a\u8981\u56e0\u304c1\u3064\u306eMMRM\uff0c\u56fa\u5b9a\u8981\u56e0\u304c2\u3064\u306eMMRM\uff0cKirk\u306b\u3088\u308b\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u30c7\u30b6\u30a4\u30f3\uff08split-plot design\uff09\u306eMMRM\uff0c\u5171\u5909\u91cf\u3092\u542b\u3080\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u30c7\u30b6\u30a4\u30f3\u306eMMRM\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<ul>\n<li>\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\uff0c<a href=\"https:\/\/cran.r-universe.dev\/lme4\/doc\/manual.html\" target=\"_blank\" rel=\"noopener\">lme4<\/a>\uff0c<a href=\"https:\/\/search.r-project.org\/CRAN\/refmans\/lmerTest\/html\/lmerTest-package.html\" target=\"_blank\" rel=\"noopener\">lmerTest<\/a>\uff0c<a href=\"https:\/\/search.r-project.org\/CRAN\/refmans\/performance\/html\/performance-package.html\" target=\"_blank\" rel=\"noopener\">performance<\/a>\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\uff0e<\/li>\n<li>lmer\u95a2\u6570\uff08\u30c7\u30d5\u30a9\u30eb\u30c8\uff09\u3067\u30e2\u30c7\u30eb\u3092\u4f5c\u6210\u3057\uff0c\u691c\u5b9a\u306edf\u306e\u8abf\u6574\u306b\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u3068\u304d\u306b\u6709\u5229\u306a<a href=\"https:\/\/mstour.hatenablog.com\/entry\/2021\/05\/05\/094355\" target=\"_blank\" rel=\"noopener\">Kenward-Roger\u6cd5<\/a>\u3092\u7528\u3044\u3066\u3044\u307e\u3059\uff08\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306fSatterthwaite\u6cd5\uff09\uff0e<\/li>\n<li>\u591a\u91cd\u6bd4\u8f03\u6cd5\u306f\uff0c<a href=\"https:\/\/cran.r-project.org\/web\/packages\/emmeans\/index.html\" target=\"_blank\" rel=\"noopener\">emmeans<\/a>\u30d1\u30c3\u30b1\u30fc\u30b8\u306elsmeans\u95a2\u6570\u3092\u7528\u3044\u3066\uff0c\u6700\u5c0f\u4e8c\u4e57\u5e73\u5747\u306e\u691c\u5b9a\u3092\u884c\u3044\u307e\u3059\uff08\u203b\u51fa\u529b\u306b\uff0c\u300eP value adjustment:<strong> tukey method<\/strong> for comparing a family of\u2026\u300f\u306e\u3088\u3046\u306a\u8a18\u8ff0\u304c\u3042\u308a\u307e\u3059\u304c\uff0c<strong>Tukey\u306e\u691c\u5b9a\u3092<span style=\"color: #800000\">\u7528\u3044\u3066\u3044\u308b\u306e\u3067\u306f\u306a\u304f<\/span><\/strong>\uff0c<strong>\u5168\u6c34\u6e96\u306e\u5bfe\u6bd4\u8f03\u3092\u884c\u3063\u305f<\/strong>\u3068\u3044\u3046\u610f\u5473\u3067\u3059\uff09\uff0e\u81ea\u7531\u5ea6\u306f\uff0cKenward-Roger\u6cd5\u3067\u3059\uff0e<\/li>\n<li>\u53c2\u8003\u8cc7\u6599\u3068\u3057\u3066<a href=\"https:\/\/www.slideshare.net\/slideshow\/ss-42957963\/42957963\" target=\"_blank\" rel=\"noopener\">\u3053\u3053<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h1 style=\"background: #F7F7F7;padding: 10px\"><span style=\"color: #3366ff\">\u25a0 <span style=\"color: #000000\">\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5<\/span><\/span><\/h1>\n<p><span style=\"color: #ff0000\">\u5bfe\u5fdc\u3059\u308b\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u306f\u5b58\u5728\u3057\u307e\u305b\u3093<\/span>\u306e\u3067\uff0c\u3069\u3046\u3057\u3066\u3082\u3068\u3044\u3046\u306e\u3067\u3042\u308c\u3070\uff0c\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u306e\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u30c7\u30b6\u30a4\u30f3\u306b\u3088\u308bANOVA\u3092\u9069\u7528\u3059\u308b\u3057\u304b\u306a\u3044\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 \u53cd\u5fa9\u6e2c\u5b9a\u306e\u6df7\u5408\u52b9\u679c\u30e2\u30c7\u30eb\uff08Mixed-effects Models for Repeated Measures\uff1bMMRM\uff09 MMRM\u306f\u7dda\u5f62\u6df7\u5408\u52b9\u679c\u30e2\u30c7\u30eb\uff08Linear Mixed Effects Model\uff1bLMM\uff09\u2026 <span class=\"read-more\"><a href=\"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/r\/3pecification\/mmrm\/\">\u7d9a\u304d\u3092\u8aad\u3080 &raquo;<\/a><\/span><\/p>\n","protected":false},"author":200,"featured_media":0,"parent":139,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"class_list":["post-767","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/pages\/767","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/users\/200"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/comments?post=767"}],"version-history":[{"count":6,"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/pages\/767\/revisions"}],"predecessor-version":[{"id":774,"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/pages\/767\/revisions\/774"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/pages\/139"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/pteiki\/wp-json\/wp\/v2\/media?parent=767"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}