{"id":344,"date":"2022-01-29T20:51:14","date_gmt":"2022-01-29T11:51:14","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-many-imputed-datasets-needed-in-muliple-imputation\/"},"modified":"2025-06-10T21:53:02","modified_gmt":"2025-06-10T12:53:02","slug":"how-many-imputed-datasets-needed-in-muliple-imputation","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-many-imputed-datasets-needed-in-muliple-imputation\/","title":{"rendered":"\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u5fc5\u8981\u306a\u88dc\u5b8c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570"},"content":{"rendered":"\n

\u6b20\u6e2c\u5024\u304c\u3042\u3063\u305f\u5834\u5408\u3001\u5bfe\u51e6\u3059\u308b\u65b9\u6cd5\u304c\u3044\u304f\u3064\u304b\u3042\u308b\u3002<\/p>\n\n\n\n

\u305d\u306e\u3046\u3061\u306e\u4e00\u3064\u304c\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u4f5c\u6210\u3059\u3079\u304d\u6b20\u6e2c\u5024\u88dc\u5b8c\u30c7\u30fc\u30bf\u306e\u6570\u306f\u3044\u304f\u3064\u304c\u3088\u3044\u306e\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u4f5c\u6210\u3059\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u3044\u304f\u3064\u304c\u3088\u3044\u3068\u8a00\u308f\u308c\u3066\u3044\u308b\u304b\uff1f<\/h2>\n\n\n\n

\u591a\u91cd\u4ee3\u5165\u6cd5\u306e\u63d0\u6848\u8005Rubin\u306f\u30015 \u304b\u3089 10 \u7a0b\u5ea6\u3067\u89e3\u6790\u53ef\u80fd\u3068\u4e3b\u5f35\u3057\u3066\u3001\u305d\u306e\u5f8c 5 \u3064\u7a0b\u5ea6\u3067\u5b9f\u969b\u884c\u308f\u308c\u3066\u304d\u305f\u3002<\/p>\n\n\n\n

Rubin\u304c\u63d0\u5531\u3057\u305f\u306e\u306f1987\u5e74\u3067\u3001\u305d\u306e\u5f53\u6642\u3068\u6bd4\u3079\u308b\u3068\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u683c\u6bb5\u306b\u9032\u5316\u3057\u3001\u73fe\u5728\u306f 100 \u7a0b\u5ea6\u306e\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b\u306e\u306f\u5927\u3057\u305f\u52b4\u529b\u304c\u304b\u304b\u3089\u306a\u3044\u3002<\/p>\n\n\n\n

\u5b9f\u969b\u3001100 \u500b\u306e\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3082\u52e7\u3081\u3089\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u4f5c\u6210\u3059\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u3092\u6c7a\u3081\u308b\u65b9\u6cd5\u306f\uff1f<\/h2>\n\n\n\n

\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u4f5c\u6210\u3059\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u6570\u3092\u6c7a\u3081\u308b\u65b9\u6cd5\u306e\u4e00\u3064\u306b\u3001\u76f8\u5bfe\u52b9\u7387\uff08Relative Efficiency\uff09\u3067\u6c7a\u3081\u308b\u3068\u3044\u3046\u65b9\u6cd5\u304c\u3042\u308b\u3002<\/p>\n\n\n\n

\u6bcd\u96c6\u56e3\u3067\u306e\u6b20\u6e2c\u60c5\u5831\u306e\u5272\u5408\u3092 $ \\lambda_0 $ \u3068\u3059\u308b\u3068\u3001\u6b20\u6e2c\u5024\u88dc\u5b8c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 D \u3068\u76f8\u5bfe\u52b9\u7387 $ Re_D $ \u306e\u9593\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n

$$ Re_D = \\left( 1 + \\frac{\\lambda_0}{D} \\right)^{-1} $$<\/p>\n\n\n\n\n\n\n\n

\u3053\u3053\u3067\u6bcd\u96c6\u56e3\u3067\u306e\u6b20\u6e2c\u60c5\u5831\u306e\u5272\u5408 $ \\lambda_0 $ \u306f\u3001\u5358\u5909\u91cf\u3067\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u306a\u6b20\u6e2c\u306e\u5834\u5408\u306f\u3001\u6b20\u6e2c\u7387\u306b\u3042\u305f\u308b\u3002<\/p>\n\n\n\n

\u76f8\u5bfe\u52b9\u7387\u306f\u9ad8\u3044\u307b\u3046\u304c\u826f\u3044\u3002<\/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>

\u76f8\u5bfe\u52b9\u7387\u3092\u7528\u3044\u3066\u6b20\u6e2c\u60c5\u5831\u5272\u5408\u3068\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u884c\u3046<\/h2>\n\n\n\n

\u76f8\u5bfe\u52b9\u7387\u3092\u6307\u6a19\u306b\u3057\u3066\u3001\u6b20\u6e2c\u60c5\u5831\u306e\u5272\u5408\u3068\u6b20\u6e2c\u5024\u88dc\u5b8c\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u3092\u5272\u308a\u5f53\u3066\u305f\u3068\u304d\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u884c\u3063\u3066\u307f\u305f\u3002<\/p>\n\n\n\n

\u6b20\u6e2c\u60c5\u5831\u5272\u5408\u306f 10 \uff05\uff080.1\uff09\u3054\u3068\u306b 0.1 \u304b\u3089 1 \u307e\u3067\u3068\u3057\u305f\u3002<\/p>\n\n\n\n

1 \u3068\u3044\u3046\u306e\u306f\u3059\u3079\u3066\u6b20\u6e2c\u60c5\u5831\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u306e\u3067\u3042\u308a\u3048\u306a\u3044\u304c\u3001\u7406\u5c48\u306e\u4e0a\u3067\u306f\u8a08\u7b97\u3067\u304d\u308b\u305f\u3081\u542b\u3081\u305f\u3002<\/p>\n\n\n\n

\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u306f\u30015, 10, 20, 50, 100, 200 \u3068\u3057\u305f\u3002<\/p>\n\n\n\n

\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u306f\u3001\u3088\u304f\u898b\u304b\u3051\u308b\u60c5\u5831\u3092\u53c2\u8003\u306b\u9078\u3093\u3060\u3002<\/p>\n\n\n\n

\u4ee5\u4e0b\u306b\u3001\u3053\u308c\u3089\u306e\u6761\u4ef6\u3067\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u72b6\u306b\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3059\u308b R \u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u793a\u3059\u3002<\/p>\n\n\n\n

lambda0 <-<\/span> 1<\/span>:<\/span>10<\/span>\/<\/span>10<\/span>\nD <-<\/span> c<\/span>(<\/span>5<\/span>,<\/span>10<\/span>,<\/span>20<\/span>,<\/span>50<\/span>,<\/span>100<\/span>,<\/span>200<\/span>)<\/span>\nres.tab <-<\/span> matrix<\/span>(<\/span>rep<\/span>(<\/span>0<\/span>,<\/span>60<\/span>),<\/span>nr=<\/span>6<\/span>)<\/span>\nfor<\/span> (<\/span>i in<\/span> 1<\/span>:<\/span>length<\/span>(<\/span>D)){<\/span>\nfor<\/span> (<\/span>j in<\/span> 1<\/span>:<\/span>length<\/span>(<\/span>lambda0)){<\/span>\nReD <-<\/span> 1<\/span>\/<\/span>(<\/span>1<\/span>+<\/span>lambda0[<\/span>j]<\/span>\/<\/span>D[<\/span>i])<\/span>\nres.tab[<\/span>i,<\/span>j]<\/span> <-<\/span> ReD\n}<\/span>\n}<\/span>\ncolnames<\/span>(<\/span>res.tab)<\/span> <-<\/span> lambda0\nrownames<\/span>(<\/span>res.tab)<\/span> <-<\/span> D\nres.tab\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c res.tab\uff08\u51fa\u529b\u306f\u7701\u7565\u3057\u3066\u3044\u308b\uff09\u3092matplot()\u95a2\u6570\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u5316\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u3069\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u3067\u3042\u3063\u3066\u3082\u3001\u6b20\u6e2c\u60c5\u5831\u306e\u5272\u5408\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u76f8\u5bfe\u52b9\u7387\u306f\u4f4e\u304f\u306a\u308b\u3002<\/p>\n\n\n\n
100 \u3068 200 \u306e\u5dee\u306f\u308f\u305a\u304b\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u3064\u307e\u308a\u3001100 \u500b\u4f5c\u6210\u3059\u308c\u3070\u3001\u307e\u305a\u9593\u9055\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
matplot<\/span>(<\/span>t<\/span>(<\/span>res.tab),<\/span>type=<\/span>\"l\"<\/span>,<\/span>xaxt=<\/span>\"n\"<\/span>,<\/span>ylab=<\/span>\"Relative Efficiency\"<\/span>,<\/span>las=<\/span>1<\/span>,<\/span>\nxlab=<\/span>\"Proportion of Missing Information in Population\"<\/span>)<\/span>\naxis<\/span>(<\/span>1<\/span>,<\/span> at=<\/span>1<\/span>:<\/span>10<\/span>,<\/span> formatC<\/span>(<\/span>1<\/span>:<\/span>10<\/span>\/<\/span>10<\/span>))<\/span>\nlegend<\/span>(<\/span>legend=<\/span>paste<\/span>(<\/span>\"D=\"<\/span>,<\/span>D),<\/span>\"bottomleft\"<\/span>,<\/span> lty=<\/span>1<\/span>:<\/span>5<\/span>,<\/span> col=<\/span>1<\/span>:<\/span>6<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"
\u76f8\u5bfe\u52b9\u7387 Relative Efficiency \u306e\u30b0\u30e9\u30d5<\/figcaption><\/figure>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u6b20\u6e2c\u5024\u306e\u88dc\u5b8c\u6cd5\u306e\u4e00\u3064\u3001\u591a\u91cd\u4ee3\u5165\u6cd5\u306b\u304a\u3044\u3066\u3001\u6b20\u6e2c\u5024\u88dc\u5b8c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u3044\u304f\u3064\u5fc5\u8981\u304b\u3068\u3044\u3046\u8cea\u554f\u306b\u306f\u3001\u76f8\u5bfe\u52b9\u7387\u3067\u6c7a\u3081\u308b\u3068\u3088\u3044\u3068\u56de\u7b54\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u6b20\u6e2c\u60c5\u5831\u5272\u5408\u3068\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u6570\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u7d50\u679c\u3001100 \u30bb\u30c3\u30c8\u4f5c\u6210\u3059\u308c\u3070\u3001\u307e\u305a\u554f\u984c\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d<\/h2>\n\n\n\n
\u6b20\u6e2c\u30c7\u30fc\u30bf\u306e\u7d71\u8a08\u79d1\u5b66\u2015\u2015\u533b\u5b66\u3068\u793e\u4f1a\u79d1\u5b66\u3078\u306e\u5fdc\u7528 (\u8abf\u67fb\u89b3\u5bdf\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u5b9f\u969b \u7b2c1\u5dfb)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u6b20\u6e2c\u5024\u304c\u3042\u3063\u305f\u5834\u5408\u3001\u5bfe\u51e6\u3059\u308b\u65b9\u6cd5\u304c\u3044\u304f\u3064\u304b\u3042\u308b\u3002 \u305d\u306e\u3046\u3061\u306e\u4e00\u3064\u304c\u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u3042\u308b\u3002 \u591a\u91cd\u4ee3\u5165\u6cd5\u3067\u4f5c\u6210\u3059\u3079\u304d\u6b20\u6e2c\u5024\u88dc\u5b8c\u30c7\u30fc\u30bf\u306e\u6570\u306f\u3044\u304f\u3064\u304c\u3088\u3044\u306e\u304b\uff1f<\/p>\n","protected":false},"author":2,"featured_media":2150,"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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,20],"tags":[],"class_list":["post-344","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-20"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/01\/20220128201801.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/344","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=344"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/344\/revisions"}],"predecessor-version":[{"id":3949,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/344\/revisions\/3949"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/2150"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}