{"id":385,"date":"2021-10-21T20:45:30","date_gmt":"2021-10-21T11:45:30","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/box-cox-transformation-in-r\/"},"modified":"2025-04-29T15:43:17","modified_gmt":"2025-04-29T06:43:17","slug":"box-cox-transformation-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/box-cox-transformation-in-r\/","title":{"rendered":"R \u3067 Box-Cox \u5909\u63db\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n

\u9023\u7d9a\u91cf\u3092\u4f55\u3089\u304b\u306e\u65b9\u6cd5\u3067\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3051\u308b\u65b9\u6cd5\u306f\u3044\u304f\u3064\u304b\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u3053\u3067\u306fBox-Cox\u5909\u63db\u306e\u65b9\u6cd5\u3092\u307e\u3068\u3081\u3066\u307f\u305f\u3002<\/p>\n\n\n\n\n\n\n\n

R \u3067 Box-Cox\u5909\u63db\u3092\u884c\u3046\u5b9f\u4f8b<\/h2>\n\n\n\n

\u307e\u305a\u3001car \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u547c\u3073\u51fa\u3059\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>car)<\/span>\n<\/code><\/pre>\n\n\n\n
car \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u4e2d\u306e\u3001powerTransform()\u3068bcpower()\u3092\u4f7f\u3063\u3066\u5909\u63db\u3059\u308b\u3002<\/p>\n\n\n\n
\u4f8b\u306b\u4f7f\u3046\u306e\u306f\u3001EZR\u516c\u5f0f\u30de\u30cb\u30e5\u30a2\u30eb<\/a>\u306e\u4ed8\u9332\u3067\u3064\u3044\u3066\u304f\u308b\u30c7\u30fc\u30bf ElderlyAML \u5185\u306eLDH\u306e\u30c7\u30fc\u30bf\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
powerTransform()\u3067\u3001\u03bb\uff08\u30e9\u30e0\u30c0\uff09\u3068\u3044\u3046\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n
Box-Cox\u5909\u63db\u306b\u306f\u3053\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
ptf.LDH1 <-<\/span> powerTransform<\/span>(<\/span>ElderlyAML$<\/span>LDH)<\/span>\n<\/code><\/pre>\n\n\n\n
\u03bb\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3068\u3001 -0.3184011\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> ptf.LDH1$<\/span>lambda\nElderlyAML$<\/span>LDH\n-<\/span>0.3184011<\/span>\n<\/code><\/pre>\n\n\n\n
\u6b21\u306b\u3001bcPower()\u3092\u4f7f\u3063\u3066\u3001\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f \u03bb\u3092\u7528\u3044\u3066\u3001Box-Cox\u5909\u63db\u3092\u884c\u3046\u3002<\/p>\n\n\n\n
bc.LDH1\u3068\u3044\u3046\u65b0\u3057\u3044\u540d\u524d\u306e\u5909\u6570\u306b\u3059\u308b\u3002<\/p>\n\n\n\n
bc.LDH1 <-<\/span> bcPower<\/span>(<\/span>ElderlyAML$<\/span>LDH,<\/span> ptf.LDH1$<\/span>lambda)<\/span>\n<\/code><\/pre>\n\n\n\n
\u8981\u7d04\u5024\u3092\u51fa\u3057\u3066\u307f\u3066\u3082\u3001\u3088\u304f\u308f\u304b\u3089\u306a\u3044\u5024\u306b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
LDH\u306f\u3001\u901a\u5e38\u3001\u6570\u767e\u7a0b\u5ea6\u306e\u5024\u306a\u306e\u3067\u3001\u5168\u7136\u60f3\u50cf\u304c\u3064\u304b\u306a\u3044\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>bc.LDH1)<\/span>\nMin. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's <\/span>\n  2.444   2.597   2.656   2.662   2.737   2.862       1<\/span>\n<\/code><\/pre>\n\n\n\n
Box-Cox\u5909\u63db\u3057\u305f\u5024\u306e\u5206\u5e03\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b<\/h2>\n\n\n\n
\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3067\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u307e\u305a\u3001\u5143\u306e\u30c7\u30fc\u30bf\u3092\u305d\u306e\u307e\u307e\u4f7f\u3063\u3066\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u63cf\u3044\u3066\u307f\u308b\u3068\u3001\u3082\u306e\u306e\u898b\u4e8b\u306b\u53f3\u306b\u88fe\u3092\u5f15\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
hist<\/span>(<\/span>ElderlyAML$<\/span>LDH)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Box-Cox\u5909\u63db\u5f8c\u306e\u5024\u3092\u4f7f\u3046\u3068\u3001\u975e\u5e38\u306b\u304d\u308c\u3044\u306a\u5de6\u53f3\u5bfe\u79f0\u306e\u5206\u5e03\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
hist<\/span>(<\/span>bc.LDH1)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u3061\u306a\u307f\u306b\u3001\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u81ea\u7136\u5bfe\u6570\u5909\u63db\u306e\u5834\u5408\u306f\u3001\u5143\u306e\u30c7\u30fc\u30bf\u3088\u308a\u306f\u5de6\u53f3\u5bfe\u79f0\u306b\u306a\u3063\u3066\u3044\u308b\u304c\u3001\u4e2d\u592e\u3088\u308a\u5c11\u3057\u4f4e\u3044\u3068\u3053\u308d\u3067\u3001\u72ed\u3044\u7bc4\u56f2\u306b\u96c6\u4e2d\u3057\u3059\u304e\u3066\u3044\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u306b\u306a\u308b\u305f\u3081\u3001Box-Cox\u5909\u63db\u306e\u307b\u3046\u304c\u512a\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u601d\u3048\u308b\u3002<\/p>\n\n\n\n
hist<\/span>(<\/span>log<\/span>(<\/span>ElderlyAML$<\/span>LDH))<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\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>
Box-Cox\u5909\u63db\u3057\u305f\u5024\u3092\u9006\u5909\u63db\u3057\u3066\u5143\u306e\u4e16\u754c\u306b\u623b\u3059\u65b9\u6cd5<\/h2>\n\n\n\n
Box-Cox\u5909\u63db\u306f\u3001\u5f0f\u3067\u8868\u3059\u3068\u03bb\u304c\u30bc\u30ed\u3067\u306a\u3044\u5834\u5408\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
$$ y(\\lambda) = \\frac{y^{\\lambda} – 1}{\\lambda} $$<\/p>\n\n\n\n\n\n\n\n
\u306a\u306e\u3067\u3001\u9006\u5909\u63db\u3059\u308b\u306a\u3089\u3070\u3001<\/p>\n\n\n\n
$$ (y \\times \\lambda + 1)^{1\/\\lambda} $$<\/p>\n\n\n\n\n\n\n\n
\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u5148\u307b\u3069\u5909\u63db\u3057\u305f\u5024 bc.LDH1 \u3092\u5143\u306b\u623b\u3059\u306a\u3089\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3059\u308b\u3068\u5143\u306b\u623b\u308b\u3002<\/p>\n\n\n\n
Box-Cox\u5909\u63db\u3057\u305f\u5024\u3092\u4f7f\u3063\u3066\u3001\u56de\u5e30\u5206\u6790\u3092\u884c\u3063\u305f\u5f8c\u306b\u3001\u4e88\u6e2c\u5024\u3092\u4f7f\u3046\u305f\u3081\u306b\u3001\u5143\u306b\u623b\u3057\u305f\u3044\u5834\u5408\u306a\u3069\u306b\u4f7f\u3046\u3002<\/p>\n\n\n\n
rev.LDH1 <-<\/span> (<\/span>bc.LDH1 *<\/span> ptf.LDH1$<\/span>lambda +<\/span> 1<\/span>)<\/span>^<\/span>(<\/span>1<\/span>\/<\/span>ptf.LDH1$<\/span>lambda)<\/span>\n<\/code><\/pre>\n\n\n\n
summary()\u3092\u3068\u3063\u3066\u307f\u308b\u3068\u3001\u5b8c\u5168\u306b\u4e00\u81f4\u3057\u3066\u3044\u3066\u3001\u5143\u306b\u623b\u3063\u305f\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>rev.LDH1)<\/span>\nMin. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's <\/span>\n  113.0   246.5   355.0   518.9   629.5  2007.0       1 <\/span>\n> summary(ElderlyAML$LDH)<\/span>\n   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA'<\/span>s\n113.0<\/span>   246.5<\/span>   355.0<\/span>   518.9<\/span>   629.5<\/span>  2007.0<\/span>       1<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u306a\u3044\u9023\u7d9a\u91cf\u3092\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3051\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001Box-Cox\u5909\u63db\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u81ea\u7136\u5bfe\u6570\u5909\u63db\u3067\u3046\u307e\u304f\u3044\u304b\u306a\u3044\u3068\u304d\u306e\u5965\u306e\u624b\u3068\u3057\u3066\u77e5\u3063\u3066\u304a\u304f\u3068\u3001\u52a9\u304b\u308b\u3053\u3068\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n
\u53c2\u8003\u306b\u306a\u308c\u3070\u3002<\/p>\n\n\n\n
\u53c2\u8003\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
Box-cox\u5909\u63db\u3092\u7528\u3044\u3066\u6b63\u898f\u5206\u5e03\u306b\u5f93\u308f\u306a\u3044\u30c7\u30fc\u30bf\u3092\u89e3\u6790\u3092\u3057\u3066\u307f\u3088\u3046\uff01\uff5c\u30b9\u30bf\u30d3\u30b8<\/a><\/p>\n\n\n\n
\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n
EZR\u3067\u3084\u3055\u3057\u304f\u5b66\u3076\u7d71\u8a08\u5b66 \u6539\u8a023\u7248 \u301cEBM\u306e\u5b9f\u8df5\u304b\u3089\u81e8\u5e8a\u7814\u7a76\u307e\u3067\u301c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u9023\u7d9a\u91cf\u3092\u4f55\u3089\u304b\u306e\u65b9\u6cd5\u3067\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3051\u308b\u65b9\u6cd5\u306f\u3044\u304f\u3064\u304b\u3042\u308b\u3002 \u3053\u3053\u3067\u306fBox-Cox\u5909\u63db\u306e\u65b9\u6cd5\u3092\u307e\u3068\u3081\u3066\u307f\u305f\u3002<\/p>\n","protected":false},"author":2,"featured_media":2229,"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":[5,25,119,28],"tags":[],"class_list":["post-385","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-25","category-119","category-28"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2021\/10\/20211021193709.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/385","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=385"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/385\/revisions"}],"predecessor-version":[{"id":3586,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/385\/revisions\/3586"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/2229"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=385"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=385"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}