{"id":4543,"date":"2026-01-02T11:34:29","date_gmt":"2026-01-02T02:34:29","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4543"},"modified":"2026-01-02T20:05:14","modified_gmt":"2026-01-02T11:05:14","slug":"how-to-determine-sample-size-for-ordinal-logistic-mixed-effects-models-using-simulation","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-for-ordinal-logistic-mixed-effects-models-using-simulation\/","title":{"rendered":"\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff08\u9806\u5e8f\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\uff09\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u6c42\u3081\u308b\u65b9\u6cd5"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u81e8\u5e8a\u7814\u7a76\u3084\u5fc3\u7406\u5b66\u3001\u793e\u4f1a\u8abf\u67fb\u306a\u3069\u3067\u300c\u975e\u5e38\u306b\u6e80\u8db3\u301c\u975e\u5e38\u306b\u4e0d\u6e80\u300d\u3068\u3044\u3063\u305f\u8a55\u4fa1\u5c3a\u5ea6\u306e\u5909\u5316\u3092\u8abf\u3079\u305f\u3044\u5834\u9762\u306f\u591a\u3044\u3002\u3053\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf\u3092\u6b63\u3057\u304f\u89e3\u6790\u3059\u308b\u306b\u306f<strong>\u9806\u5e8f\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30<\/strong>\u304c\u9069\u3057\u3066\u3044\u308b\u304c\u3001\u540c\u3058\u4eba\u306b\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\u3092\u884c\u3046\u5834\u5408\u306f\u3001\u3055\u3089\u306b<span class=\"swl-marker mark_orange\">\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff08GLMM\uff09<\/span>\u3068\u3044\u3046\u9ad8\u5ea6\u306a\u67a0\u7d44\u307f\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u3053\u306e\u30e2\u30c7\u30eb\u306f\u69cb\u9020\u304c\u8907\u96d1\u306a\u305f\u3081\u3001\u6a19\u6e96\u7684\u306a\u30bd\u30d5\u30c8\u3067\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u304c\u3067\u304d\u306a\u3044\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001R\u3092\u7528\u3044\u305f<strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30fb\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong>\u306b\u3088\u3063\u3066\u3001\u6839\u62e0\u306e\u3042\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u5c0e\u304d\u51fa\u3059\u65b9\u6cd5\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u822c\u5316\u7dda\u5f62\u6df7\u5408\u30e2\u30c7\u30eb\uff08\u9806\u5e8f\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\uff09\u3068\u306f<\/h2>\n\n\n\n<p>\u3053\u306e\u30e2\u30c7\u30eb\u306f\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u8981\u7d20\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u9806\u5e8f\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af<\/strong>: \u300c\u975e\u5e38\u306b\u4e0d\u6e80\u3001\u3084\u3084\u4e0d\u6e80\u3001\u3084\u3084\u6e80\u8db3\u3001\u975e\u5e38\u306b\u6e80\u8db3\u300d\u306e\u3088\u3046\u306b\u3001\u6570\u5024\u3068\u3057\u3066\u306e\u610f\u5473\uff08\u9593\u9694\uff09\u306f\u53b3\u5bc6\u3067\u306f\u306a\u3044\u304c\u3001\u9806\u5e8f\u306b\u306f\u660e\u78ba\u306a\u610f\u5473\u304c\u3042\u308b\u30c7\u30fc\u30bf\u3092\u6271\u3046\u3002<\/li>\n\n\n\n<li><strong>\u6df7\u5408\u30e2\u30c7\u30eb<\/strong>: \u300c\u540c\u3058\u88ab\u9a13\u8005\u306b3\u56de\u6e2c\u5b9a\u3059\u308b\u300d\u3068\u3044\u3063\u305f\u3001\u30c7\u30fc\u30bf\u9593\u306e\u76f8\u95a2\uff08\u500b\u4eba\u306e\u56de\u7b54\u306e\u7656\u306a\u3069\uff09\u3092\u300c\u5909\u91cf\u52b9\u679c\u300d\u3068\u3057\u3066\u8003\u616e\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u5fc5\u8981\u6027<\/h2>\n\n\n\n<p>\u7279\u306b\u89b3\u5bdf\u7814\u7a76\u306b\u304a\u3044\u3066\u3001\u7d50\u679c\u304c\u300c\u6709\u610f\u3067\u306f\u306a\u304b\u3063\u305f\uff08$p \\ge 0.05$\uff09\u300d\u3068\u306a\u3063\u305f\u5834\u5408\u3001\u305d\u308c\u304c\u300c\u672c\u5f53\u306b\u5dee\u304c\u306a\u3044\u300d\u306e\u304b\u300c\u4eba\u6570\u304c\u8db3\u308a\u306a\u304f\u3066\u691c\u51fa\u3067\u304d\u306a\u304b\u3063\u305f\u3060\u3051\u300d\u306a\u306e\u304b\u3092\u533a\u5225\u3057\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\u3002\u3042\u3089\u304b\u3058\u3081\u691c\u5b9a\u529b\u5206\u6790\u3092\u884c\u3044\u3001\u5fc5\u8981\u306a\u4eba\u6570\u3092\u78ba\u4fdd\u3057\u3066\u304a\u304f\u3053\u3068\u306f\u3001\u7814\u7a76\u306e\u59a5\u5f53\u6027\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u306b\u975e\u5e38\u306b\u91cd\u8981\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-3904259656\" 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\">\u306a\u305c\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u304c\u5fc5\u8981\u306a\u306e\u304b<\/h2>\n\n\n\n<p>\u901a\u5e38\u306et\u691c\u5b9a\u306a\u3069\u3068\u9055\u3044\u3001\u9806\u5e8f\u6df7\u5408\u30e2\u30c7\u30eb\u306b\u306f\u300c\u8907\u6570\u306e\u5883\u754c\u70b9\uff08\u95be\u5024\uff09\u300d\u3084\u300c\u500b\u4eba\u5185\u306e\u76f8\u95a2\u300d\u304c\u542b\u307e\u308c\u308b\u3002\u3053\u308c\u3089\u304c\u8907\u96d1\u306b\u7d61\u307f\u5408\u3046\u305f\u3081\u3001\u5358\u7d14\u306a\u6570\u5f0f\uff08\u516c\u5f0f\uff09\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u7b97\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u305d\u3053\u3067\u3001<span class=\"swl-marker mark_orange\">\u300c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4e0a\u3067\u4eee\u60f3\u306e\u5b9f\u9a13\u3092\u6570\u5343\u56de\u7e70\u308a\u8fd4\u3057\u3001\u4f55\u56de\u6709\u610f\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u304b\u300d<\/span>\u3092\u76f4\u63a5\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u624b\u6cd5\u304c\u3001\u73fe\u5728\u6700\u3082\u4fe1\u983c\u3067\u304d\u308b\u89e3\u6c7a\u7b56\u3068\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\">R \u3067\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u5b9f\u4f8b<\/h2>\n\n\n\n<p>\u4ee5\u4e0b\u306b\u3001\u8907\u6570\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff0830\u301c120\u540d\uff09\u306b\u5bfe\u3057\u3066\u691c\u5b9a\u529b\u3092\u4e00\u62ec\u8a08\u7b97\u3057\u3001\u30b0\u30e9\u30d5\u5316\u3059\u308bR\u30b3\u30fc\u30c9\u3092\u63b2\u8f09\u3059\u308b\u30024 \u4ef6\u6cd5\u306e\u30a2\u30a6\u30c8\u30ab\u30e0\u3067\u30012 \u7fa4 \u00d7 3 \u56de\u6e2c\u5b9a\uff08\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u30011\u304b\u6708\u5f8c\u30013\u304b\u6708\u5f8c\u306a\u3069\uff09\u3092\u60f3\u5b9a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># --- 0. \u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u78ba\u8a8d\u3068\u8aad\u307f\u8fbc\u307f ---\nif (!require(\"ordinal\")) install.packages(\"ordinal\")\nif (!require(\"dplyr\")) install.packages(\"dplyr\")\nif (!require(\"ggplot2\")) install.packages(\"ggplot2\")\n\nlibrary(ordinal)\nlibrary(dplyr)\nlibrary(ggplot2)\n\n# --- 1. \u57fa\u672c\u8a2d\u5b9a ---\n# \u691c\u8a3c\u3057\u305f\u30441\u7fa4\u3042\u305f\u308a\u306e\u4eba\u6570\u30ea\u30b9\u30c8\nn_list &lt;- c(30, 50, 80, 100, 120) \nn_time &lt;- 3\n# \u4fe1\u983c\u6027\u3092\u62c5\u4fdd\u3059\u308b\u305f\u3081\u3001\u6700\u7d42\u7684\u306b\u306f1000\u56de\u3092\u63a8\u5968\u3059\u308b\niterations &lt;- 100 \nset.seed(123)\n\n# \u52b9\u679c\u91cf\u3068\u30d0\u30e9\u30c4\u30ad\u306e\u8a2d\u5b9a\nbeta_interaction &lt;- 0.8  # \u4ecb\u5165\u306b\u3088\u308b\u6539\u5584\u52b9\u679c\uff08\u4ea4\u4e92\u4f5c\u7528\uff09\nsigma_u &lt;- 1.0           # \u500b\u4eba\u5dee\u306e\u5927\u304d\u3055\nthresholds &lt;- c(-1.5, 0, 1.5) # 4\u4ef6\u6cd5\u306e\u5883\u754c\u70b9\n\n# --- 2. \u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u7528\u95a2\u6570 ---\nget_power &lt;- function(n_target) {\n  message(paste(\"\u8a08\u7b97\u4e2d: n =\", n_target, \"...\"))\n  \n  results &lt;- replicate(iterations, {\n    # \u4eee\u60f3\u30c7\u30fc\u30bf\u306e\u751f\u6210\n    df &lt;- expand.grid(id = 1:(n_target * 2), time = 0:(n_time - 1)) %>%\n      mutate(\n        group = ifelse(id &lt;= n_target, 0, 1),\n        u_i = rep(rnorm(n_target * 2, 0, sigma_u), each = n_time),\n        eta = 0.5 * time + beta_interaction * (group * time) + u_i\n      )\n    \n    df$y &lt;- as.factor(sapply(df$eta, function(e) {\n      latent &lt;- e + rlogis(1)\n      if(latent &lt;= thresholds&#91;1]) return(1) # \u975e\u5e38\u306b\u4e0d\u6e80\n      if(latent &lt;= thresholds&#91;2]) return(2) # \u3084\u3084\u4e0d\u6e80\n      if(latent &lt;= thresholds&#91;3]) return(3) # \u3084\u3084\u6e80\u8db3\n      return(4)                             # \u975e\u5e38\u306b\u6e80\u8db3\n    }))\n    \n    # \u30e2\u30c7\u30eb\u9069\u5408\u3068\u691c\u5b9a\n    tryCatch({\n      mod &lt;- clmm(y ~ group * time + (1|id), data = df)\n      p_val &lt;- summary(mod)$coefficients&#91;\"group:time\", \"Pr(>|z|)\"]\n      return(p_val &lt; 0.05)\n    }, error = function(e) return(NA))\n  })\n  return(mean(results, na.rm = TRUE))\n}\n\n# --- 3. \u5b9f\u884c\u3068\u7d50\u679c\u306e\u30b0\u30e9\u30d5\u5316 ---\npower_results &lt;- data.frame(\n  n_per_group = n_list,\n  power = sapply(n_list, get_power)\n)\n\nggplot(power_results, aes(x = n_per_group, y = power)) +\n  geom_line(linewidth = 1) + geom_point(size = 3, color = \"red\") +\n  geom_hline(yintercept = 0.8, linetype = \"dashed\", color = \"blue\") +\n  scale_y_continuous(limits = c(0, 1), breaks = seq(0, 1, 0.1)) +\n  labs(title = \"\u30d1\u30ef\u30fc\u30ab\u30fc\u30d6: CLMM\u4ea4\u4e92\u4f5c\u7528\u306e\u691c\u5b9a\u529b\",\n       x = \"\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff081\u7fa4\u3042\u305f\u308a\uff09\", y = \"\u691c\u5b9a\u529b (Power)\") +\n  theme_minimal()\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"963\" height=\"709\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-3.png\" alt=\"\" class=\"wp-image-4544\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-3.png 963w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-3-300x221.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/01\/image-3-768x565.png 768w\" sizes=\"(max-width: 963px) 100vw, 963px\" \/><figcaption class=\"wp-element-caption\">\u30d1\u30ef\u30fc\u30ab\u30fc\u30d6\u4f8b<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u30d1\u30ef\u30fc\u30ab\u30fc\u30d6\u306e\u89e3\u91c8<\/h2>\n\n\n\n<p>\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u7d50\u679c\u3092\u30b0\u30e9\u30d5\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u8996\u899a\u7684\u306b\u5fc5\u8981\u4eba\u6570\u3092\u5224\u65ad\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76ee\u6a19\u5024<\/strong>: \u4e00\u822c\u7684\u306b\u3001\u691c\u5b9a\u529b\uff08Power\uff09\u304c<span class=\"swl-marker mark_orange\">0.8\uff0880%\uff09<\/span>\u3092\u8d85\u3048\u308b\u30dd\u30a4\u30f3\u30c8\u3092\u6700\u5c0f\u5fc5\u8981\u4eba\u6570\u3068\u3059\u308b\uff08\u4e0a\u8a18\u306e\u5834\u5408 70 \u4f8b\u3042\u305f\u308a\u3067 80 \uff05\u3092\u8d85\u3048\u300180 \u4f8b\u3042\u308c\u3070\u307e\u305a\u9593\u9055\u3044\u306a\u304f 80 \uff05\u3092\u8d85\u3048\u308b\u3068\u8003\u3048\u3089\u308c\u308b\uff09\u3002<\/li>\n\n\n\n<li><strong>\u50be\u5411<\/strong>: \u4eba\u6570\u3092\u5897\u3084\u3059\u307b\u3069\u691c\u5b9a\u529b\u306f\u4e0a\u304c\u308b\u304c\u3001\u3042\u308b\u4e00\u70b9\u3092\u8d85\u3048\u308b\u3068\u4f38\u3073\u304c\u920d\u5316\u3059\u308b\u3002\u30b3\u30b9\u30c8\u3068\u7cbe\u5ea6\u306e\u30d0\u30e9\u30f3\u30b9\u304c\u826f\u3044\u70b9\u3092\u898b\u6975\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5b89\u5b9a\u6027<\/strong>: \u8a66\u884c\u56de\u6570\u304c\u5c11\u306a\u3044\u3068\u30b0\u30e9\u30d5\u304c\u30ac\u30bf\u3064\u304f\u3002\u6700\u7d42\u5224\u65ad\u306b\u306f\u5fc5\u305a<strong>1000\u56de<\/strong>\u306e\u8a66\u884c\u3092\u884c\u3044\u3001\u66f2\u7dda\u3092\u5b89\u5b9a\u3055\u305b\u308b\u3079\u304d\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b9f\u8df5\u3059\u308b\u969b\u306e\u30ac\u30a4\u30c9\u30fb\u6ce8\u610f\u70b9<\/h2>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>\u8131\u843d\u7387\uff08\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8\uff09\u3092\u8003\u616e\u3059\u308b:\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u5f97\u3089\u308c\u308b\u6570\u5024\u306f\u3001\u89e3\u6790\u306b\u56de\u305b\u308b\u5b8c\u9042\u8005\u306e\u4eba\u6570\u3067\u3042\u308b\u300220%\u306e\u8131\u843d\u304c\u898b\u8fbc\u307e\u308c\u308b\u306a\u3089\u3001\u5fc5\u8981\u4eba\u6570\u30920.8\u3067\u5272\u3063\u305f\u6570\u3092\u76ee\u6a19\u306b\u30ea\u30af\u30eb\u30fc\u30c8\u3059\u3079\u304d\u3067\u3042\u308b\uff0880 \u4f8b\u3067\u3042\u308c\u3070\u300180 \/ 0.8 = 100\uff09\u3002<\/li>\n\n\n\n<li>\u8a66\u884c\u56de\u6570\u306e\u30b9\u30c6\u30c3\u30d7\u30a2\u30c3\u30d7:\u30b3\u30fc\u30c9\u306e\u4fee\u6b63\u4e2d\u306f100\u56de\u7a0b\u5ea6\u306e\u5c11\u306a\u3044\u8a66\u884c\u56de\u6570\u3067\u52d5\u4f5c\u3092\u78ba\u8a8d\u3057\u3001\u6700\u7d42\u7684\u306b1000\u56de\u3067\u56de\u3059\u306e\u304c\u52b9\u7387\u7684\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6839\u62e0:\u300c\u6539\u5584\u52b9\u679c\u300d\u3084\u300c\u500b\u4eba\u5dee\u300d\u306e\u6570\u5024\u306f\u3001\u5148\u884c\u7814\u7a76\u3084\u30d1\u30a4\u30ed\u30c3\u30c8\u30c7\u30fc\u30bf\u3092\u53c2\u8003\u306b\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001\u7d50\u679c\u306e\u8aac\u5f97\u529b\u304c\u5897\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 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