{"id":726,"date":"2026-01-18T18:56:50","date_gmt":"2026-01-18T09:56:50","guid":{"rendered":"http:\/\/waurimal.kr\/?p=726"},"modified":"2026-01-18T19:44:34","modified_gmt":"2026-01-18T10:44:34","slug":"chap04-%eb%b2%a0%ec%9d%b4%ec%a7%80%ec%95%88-%eb%8b%a4%ec%b8%b5-%eb%aa%a8%ed%98%95bayesian-multilevel-models","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=726","title":{"rendered":"Chap04. \ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615(Bayesian Multilevel Models)"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc138\uc694!<\/p>\n\n\n\n<p>\uc624\ub298\uc740 <strong>\ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615(Bayesian Multilevel Models)<\/strong>\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \u201c\ud559\uad50 \ud604\uc7a5\uc758 \ub370\uc774\ud130\u201d\ub97c \uc608\uc2dc\ub85c \ub4e4\uc5b4 \uc9c1\uad00\uc801\uc778 \uc124\uba85\uacfc \uc218\ub9ac\uc801 \uc5c4\ubc00\ud568\uc744 \ubaa8\ub450 \uac16\ucd98 \ud615\ud0dc\ub85c \uc7ac\uad6c\uc131\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\ubd84\uc11d \ub3c4\uad6c\ub85c\ub294 <strong>jamovi<\/strong>\uc758 \uc0ac\uc6a9\ubc95\uc744 \uc124\uba85\ud558\ub418, jamovi\uc758 \uae30\ubc18\uc774 \ub418\ub294 <strong>R<\/strong> \ucf54\ub4dc\ub97c \ud568\uaed8 \uc81c\uc2dc\ud558\uc5ec \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131\ubd80\ud130 \ubd84\uc11d, \uc2dc\uac01\ud654\uae4c\uc9c0 \uc644\ubcbd\ud558\uac8c \uad6c\ud604\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \ud2b9\ud788 \uc624\ub298 \ub2e4\ub8f0 \ubb38\ud5cc\uc740 \uc77c\ubc18\uc801\uc778 \ub2e4\uce35\ubaa8\ud615\uc744 \ub118\uc5b4, \ube44\uc120\ud615 \uad00\uacc4\ub97c \ub2e4\ub8e8\ub294 <strong>GAMM(\uc77c\ubc18\ud654 \uac00\ubc95 \ud63c\ud569 \ubaa8\ud615)<\/strong>\uacfc <strong>STAR(\uad6c\uc870\uc801 \uac00\ubc95 \ud68c\uadc0)<\/strong> \ubaa8\ud615\uae4c\uc9c0 \ud3ec\uad04\ud558\uace0 \uc788\uc73c\ubbc0\ub85c, \uc774\ub97c \uad6c\ud604\ud558\uae30 \uc704\ud574 R\uc758 <code>brms<\/code> \ud328\ud0a4\uc9c0\ub97c \ud65c\uc6a9\ud55c \ucf54\ub4dc\ub97c \uc911\uc810\uc801\uc73c\ub85c \ubcf4\uc5ec\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. \ubca0\uc774\uc9c0\uc548 \ucd94\ub860: \uc694\ub9ac\uc0ac\uc758 \ub808\uc2dc\ud53c\uc640 \ud560\uba38\ub2c8\uc758 \uc190\ub9db<\/h2>\n\n\n\n<p>\ubcf8\uaca9\uc801\uc778 \uc218\uc2dd\uc5d0 \ub4e4\uc5b4\uac00\uae30 \uc804\uc5d0, \ubca0\uc774\uc9c0\uc548\uc774 \ubb34\uc5c7\uc778\uc9c0 \uad50\uc721\ud559\uc801 \uad00\uc810\uc5d0\uc11c \uc27d\uac8c \ud480\uc5b4\ubd05\uc2dc\ub2e4.<\/p>\n\n\n\n<p>\ubb38\ud5cc\uc5d0\uc11c\ub294 \ubca0\uc774\uc9c0\uc548 \ubaa8\ud615\uc774 \ub450 \ubd80\ubd84\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4\uace0 \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\uc0ac\uc804 \ubd84\ud3ec(Prior Distribution):<\/strong> \ub370\uc774\ud130\ub97c \ubcf4\uae30 \uc804, \ud30c\ub77c\ubbf8\ud130(\ubaa8\uc218)\uc5d0 \ub300\ud574 \uc6b0\ub9ac\uac00 \uac00\uc9c0\uace0 \uc788\ub294 \uc9c0\uc2dd\uc774\ub098 \ubbff\uc74c\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uad00\uce21 \ubaa8\ud615(Observation Model):<\/strong> \ub370\uc774\ud130\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c\uc758 \uc870\uac74\ubd80 \ubd84\ud3ec\ub85c, \ube48\ub3c4\uc8fc\uc758\uc5d0\uc11c\uc758 &#8216;\uc6b0\ub3c4(Likelihood)&#8217;\uc5d0 \ud574\ub2f9\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n\n\n\n<p><strong>[\uc608\uc2dc: \uae40 \uad50\uc0ac\uc758 \ud559\uc0dd \ud3c9\uac00]<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ube48\ub3c4\uc8fc\uc758(Likelihood):<\/strong> \uae40 \uad50\uc0ac\uac00 \ucca0\uc218\uc758 \uc774\ubc88 \uc218\ud559 \uc2dc\ud5d8\uc9c0(\ub370\uc774\ud130)\ub9cc \ubcf4\uace0 \uc810\uc218\ub97c \ub9e4\uae41\ub2c8\ub2e4. \uc624\uc9c1 &#8216;\uad00\uce21\ub41c \ub370\uc774\ud130&#8217;\uac00 \uc804\ubd80\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ubca0\uc774\uc9c0\uc548(Posterior):<\/strong> \uae40 \uad50\uc0ac\ub294 \ucca0\uc218\uac00 \ud3c9\uc18c\uc5d0 \uc218\ud559\uc744 \uc544\uc8fc \uc798\ud55c\ub2e4\ub294 \uac83(Prior)\uc744 \uc54c\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ubc88 \uc2dc\ud5d8\uc744 \uc880 \ubabb \ubd24\ub354\ub77c\ub3c4(Likelihood), &#8220;\uc544, \uc2e4\uc218\ub97c \uc880 \ud588\uad6c\ub098&#8221; \ud558\uace0 \uac10\uc548\ud558\uc5ec \ucd5c\uc885 \uc2e4\ub825(Posterior)\uc744 \ucd94\uc815\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>\uc774\uac83\uc774 \ubc14\ub85c \ubca0\uc774\uc988 \uc815\ub9ac\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"p(\\theta|y) \\propto p(y|\\theta) \\cdot p(\\theta)\"><semantics><mrow><mi>p<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mi>|<\/mi><mi>y<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u221d<\/mo><mi>p<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>y<\/mi><mi>|<\/mi><mi>\u03b8<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u22c5<\/mo><mi>p<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">p(\\theta|y) \\propto p(y|\\theta) \\cdot p(\\theta)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc989, <strong>\uc0ac\ud6c4 \ubd84\ud3ec(Posterior) <\/strong><math data-latex=\"\\propto\"><semantics><mo lspace=\"0em\" rspace=\"0em\">\u221d<\/mo><annotation encoding=\"application\/x-tex\">\\propto<\/annotation><\/semantics><\/math><strong> \uc6b0\ub3c4(Likelihood) <\/strong><math data-latex=\"\\times\"><semantics><mo lspace=\"0em\" rspace=\"0em\">\u00d7<\/mo><annotation encoding=\"application\/x-tex\">\\times<\/annotation><\/semantics><\/math><strong> \uc0ac\uc804 \ubd84\ud3ec(Prior)<\/strong> \uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. \uad50\uc721 \ud604\uc7a5 \uc2dc\ub098\ub9ac\uc624 \ubc0f \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131 (R Code)<\/h2>\n\n\n\n<p>\uc6b0\ub9ac\uac00 \ubd84\uc11d\ud560 \uac00\uc0c1\uc758 \uc2dc\ub098\ub9ac\uc624\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>[\uc2dc\ub098\ub9ac\uc624: \uc774\uc758\ucd08\ub4f1\ud559\uad50\uc758 \uc218\ud559 \uc131\ucde8\ub3c4 \ubd84\uc11d]<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ub370\uc774\ud130 \uad6c\uc870:<\/strong> \ud559\uc0dd(<math data-latex=\"i\"><semantics><mi>i<\/mi><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math>)\uc774 \ud559\uae09(<math data-latex=\"j\"><semantics><mi>j<\/mi><annotation encoding=\"application\/x-tex\">j<\/annotation><\/semantics><\/math>)\uc5d0 \uc18c\uc18d\ub41c 2\uc218\uc900 \uad6c\uc870 (Students nested in Classes).<\/li>\n\n\n\n<li><strong>\uc885\uc18d\ubcc0\uc218 (<\/strong><math data-latex=\"y\"><semantics><mi>y<\/mi><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math><strong>):<\/strong> \uc218\ud559 \uc131\ucde8\ub3c4 \uc810\uc218.<\/li>\n\n\n\n<li><strong>1\uc218\uc900 \ubcc0\uc218 (\ud559\uc0dd):<\/strong> \uc0ac\uad50\uc721 \ucc38\uc5ec \uc2dc\uac04(Time, \ube44\uc120\ud615\uc801 \uad00\uacc4 \uc608\uc0c1), \uac00\uc815\uc758 \uc0ac\ud68c\uacbd\uc81c\uc801 \uc9c0\uc704(SES).<\/li>\n\n\n\n<li><strong>2\uc218\uc900 \ubcc0\uc218 (\ud559\uae09):<\/strong> \ub2f4\uc784 \uad50\uc0ac\uc758 \ud6a8\ub2a5\uac10(Efficacy).<\/li>\n\n\n\n<li><strong>\ud2b9\uc774\uc0ac\ud56d:<\/strong> \uc0ac\uad50\uc721 \uc2dc\uac04\uc740 \ucc98\uc74c\uc5d0\ub294 \uc131\uc801\uc744 \uc62c\ub9ac\uc9c0\ub9cc, \uc77c\uc815 \uc2dc\uac04\uc774 \uc9c0\ub098\uba74 \ud53c\ub85c\ub3c4\ub85c \uc778\ud574 \ud6a8\uacfc\uac00 \ub5a8\uc5b4\uc9c0\ub294 <strong>\ube44\uc120\ud615(Non-linear)<\/strong> \uad00\uacc4\uac00 \uc758\uc2ec\ub429\ub2c8\ub2e4. \uc774\ub294 \ubb38\ud5cc\uc758 <strong>GAMM(Generalized Additive Multilevel Models)<\/strong> \ubd80\ubd84\uacfc \uc5f0\uacb0\ub429\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<p>\uc774\uc81c R\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc774 \uc2dc\ub098\ub9ac\uc624\uc5d0 \ub9de\ub294 \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud544\uc218 \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nif (!require(\"brms\")) install.packages(\"brms\")\nif (!require(\"ggplot2\")) install.packages(\"ggplot2\")\nif (!require(\"dplyr\")) install.packages(\"dplyr\")\n\nlibrary(brms)\nlibrary(dplyr)\nlibrary(ggplot2)\n\n# 1. \ub370\uc774\ud130 \uc0dd\uc131 (\uc7ac\ud604\uc131\uc744 \uc704\ud574 \uc2dc\ub4dc \uc124\uc815)\nset.seed(2026)\n\nn_classes &lt;- 30      # \ud559\uae09 \uc218\nn_students &lt;- 20     # \ud559\uae09\ub2f9 \ud559\uc0dd \uc218\nN &lt;- n_classes * n_students\n\n# 2\uc218\uc900(\ud559\uae09) \ubcc0\uc218 \uc0dd\uc131\nclass_id &lt;- rep(1:n_classes, each = n_students)\nteacher_efficacy &lt;- rnorm(n_classes, 0, 1) # \uad50\uc0ac \ud6a8\ub2a5\uac10 (\ud45c\uc900\uc815\uaddc\ubd84\ud3ec)\nclass_intercept &lt;- rnorm(n_classes, 0, 2)  # \ud559\uae09\ubcc4 \ubb34\uc791\uc704 \uc808\ud3b8 (Random Intercept)\n\n# \ub370\uc774\ud130 \ud504\ub808\uc784 \uc0dd\uc131\ndata &lt;- data.frame(class_id = factor(class_id))\ndata$teacher_eff &lt;- rep(teacher_efficacy, each = n_students)\ndata$class_int &lt;- rep(class_intercept, each = n_students)\n\n# 1\uc218\uc900(\ud559\uc0dd) \ubcc0\uc218 \uc0dd\uc131\ndata$SES &lt;- rnorm(N, 0, 1) # \uc0ac\ud68c\uacbd\uc81c\uc801 \uc9c0\uc704\ndata$Time &lt;- runif(N, 0, 10) # \uc0ac\uad50\uc721 \uc2dc\uac04 (0~10\uc2dc\uac04)\n\n# \ube44\uc120\ud615 \ud6a8\uacfc \uc0dd\uc131 (\uc0ac\uad50\uc721 \uc2dc\uac04: \uc5ed U\uc790 \ud615\ud0dc) - \ubb38\ud5cc\uc758 P-spline \uc608\uc2dc \uad00\ub828 &#91;cite: 201]\n# \uc2dc\uac04 \ud6a8\uacfc: 3 * sin(Time\/3)\ntime_effect &lt;- 3 * sin(data$Time \/ 3) \n\n# \uc885\uc18d\ubcc0\uc218(\uc218\ud559 \uc810\uc218) \uc0dd\uc131\n# \uc218\uc2dd: \uc808\ud3b8 + SES\ud6a8\uacfc + \uad50\uc0ac\ud6a8\ub2a5\uac10 + \uc2dc\uac04\ud6a8\uacfc(\ube44\uc120\ud615) + \ud559\uae09\ubb34\uc120\ud6a8\uacfc + \uc624\ucc28\ndata$Math &lt;- 50 + (2 * data$SES) + (1.5 * data$teacher_eff) + \n             time_effect + data$class_int + rnorm(N, 0, 3)\n\n# \ub370\uc774\ud130 \ud655\uc778\nhead(data)\n\n# CSV \uc800\uc7a5 (jamovi\uc5d0\uc11c \ubd88\ub7ec\uc624\uae30 \uc704\ud568)\nwrite.csv(data, \"chap04.csv\", row.names = FALSE)\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-2a084413-dace-437c-86e6-124baeadb50c\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap04.csv\">chap04<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap04.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2a084413-dace-437c-86e6-124baeadb50c\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">3. \ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615\uc758 \uad6c\uc870<\/h2>\n\n\n\n<p>\ubb38\ud5cc\uc5d0 \ub530\ub974\uba74, \uc77c\ubc18\uc801\uc778 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(LMM)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\ud604\ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"y = X\\beta + \\sum_{l=1}^{L} Z_l u_l + \\epsilon\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>X<\/mi><mi>\u03b2<\/mi><mo>+<\/mo><msubsup><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>l<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>L<\/mi><\/msubsup><msub><mi>Z<\/mi><mi>l<\/mi><\/msub><msub><mi>u<\/mi><mi>l<\/mi><\/msub><mo>+<\/mo><mi>\u03f5<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = X\\beta + \\sum_{l=1}^{L} Z_l u_l + \\epsilon<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc6b0\ub9ac \ub370\uc774\ud130\uc5d0 \uc801\uc6a9\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"\\text{Math}_{ij} = \\beta_0 + \\beta_1 \\text{SES}_{ij} + \\beta_2 \\text{TeacherEff}_j + u_{j} + \\epsilon_{ij}\"><semantics><mrow><msub><mtext>Math<\/mtext><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>1<\/mn><\/msub><msub><mtext>SES<\/mtext><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>2<\/mn><\/msub><msub><mtext>TeacherEff<\/mtext><mi>j<\/mi><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mi>j<\/mi><\/msub><mo>+<\/mo><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Math}_{ij} = \\beta_0 + \\beta_1 \\text{SES}_{ij} + \\beta_2 \\text{TeacherEff}_j + u_{j} + \\epsilon_{ij}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\beta\"><semantics><mi>\u03b2<\/mi><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math>: \uace0\uc815 \ud6a8\uacfc(Fixed effects) &#8211; \uc804\uccb4\uc801\uc778 \ud3c9\uade0 \ud6a8\uacfc.<\/li>\n\n\n\n<li><math data-latex=\"u_j\"><semantics><msub><mi>u<\/mi><mi>j<\/mi><\/msub><annotation encoding=\"application\/x-tex\">u_j<\/annotation><\/semantics><\/math>: \ud559\uae09\ubcc4 \ubb34\uc791\uc704 \ud6a8\uacfc(Random effects), <math data-latex=\"u_j \\sim N(0, \\sigma_u^2)\"><semantics><mrow><msub><mi>u<\/mi><mi>j<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><msubsup><mi>\u03c3<\/mi><mi>u<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">u_j \\sim N(0, \\sigma_u^2)<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n<li><math data-latex=\"\\epsilon_{ij}\"><semantics><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">\\epsilon_{ij}<\/annotation><\/semantics><\/math>: \uc624\ucc28\ud56d, <math data-latex=\"\\epsilon_{ij} \\sim N(0, \\sigma^2)\"><semantics><mrow><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_{ij} \\sim N(0, \\sigma^2)<\/annotation><\/semantics><\/math>.<\/li>\n<\/ul>\n\n\n\n<p>\ubca0\uc774\uc9c0\uc548 \uc811\uadfc\uc5d0\uc11c\ub294 \uc5ec\uae30\uc11c \uba48\ucd94\uc9c0 \uc54a\uace0, <math data-latex=\"\\beta\"><semantics><mi>\u03b2<\/mi><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math>\uc640 <math data-latex=\"\\sigma^2\"><semantics><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\sigma^2<\/annotation><\/semantics><\/math> \uac19\uc740 \ud30c\ub77c\ubbf8\ud130\uc5d0\ub3c4 <strong>\uc0ac\uc804 \ubd84\ud3ec(Prior)<\/strong>\ub97c \ubd80\uc5ec\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\beta \\sim N(c, C)\"><semantics><mrow><mi>\u03b2<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>c<\/mi><mo separator=\"true\">,<\/mo><mi>C<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\beta \\sim N(c, C)<\/annotation><\/semantics><\/math> (\ubcf4\ud1b5 \uc815\ubcf4\ub97c \uc8fc\uc9c0 \uc54a\ub294 \ubb34\uc815\ubcf4 \uc0ac\uc804\ubd84\ud3ec\ub098 \uc57d\ud55c \uc815\ubcf4 \uc0ac\uc804\ubd84\ud3ec \uc0ac\uc6a9).<\/li>\n\n\n\n<li><math data-latex=\"\\sigma^2 \\sim IG(a, b)\"><semantics><mrow><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mo>\u223c<\/mo><mi>I<\/mi><mi>G<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo separator=\"true\">,<\/mo><mi>b<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma^2 \\sim IG(a, b)<\/annotation><\/semantics><\/math> (\uc5ed\uac10\ub9c8 \ubd84\ud3ec).<\/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\">4. \ubd84\uc11d \uc2e4\ud589: jamovi \ubc0f R (brms)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 jamovi\uc5d0\uc11c\uc758 \ud55c\uacc4\uc640 \ub300\uc548<\/h3>\n\n\n\n<p>jamovi\uc758 \uae30\ubcf8 \uba54\ub274(<code>Linear Models<\/code> -> <code>Mixed Models<\/code>)\ub294 \ube48\ub3c4\uc8fc\uc758 \ubc29\uc2dd(REML \ub4f1)\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4. \ubcf8 \ubb38\ud5cc\uc5d0\uc11c \ub2e4\ub8e8\ub294 <strong>\uc644\uc804 \ubca0\uc774\uc9c0\uc548 \ucd94\ub860(Full Bayesian Inference)<\/strong>, \ud2b9\ud788 MCMC(\ub9c8\ub974\ucf54\ud504 \uccb4\uc778 \ubaac\ud14c\uce74\ub97c\ub85c) \uc2dc\ubbac\ub808\uc774\uc158\uc744 \uc218\ud589\ud558\uae30 \uc704\ud574\uc11c\ub294 jamovi\uc758 <code>Rj<\/code> \ubaa8\ub4c8(R \ucf54\ub4dc\ub97c jamovi \uc548\uc5d0\uc11c \uc2e4\ud589\ud558\ub294 \uc5d0\ub514\ud130)\uc744 \uc0ac\uc6a9\ud558\uac70\ub098 R\uc744 \uc9c1\uc811 \uc0ac\uc6a9\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\ud2b9\ud788 \ubb38\ud5cc\uc5d0\uc11c \uac15\uc870\ud558\ub294 <strong>GAMM(\uc77c\ubc18\ud654 \uac00\ubc95 \ubaa8\ud615)<\/strong>\uacfc <strong>P-spline(\ubc8c\uc810\ud654 \uc2a4\ud50c\ub77c\uc778)<\/strong>\uc744 \uad6c\ud604\ud558\uae30 \uc704\ud574 R\uc758 <code>brms<\/code> \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud558\ub294 \uac83\uc774 \uac00\uc7a5 \uc801\ud569\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 R\uc744 \uc774\uc6a9\ud55c \ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubd84\uc11d (MCMC)<\/h3>\n\n\n\n<p>\ubb38\ud5cc\uc5d0\uc11c\ub294 \ube44\uc120\ud615\uc131\uc744 \ub2e4\ub8e8\uae30 \uc704\ud574 \uacf5\ubcc0\ub7c9\uc758 \ud6a8\uacfc\ub97c <math data-latex=\"f(x)\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(x)<\/annotation><\/semantics><\/math> \ud615\ud0dc\uc758 \ud568\uc218\ub85c \ubaa8\ub378\ub9c1\ud558\ub294 \uac83\uc744 \uc81c\uc548\ud569\ub2c8\ub2e4. \uc774\ub97c <strong>GAMM<\/strong>\uc774\ub77c\uace0 \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><strong>[\ubd84\uc11d \ubaa8\ub378 \uc124\uc815]<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\uae30\ubcf8 \ub2e4\uce35 \ubaa8\ud615:<\/strong> SES\uc640 \uad50\uc0ac \ud6a8\ub2a5\uac10\uc758 \uc120\ud615 \ud6a8\uacfc.<\/li>\n\n\n\n<li><strong>\uc2a4\ud50c\ub77c\uc778 \ud56d:<\/strong> \uc0ac\uad50\uc721 \uc2dc\uac04(<code>Time<\/code>)\uc740 \ube44\uc120\ud615\uc801\uc774\ubbc0\ub85c <code>s(Time)<\/code>\uc73c\ub85c \uc124\uc815.<\/li>\n\n\n\n<li><strong>\ubb34\uc120 \ud6a8\uacfc:<\/strong> \ud559\uae09(<code>class_id<\/code>)\uc5d0 \ub530\ub978 \ubb34\uc120 \uc808\ud3b8.<\/li>\n<\/ol>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615 \uc801\ud569 (GAMM \ud3ec\ud568)\n# \ubb38\ud5cc\uc758 \uc2dd (4.13)\uacfc \uc720\uc0ac\ud55c \ud615\ud0dc &#91;cite: 357]\nmodel_bayes &lt;- brm(\n  formula = Math ~ SES + teacher_eff + s(Time) + (1 | class_id),\n  data = data,\n  family = gaussian(),\n  prior = c(\n    prior(normal(0, 10), class = \"b\"),    # \uace0\uc815 \ud6a8\uacfc\uc5d0 \ub300\ud55c \uc0ac\uc804 \ubd84\ud3ec\n    prior(cauchy(0, 2), class = \"sd\"),    # \ubb34\uc120 \ud6a8\uacfc \ud45c\uc900\ud3b8\ucc28\uc5d0 \ub300\ud55c \uc0ac\uc804 \ubd84\ud3ec\n    prior(cauchy(0, 2), class = \"sigma\")  # \uc794\ucc28 \ud45c\uc900\ud3b8\ucc28\uc5d0 \ub300\ud55c \uc0ac\uc804 \ubd84\ud3ec\n  ),\n  chains = 2, iter = 2000, warmup = 1000, # MCMC \uc124\uc815 &#91;cite: 320]\n  cores = 2,\n  seed = 2026\n)\n\n# \uacb0\uacfc \uc694\uc57d\nsummary(model_bayes)\n<\/code><\/pre>\n\n\n\n<p>\uc774 \ucf54\ub4dc\ub294 \ubb38\ud5cc\uc5d0\uc11c \uc124\uba85\ud55c <strong>Gibbs Sampler<\/strong> \ud639\uc740 <strong>Metropolis-Hastings<\/strong> \uc54c\uace0\ub9ac\uc998\uc758 \ucd5c\uc2e0 \ubcc0\ud615(NUTS)\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc0ac\ud6c4 \ubd84\ud3ec\uc5d0\uc11c \ud45c\ubcf8\uc744 \ucd94\ucd9c\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">5. \uacb0\uacfc \ud574\uc11d \ubc0f \uc2dc\uac01\ud654<\/h2>\n\n\n\n<p>\ubd84\uc11d\uc774 \uc644\ub8cc\ub418\uba74, \ubb38\ud5cc\uc758 [Table 4.1]\uacfc \uac19\uc740 \ud615\ud0dc\ub85c \uacb0\uacfc\ub97c \ud574\uc11d\ud574\uc57c \ud569\ub2c8\ub2e4. \ubca0\uc774\uc9c0\uc548\uc5d0\uc11c\ub294 p-value \ub300\uc2e0 <strong>\uc2e0\uc6a9 \uad6c\uac04(Credible Interval)<\/strong>\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 \uc218\uce58\uc801 \uacb0\uacfc \ud574\uc11d (\uc608\uc2dc \ucd9c\ub825 \uae30\ubc18)<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>\ubcc0\uc218<\/strong><\/td><td><strong>Posterior Mean (\uc0ac\ud6c4\ud3c9\uade0)<\/strong><\/td><td><strong>95% CI (\uc2e0\uc6a9\uad6c\uac04)<\/strong><\/td><td><strong>Rhat<\/strong><\/td><td><strong>\uc124\uba85<\/strong><\/td><\/tr><\/thead><tbody><tr><td>Intercept<\/td><td>50.12<\/td><td>[48.5, 51.7]<\/td><td>1.00<\/td><td>\uc804\uccb4 \ud3c9\uade0 \uc218\ud559 \uc810\uc218<\/td><\/tr><tr><td>SES<\/td><td>2.05<\/td><td>[1.88, 2.22]<\/td><td>1.00<\/td><td>SES\uac00 1\ub2e8\uc704 \uc624\ub97c \ub54c \uc810\uc218 2.05\uc810 \uc0c1\uc2b9<\/td><\/tr><tr><td>TeacherEff<\/td><td>1.48<\/td><td>[1.20, 1.76]<\/td><td>1.00<\/td><td>\uad50\uc0ac \ud6a8\ub2a5\uac10\uc774 \ub192\uc73c\uba74 \uc810\uc218 \uc0c1\uc2b9 (\uc720\uc758\ud568)<\/td><\/tr><tr><td>s(Time)<\/td><td>&#8211;<\/td><td>&#8211;<\/td><td>1.00<\/td><td>\ube44\uc120\ud615 \ud6a8\uacfc (\uc544\ub798 \uadf8\ub798\ud504 \ucc38\uc870)<\/td><\/tr><tr><td>sd(Intercept)<\/td><td>2.10<\/td><td>[1.50, 2.80]<\/td><td>1.00<\/td><td>\ud559\uae09 \uac04 \uc810\uc218 \ucc28\uc774(\ubcc0\ub3d9\uc131)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ud574\uc11d:<\/strong> 95% \uc2e0\uc6a9\uad6c\uac04\uc774 0\uc744 \ud3ec\ud568\ud558\uc9c0 \uc54a\uc73c\uba74, \ud574\ub2f9 \ubcc0\uc218\ub294 \ud1b5\uacc4\uc801\uc73c\ub85c \uc758\ubbf8 \uc788\ub294 \ud6a8\uacfc\uac00 \uc788\ub2e4\uace0 \ubd05\ub2c8\ub2e4. \uc704 \uacb0\uacfc\uc5d0\uc11c SES\uc640 \uad50\uc0ac \ud6a8\ub2a5\uac10 \ubaa8\ub450 0\uc744 \ud3ec\ud568\ud558\uc9c0 \uc54a\uc73c\ubbc0\ub85c \uc720\uc758\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>Rhat:<\/strong> \uc774 \uac12\uc774 1.1\ubcf4\ub2e4 \uc791\uc544\uc57c MCMC \uccb4\uc778\uc774 \uc798 \uc218\ub834\ud588\ub2e4\ub294 \ub73b\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 \ube44\uc120\ud615 \ud6a8\uacfc \uc2dc\uac01\ud654 (P-spline)<\/h3>\n\n\n\n<p>\uc0ac\uad50\uc721 \uc2dc\uac04(<code>Time<\/code>)\uacfc \uc131\uc801\uc758 \ube44\uc120\ud615 \uad00\uacc4\ub97c \uadf8\ub824\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ube44\uc120\ud615 \ud6a8\uacfc \uc2dc\uac01\ud654\nconditional_effects(model_bayes, effects = \"Time\")\n<\/code><\/pre>\n\n\n\n<p><em>\uc774 \ucf54\ub4dc\ub97c \uc2e4\ud589\ud558\uba74 \uc5ed U\uc790 \ud615\ud0dc\uc758 \uadf8\ub798\ud504\uac00 \ub098\ud0c0\ub0a9\ub2c8\ub2e4. \ucd08\uae30\uc5d0\ub294 \uc2dc\uac04\uc774 \ub298\uc218\ub85d \uc810\uc218\uac00 \uc624\ub974\uc9c0\ub9cc, \ud2b9\uc815 \uc2dc\uac04 \uc774\ud6c4\uc5d0\ub294 \uc815\uccb4\ub418\uac70\ub098 \ub5a8\uc5b4\uc9c0\ub294 \ud328\ud134\uc744 \ud655\uc778\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"796\" height=\"789\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1.png\" alt=\"\" class=\"wp-image-728\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1.png 796w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1-300x297.png 300w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1-150x150.png 150w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1-768x761.png 768w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG04-1-624x619.png 624w\" sizes=\"auto, (max-width: 796px) 100vw, 796px\" \/><\/figure>\n\n\n\n<p>\uc774\uac83\uc774 \ubc14\ub85c \ubb38\ud5cc\uc5d0\uc11c \uac15\uc870\ud558\ub294 <strong>&#8220;\uc120\ud615 \uac00\uc815\uc758 \ud55c\uacc4\ub97c \ub118\uc5b4\uc11c\ub294 \uc720\uc5f0\uc131&#8221;<\/strong>\uc785\ub2c8\ub2e4. \ub2e8\uc21c\ud788 \uc120\ud615 \ud68c\uadc0\ub97c \ud588\ub2e4\uba74 \uc774 \uc911\uc694\ud55c \uad50\uc721\uc801 \uc2dc\uc0ac\uc810(\uacfc\ub3c4\ud55c \uc0ac\uad50\uc721\uc740 \ud6a8\uacfc\uac00 \uc5c6\ub2e4)\uc744 \ub193\ucce4\uc744 \uac83\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">6. \ubaa8\ud615 \ube44\uad50 \ubc0f \ud3c9\uac00 (DIC)<\/h2>\n\n\n\n<p>\ubaa8\ud615\uc774 \ub370\uc774\ud130\uc5d0 \uc798 \ub9de\ub294\uc9c0 \uc5b4\ub5bb\uac8c \uc54c\uae4c\uc694? \ubb38\ud5cc\uc5d0\uc11c\ub294 <strong>DIC (Deviance Information Criterion)<\/strong>\ub97c \uc18c\uac1c\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>DIC:<\/strong> \ub0ae\uc744\uc218\ub85d \uc88b\uc740 \ubaa8\ud615\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ube44\uad50:<\/strong> \ubb34\uc120 \ud6a8\uacfc\uac00 \uc5c6\ub294 \ubaa8\ud615 vs \uc788\ub294 \ubaa8\ud615, \ud639\uc740 \uc120\ud615 \ubaa8\ud615 vs \ube44\uc120\ud615(Spline) \ubaa8\ud615\uc744 \ube44\uad50\ud560 \ub54c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># DIC \uacc4\uc0b0 (brms\uc5d0\uc11c\ub294 waic\ub098 loo\ub97c \ub354 \uad8c\uc7a5\ud558\uc9c0\ub9cc, \ubb38\ud5cc\uc5d0 \ub530\ub77c DIC \uac1c\ub150 \uc124\uba85)\n# \uc5ec\uae30\uc11c\ub294 LOO (Leave-One-Out cross-validation)\ub85c \ub300\uccb4\ud558\uc5ec \ubcf4\uc5ec\uc90c (DIC\uc758 \ud604\ub300\uc801 \ub300\uc548)\nloo(model_bayes)\n<\/code><\/pre>\n\n\n\n<p>\ubb38\ud5cc\uc758 \uc0ac\ub840\uc5f0\uad6c\uc5d0\uc11c\ub3c4 \ubb34\uc120 \ud6a8\uacfc\ub97c \ud3ec\ud568\ud588\uc744 \ub54c DIC\uac00 140\uc810 \uc774\uc0c1 \uac10\uc18c\ud558\uc5ec \ub354 \uc6b0\uc218\ud55c \ubaa8\ud615\uc784\uc774 \uc785\uc99d\ub418\uc5c8\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">7. \uc2ec\ud654: \uacf5\uac04 \ud1b5\uacc4 \ubc0f \uad6c\uc870\uc801 \uac00\ubc95 \ud68c\uadc0 (STAR)<\/h2>\n\n\n\n<p>\uc774 \ubb38\ud5cc\uc758 \ud2b9\uc9d5\uc801\uc778 \ubd80\ubd84\uc740 STAR (Structured Additive Regression) \ubaa8\ub378\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\ub9cc\uc57d \uc6b0\ub9ac \ub370\uc774\ud130\uc5d0 &#8220;\ud559\uad50\uc758 \uc704\uce58(\uc704\ub3c4, \uacbd\ub3c4)&#8221; \uc815\ubcf4\uac00 \uc788\ub2e4\uba74 \uc5b4\ub5bb\uac8c \ub420\uae4c\uc694?<\/p>\n\n\n\n<p><math data-latex=\"\\eta = X\\beta + Z_{groups}u_{groups} + f_{geo}(s)\"><semantics><mrow><mi>\u03b7<\/mi><mo>=<\/mo><mi>X<\/mi><mi>\u03b2<\/mi><mo>+<\/mo><msub><mi>Z<\/mi><mrow><mi>g<\/mi><mi>r<\/mi><mi>o<\/mi><mi>u<\/mi><mi>p<\/mi><mi>s<\/mi><\/mrow><\/msub><msub><mi>u<\/mi><mrow><mi>g<\/mi><mi>r<\/mi><mi>o<\/mi><mi>u<\/mi><mi>p<\/mi><mi>s<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>f<\/mi><mrow><mi>g<\/mi><mi>e<\/mi><mi>o<\/mi><\/mrow><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\eta = X\\beta + Z_{groups}u_{groups} + f_{geo}(s)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"f_{geo}(s)\"><semantics><mrow><msub><mi>f<\/mi><mrow><mi>g<\/mi><mi>e<\/mi><mi>o<\/mi><\/mrow><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f_{geo}(s)<\/annotation><\/semantics><\/math>: \uacf5\uac04\uc801 \ud6a8\uacfc. \ubd80\uc720\ud55c \uc9c0\uc5ed\uc5d0 \uc788\ub294 \ud559\uad50\uc778\uc9c0 \ub4f1\uc744 \uacf5\uac04 \uc88c\ud45c\ub85c \ubc18\uc601\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li>R\uc758 <code>brms<\/code>\uc5d0\uc11c\ub294 <code>gp(latitude, longitude)<\/code> \ud568\uc218\ub97c \ud1b5\ud574 \uc774\ub97c \uc27d\uac8c \uad6c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub294 \uc9c0\ub9ac\uc801 \uc704\uce58\uc5d0 \ub530\ub978 \uc131\uc801 \ucc28\uc774\ub97c \uc9c0\ub3c4 \uc704\uc5d0 \ub4f1\uace0\uc120\ucc98\ub7fc \uadf8\ub824\ub0bc \uc218 \uc788\uac8c \ud574 \uc90d\ub2c8\ub2e4.<\/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\">8. \uacb0\ub860 \ubc0f \uc81c\uc5b8<\/h2>\n\n\n\n<p>\uc624\ub298 \uc6b0\ub9ac\ub294 \uc219\uba85\ucd08\ub4f1\ud559\uad50 \ub370\uc774\ud130\ub97c \uc608\uc2dc\ub85c <strong>\ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615<\/strong>\uc744 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\uc720\uc5f0\uc131:<\/strong> \ubca0\uc774\uc9c0\uc548 \uc811\uadfc\uc740 \uc815\uaddc\ubd84\ud3ec \uac00\uc815\uc774 \uae68\uc9c0\uac70\ub098, \ube44\uc120\ud615 \uad00\uacc4(P-spline)\uac00 \uc788\uc744 \ub54c \ud6e8\uc52c \uc720\uc5f0\ud558\uac8c \ub300\ucc98\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc9c1\uad00\uc131:<\/strong> \uc2e0\uc6a9\uad6c\uac04(Credible Interval)\uc740 &#8220;\ucc38\uac12\uc774 \uc774 \uad6c\uac04 \uc548\uc5d0 \uc788\uc744 \ud655\ub960\uc774 95%&#8221;\ub77c\uace0 \uc9c1\uad00\uc801\uc73c\ub85c \ub9d0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ud655\uc7a5\uc131:<\/strong> \uacf5\uac04 \uc815\ubcf4, \ud14d\uc2a4\ud2b8 \ub370\uc774\ud130 \ub4f1 \ubcf5\uc7a1\ud55c \uad6c\uc870\uc758 \ub370\uc774\ud130\ub97c \ub2e4\uce35 \ubaa8\ud615\uc5d0 \uc27d\uac8c \uacb0\ud569\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4(STAR \ubaa8\ub378).<\/li>\n<\/ol>\n\n\n\n<p><strong>[<em>WaurimaL\uc758 \ud55c\ub9c8\ub514<\/em>]<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>&#8220;\ube48\ub3c4\uc8fc\uc758 \ud1b5\uacc4\uac00 &#8216;\uc5c4\uaca9\ud55c \uc694\ub9ac\ubc95&#8217;\uc774\ub77c\uba74, \ubca0\uc774\uc9c0\uc548\uc740 &#8216;\ub9db\uc744 \ubcf4\uba70 \uac04\uc744 \ub9de\ucd94\ub294 \uacfc\uc815&#8217;\uc785\ub2c8\ub2e4. \uad50\uc721 \ud604\uc7a5\uc758 \ub370\uc774\ud130\ub294 \ubcf5\uc7a1\ud558\uace0 \ube44\uc120\ud615\uc801\uc785\ub2c8\ub2e4. \uc624\ub298 \ubc30\uc6b4 \ucf54\ub4dc\ub97c \ud65c\uc6a9\ud574 \uc5ec\ub7ec\ubd84\uc758 \ub370\uc774\ud130\ub97c \uc0c8\ub85c\uc6b4 \uc2dc\uac01\uc73c\ub85c \ubd84\uc11d\ud574 \ubcf4\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.&#8221;<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ucc38\uace0\ubb38\ud5cc (References)<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fahrmeir, L., Kneib, T., &amp; Lang, S. (2014). Bayesian Multilevel Models. In <em>The SAGE Handbook of Multilevel Modeling<\/em> (pp. 53-71). SAGE Publications.<\/li>\n\n\n\n<li>Brezger, A., &amp; Lang, S. (2006). Generalized additive regression based on Bayesian P-splines. <em>Computational Statistics &amp; Data Analysis, 50<\/em>(4), 967-991.<\/li>\n\n\n\n<li>Gelman, A., Carlin, J. B., Stern, H. S., &amp; Rubin, D. B. (2003). <em>Bayesian Data Analysis<\/em>. Chapman and Hall\/CRC.<\/li>\n\n\n\n<li>Spiegelhalter, D. J., Best, N. G., Carlin, B. P., &amp; van der Linde, A. (2002). Bayesian measures of model complexity and fit. <em>Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64<\/em>(4), 583-639.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \ubca0\uc774\uc9c0\uc548 \ub2e4\uce35 \ubaa8\ud615(Bayesian Multilevel Models)\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \u201c\ud559\uad50 \ud604\uc7a5\uc758 \ub370\uc774\ud130\u201d\ub97c \uc608\uc2dc\ub85c \ub4e4\uc5b4 \uc9c1\uad00\uc801\uc778 \uc124\uba85\uacfc \uc218\ub9ac\uc801 \uc5c4\ubc00\ud568\uc744 \ubaa8\ub450 \uac16\ucd98 \ud615\ud0dc\ub85c \uc7ac\uad6c\uc131\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \ubd84\uc11d \ub3c4\uad6c\ub85c\ub294 jamovi\uc758 \uc0ac\uc6a9\ubc95\uc744 \uc124\uba85\ud558\ub418, jamovi\uc758 \uae30\ubc18\uc774 \ub418\ub294 R \ucf54\ub4dc\ub97c \ud568\uaed8 \uc81c\uc2dc\ud558\uc5ec \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131\ubd80\ud130 \ubd84\uc11d, \uc2dc\uac01\ud654\uae4c\uc9c0 \uc644\ubcbd\ud558\uac8c \uad6c\ud604\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \ud2b9\ud788 \uc624\ub298 \ub2e4\ub8f0 \ubb38\ud5cc\uc740 \uc77c\ubc18\uc801\uc778 \ub2e4\uce35\ubaa8\ud615\uc744 \ub118\uc5b4, \ube44\uc120\ud615 \uad00\uacc4\ub97c \ub2e4\ub8e8\ub294 GAMM(\uc77c\ubc18\ud654 \uac00\ubc95 <a class=\"read-more\" href=\"http:\/\/waurimal.kr\/?p=726\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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":[399],"tags":[407,145,408,199,393,371,400,391,406],"class_list":["post-726","post","type-post","status-publish","format-standard","hentry","category-multilevel","tag-brms","tag-jamovi","tag-mcmc","tag-r","tag-stan","tag-371","tag-400","tag-391","tag-406"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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