{"id":714,"date":"2026-01-18T01:09:42","date_gmt":"2026-01-17T16:09:42","guid":{"rendered":"http:\/\/waurimal.kr\/?p=714"},"modified":"2026-01-18T16:43:50","modified_gmt":"2026-01-18T07:43:50","slug":"%eb%8b%a4%ec%b8%b5%eb%aa%a8%ed%98%95%ec%9d%98-%ed%91%9c%ea%b8%b0%eb%b2%95%ea%b3%bc-%eb%b6%84%ec%84%9dmultilevel-model-notation-and-analysis","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=714","title":{"rendered":"Chap02. \ub2e4\uce35\ubaa8\ud615\uc758 \ud45c\uae30\ubc95\uacfc \ubd84\uc11d(Multilevel Model Notation and Analysis)"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc138\uc694!<\/p>\n\n\n\n<p>\uc624\ub298\uc740 <strong>&#8220;\ub2e4\uce35\ubaa8\ud615\uc758 \ud45c\uae30\ubc95\uacfc \ubd84\uc11d(Multilevel Model Notation and Analysis)&#8221;<\/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 \ucf54\ub4dc<\/strong>\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.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. \ub4e4\uc5b4\uac00\uba70: \ub2e4\uce35\ubaa8\ud615, \ub3c4\ub300\uccb4 \uc65c \ud45c\uae30\ubc95\uc774 \uc911\uc694\ud55c\uac00?<\/h2>\n\n\n\n<p>\ub2e4\uce35\ubaa8\ud615(Multilevel Models, MLM)\uc740 \uad50\uc721\ud559, \uc0dd\ubb3c\ud559, \uc0ac\ud68c\ud559 \ub4f1 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ud65c\uc6a9\ub429\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \uad50\uc7ac\ub9c8\ub2e4, \uc18c\ud504\ud2b8\uc6e8\uc5b4\ub9c8\ub2e4 \uc218\uc2dd\uc744 \uc4f0\ub294 \ubc29\uc2dd\uc774 \ub2ec\ub77c\uc11c \ud559\uc0dd\ub4e4\uc774 \ucc98\uc74c \uc811\ud560 \ub54c \ud070 \ud63c\ub780\uc744 \uacaa\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc5b4\ub5a4 \ucc45\uc740 \ud68c\uadc0\ubd84\uc11d \uc2dd\uc744 \ud558\ub098\ub85c \uae38\uac8c \uc4f0\uace0(\ubcf5\ud569 \ud45c\uae30\ubc95), \uc5b4\ub5a4 \ucc45\uc740 1\uc218\uc900 \uc2dd\uacfc 2\uc218\uc900 \uc2dd\uc744 \ub530\ub85c \uc501\ub2c8\ub2e4(\uc704\uacc4\uc801 \ud45c\uae30\ubc95). \ud558\uc9c0\ub9cc \uac71\uc815\ud558\uc9c0 \ub9c8\uc138\uc694. \uc774\ub4e4\uc740 \uacb0\uad6d <strong>\uac19\uc740 \uac1c\ub150\uc744 \ub2e4\ub978 \uadf8\ub987\uc5d0 \ub2f4\uc740 \uac83<\/strong>\uc77c \ubfd0\uc785\ub2c8\ub2e4. \uc624\ub298 \uc6b0\ub9ac\ub294 \uac00\uc0c1\uc758 \ucd08\ub4f1\ud559\uad50 \ub370\uc774\ud130\ub97c \ud1b5\ud574 \uc774 \ud45c\uae30\ubc95\ub4e4\uc774 \uc2e4\uc81c \ubd84\uc11d\uc5d0\uc11c \uc5b4\ub5bb\uac8c \uc5f0\uacb0\ub418\ub294\uc9c0 \uc544\uc8fc \uc27d\uac8c \ud30c\ud5e4\uccd0 \ubcf4\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\">2. \ubd84\uc11d \uc2dc\ub098\ub9ac\uc624: \ud589\ubcf5\ucd08\ub4f1\ud559\uad50\uc758 \uc218\ud559 \uc131\ucde8\ub3c4<\/h2>\n\n\n\n<p>\uc6b0\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uad50\uc721\uc801 \uac00\uc124\uc744 \uac80\uc99d\ud558\uace0\uc790 \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc5f0\uad6c \ubb38\uc81c:<\/strong> \ud559\uc0dd\uc758 <strong>\uc218\ud559 \ubd88\uc548(Math Anxiety)<\/strong>\uc740 <strong>\uc218\ud559 \uc131\ucde8\ub3c4(Math Achievement)<\/strong>\uc5d0 \ubd80\uc815\uc801\uc778 \uc601\ud5a5\uc744 \ubbf8\uce58\ub294\uac00? \uadf8\ub9ac\uace0 \uc774 \uad00\uacc4\ub294 \ud559\uad50\uc758 <strong>\uad50\uc0ac \uc9c0\uc9c0(Teacher Support)<\/strong> \ubd84\uc704\uae30\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c0\ub294\uac00?<\/li>\n\n\n\n<li><strong>\ub370\uc774\ud130 \uad6c\uc870:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>1\uc218\uc900 (\ud559\uc0dd, <\/strong><math data-latex=\"i\"><semantics><mi>i<\/mi><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math><strong>):<\/strong> 50\uac1c \ud559\uad50, \ucd1d 1,000\uba85\uc758 \ud559\uc0dd.<\/li>\n\n\n\n<li><strong>2\uc218\uc900 (\ud559\uad50, <\/strong><math data-latex=\"j\"><semantics><mi>j<\/mi><annotation encoding=\"application\/x-tex\">j<\/annotation><\/semantics><\/math><strong>):<\/strong> \uac01 \ud559\uad50\uc758 \uad50\uc0ac \uc9c0\uc9c0 \uc810\uc218.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\ubcc0\uc218:<\/strong>\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"Y_{ij}\"><semantics><msub><mi>Y<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">Y_{ij}<\/annotation><\/semantics><\/math>: \uc218\ud559 \uc131\ucde8\ub3c4 (\uc885\uc18d\ubcc0\uc218)<\/li>\n\n\n\n<li><math data-latex=\"X_{ij}\"><semantics><msub><mi>X<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">X_{ij}<\/annotation><\/semantics><\/math>: \uc218\ud559 \ubd88\uc548 (1\uc218\uc900 \ub3c5\ub9bd\ubcc0\uc218, <math data-latex=\"Anxiety\"><semantics><mrow><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mi>i<\/mi><mi>e<\/mi><mi>t<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Anxiety<\/annotation><\/semantics><\/math>)<\/li>\n\n\n\n<li><math data-latex=\"W_{j}\"><semantics><msub><mi>W<\/mi><mi>j<\/mi><\/msub><annotation encoding=\"application\/x-tex\">W_{j}<\/annotation><\/semantics><\/math>: \uad50\uc0ac \uc9c0\uc9c0 (2\uc218\uc900 \ub3c5\ub9bd\ubcc0\uc218, <math data-latex=\"Support\"><semantics><mrow><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>r<\/mi><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Support<\/annotation><\/semantics><\/math>)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\uc774 \uc2dc\ub098\ub9ac\uc624\ub97c \ubc14\ud0d5\uc73c\ub85c <strong>R<\/strong>\uc744 \uc774\uc6a9\ud574 \uc2e4\uc81c\uc640 \uc720\uc0ac\ud55c \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">[R Code] \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131<\/h3>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud544\uc694\ud55c \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nlibrary(MASS)\nlibrary(lme4)\nlibrary(tidyverse)\n\nset.seed(2026)\n\n# 1. \ud30c\ub77c\ubbf8\ud130 \uc124\uc815\nJ &lt;- 50          # \ud559\uad50 \uc218\nN_per_J &lt;- 20    # \ud559\uad50\ub2f9 \ud559\uc0dd \uc218 (\ucd1d 1000\uba85)\ngamma_00 &lt;- 50   # \uc804\uccb4 \ud3c9\uade0 \uc131\ucde8\ub3c4\ngamma_10 &lt;- -5   # \uc218\ud559 \ubd88\uc548\uc758 \uc8fc\ud6a8\uacfc (\ubd88\uc548 \ub192\uc73c\uba74 \uc131\uc801 \ud558\ub77d)\ngamma_01 &lt;- 10   # \uad50\uc0ac \uc9c0\uc9c0\uc758 \uc8fc\ud6a8\uacfc (\uc9c0\uc9c0 \ub192\uc73c\uba74 \uc131\uc801 \uc0c1\uc2b9)\ngamma_11 &lt;- 3    # \uc0c1\ud638\uc791\uc6a9 \ud6a8\uacfc (\uad50\uc0ac \uc9c0\uc9c0\uac00 \ub192\uc73c\uba74 \ubd88\uc548\uc758 \ubd80\uc815\uc801 \ud6a8\uacfc \uc644\ud654)\n\ntau_0 &lt;- 15      # \uc808\ud3b8\uc758 \ud559\uad50 \uac04 \ubd84\uc0b0 (SD)\ntau_1 &lt;- 5       # \uae30\uc6b8\uae30\uc758 \ud559\uad50 \uac04 \ubd84\uc0b0 (SD)\nsigma &lt;- 10      # \ud559\uc0dd \uac1c\uc778 \uc624\ucc28 (SD)\n\n# 2. \ub370\uc774\ud130 \uc0dd\uc131\nschools &lt;- data.frame(school_id = 1:J, \n                      support = rnorm(J, 0, 1)) # \uad50\uc0ac \uc9c0\uc9c0 (\ud45c\uc900\ud654 \uc810\uc218)\n\n# \ud559\uad50\ubcc4 \ub79c\ub364 \ud6a8\uacfc (\uc808\ud3b8 u0, \uae30\uc6b8\uae30 u1) \uc0dd\uc131 (\uc0c1\uad00\uad00\uacc4 0.3 \uac00\uc815)\ncov_matrix &lt;- matrix(c(tau_0^2, 0.3*tau_0*tau_1, \n                       0.3*tau_0*tau_1, tau_1^2), 2, 2)\nrandom_effects &lt;- mvrnorm(J, mu = c(0, 0), Sigma = cov_matrix)\nschools$u0j &lt;- random_effects&#91;,1]\nschools$u1j &lt;- random_effects&#91;,2]\n\n# \ud559\uc0dd \ub370\uc774\ud130 \uc0dd\uc131 \ubc0f \ubcd1\ud569\ndata &lt;- expand.grid(student_id = 1:N_per_J, school_id = 1:J) %>%\n  left_join(schools, by = \"school_id\") %>%\n  mutate(\n    anxiety = rnorm(n(), 0, 1), # \uc218\ud559 \ubd88\uc548 (\ud45c\uc900\ud654 \uc810\uc218)\n    e_ij = rnorm(n(), 0, sigma), # \uac1c\uc778 \uc624\ucc28\n    # \ub2e4\uce35\ubaa8\ud615 \uc218\uc2dd \uc801\uc6a9 (\ub370\uc774\ud130 \uc0dd\uc131\uc758 \ud575\uc2ec)\n    math_score = (gamma_00 + u0j + gamma_01 * support) + \n                 (gamma_10 + u1j + gamma_11 * support) * anxiety + e_ij\n  )\n\nhead(data)\n\n# CSV \uc800\uc7a5 (jamovi\uc5d0\uc11c \ubd88\ub7ec\uc624\uae30 \uc704\ud568)\nwrite.csv(data, \"chap02.csv\", row.names = FALSE)<\/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-cf8683d2-d16e-4eaa-9347-08cd727b9bcb\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap02.csv\">chap02<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap02.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-cf8683d2-d16e-4eaa-9347-08cd727b9bcb\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">3. \ub2e4\uce35\ubaa8\ud615\uc758 \ud45c\uae30\ubc95 \uc644\uc804 \uc815\ubcf5<\/h2>\n\n\n\n<p>\uc774 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud558\uae30 \uc704\ud574 \ubaa8\ud615\uc744 \uc138\uc6b8 \ub54c, \ud06c\uac8c \ub450 \uac00\uc9c0 \ubc29\uc2dd\uc774 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1. \uc704\uacc4\uc801 \ud45c\uae30\ubc95 (Hierarchical\/Level Notation)<\/h3>\n\n\n\n<p>HLM \uc18c\ud504\ud2b8\uc6e8\uc5b4\ub098 WinBUGS \uac19\uc740 \ubca0\uc774\uc9c0\uc548 \ub3c4\uad6c\uc5d0\uc11c \uc8fc\ub85c \uc0ac\uc6a9\ud569\ub2c8\ub2e4. \uc9c1\uad00\uc801\uc73c\ub85c &#8220;\uc218\uc900(Level)&#8221;\uc744 \ub098\ub204\uc5b4 \uc0dd\uac01\ud558\uae30 \uc88b\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\uc218\uc900 (\ud559\uc0dd \uc218\uc900): \ud559\uc0dd \uac1c\uc778\uc758 \uc131\uc801\uc740 \uadf8 \ud559\uad50\uc758 \ud3c9\uade0(<math data-latex=\"\\beta_{0j}\"><semantics><msub><mi>\u03b2<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">\\beta_{0j}<\/annotation><\/semantics><\/math>)\uacfc \ubd88\uc548\uc774 \ubbf8\uce58\ub294 \uc601\ud5a5(<math data-latex=\"\\beta_{1j}\"><semantics><msub><mi>\u03b2<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">\\beta_{1j}<\/annotation><\/semantics><\/math>)\uc5d0 \uc758\ud574 \uacb0\uc815\ub429\ub2c8\ub2e4.<br><math data-latex=\"Y_{ij} = \\beta_{0j} + \\beta_{1j}(Anxiety)_{ij} + \\epsilon_{ij}\"><semantics><mrow><msub><mi>Y<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b2<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mi>i<\/mi><mi>e<\/mi><mi>t<\/mi><mi>y<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_{ij} = \\beta_{0j} + \\beta_{1j}(Anxiety)_{ij} + \\epsilon_{ij}<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li>2\uc218\uc900 (\ud559\uad50 \uc218\uc900): 1\uc218\uc900\uc758 \uacc4\uc218\ub4e4(<math data-latex=\"\\beta\"><semantics><mi>\u03b2<\/mi><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math>)\uc774 \ud559\uad50 \ud2b9\uc131(\uad50\uc0ac \uc9c0\uc9c0)\uc5d0 \ub530\ub77c \uc5b4\ub5bb\uac8c \ubcc0\ud558\ub294\uc9c0 \uc124\uba85\ud569\ub2c8\ub2e4.<br><math data-latex=\"\\beta_{0j} = \\gamma_{00} + \\gamma_{01}(Support)_j + u_{0j}\"><semantics><mrow><msub><mi>\u03b2<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b3<\/mi><mn>00<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>01<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>r<\/mi><mi>t<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>j<\/mi><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{0j} = \\gamma_{00} + \\gamma_{01}(Support)_j + u_{0j}<\/annotation><\/semantics><\/math><br><math data-latex=\"\\beta_{1j} = \\gamma_{10} + \\gamma_{11}(Support)_j + u_{1j}\"><semantics><mrow><msub><mi>\u03b2<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b3<\/mi><mn>10<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>11<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>r<\/mi><mi>t<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>j<\/mi><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{1j} = \\gamma_{10} + \\gamma_{11}(Support)_j + u_{1j}<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>WaurimaL\uc758 \ud301:<\/strong> \uc774 \ud45c\uae30\ubc95\uc758 \uc7a5\uc810\uc740 \uac01 \uc218\uc900\uc5d0\uc11c \uc5b4\ub5a4 \ubcc0\uc218\uac00 \uc601\ud5a5\uc744 \ubbf8\uce58\ub294\uc9c0 \uba85\ud655\ud788 \ubcf4\uc5ec\uc900\ub2e4\ub294 \uc810\uc785\ub2c8\ub2e4. \ud2b9\ud788 &#8220;\ubc30\uacbd \ubcc0\uc218&#8221;\uc640 &#8220;\ud6a8\uacfc&#8221;\ub97c \uad6c\ubd84\ud558\uae30 \uc88b\uc2b5\ub2c8\ub2e4.<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">3.2. \ubcf5\ud569 \ud45c\uae30\ubc95 (Composite Notation)<\/h3>\n\n\n\n<p>SAS(PROC MIXED), SPSS, Stata(xtmixed), R(lmer), jamovi \ub4f1\uc774 \ucc44\ud0dd\ud55c \ubc29\uc2dd\uc785\ub2c8\ub2e4. \uc704\uacc4\uc801 \ud45c\uae30\ubc95\uc758 \uc2dd\uc744 \ub300\uc785\ud558\uc5ec \ud558\ub098\ub85c \ud569\uce5c \uac83\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"Y_{ij} = [\\gamma_{00} + \\gamma_{01}(Support)_j + \\gamma_{10}(Anxiety)_{ij} + \\gamma_{11}(Support \\times Anxiety)_{ij}] + [u_{0j} + u_{1j}(Anxiety)_{ij} + \\epsilon_{ij}]\"><semantics><mrow><msub><mi>Y<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><mo form=\"prefix\" stretchy=\"false\">[<\/mo><msub><mi>\u03b3<\/mi><mn>00<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>01<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>r<\/mi><mi>t<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>j<\/mi><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>10<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mi>i<\/mi><mi>e<\/mi><mi>t<\/mi><mi>y<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>11<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>r<\/mi><mi>t<\/mi><mo>\u00d7<\/mo><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mi>i<\/mi><mi>e<\/mi><mi>t<\/mi><mi>y<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">[<\/mo><msub><mi>u<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mi>i<\/mi><mi>e<\/mi><mi>t<\/mi><mi>y<\/mi><msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Y_{ij} = [\\gamma_{00} + \\gamma_{01}(Support)_j + \\gamma_{10}(Anxiety)_{ij} + \\gamma_{11}(Support \\times Anxiety)_{ij}] + [u_{0j} + u_{1j}(Anxiety)_{ij} + \\epsilon_{ij}]<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uace0\uc815 \ud6a8\uacfc(Fixed Effects):<\/strong> \uc55e\uc758 \ub300\uad04\ud638 \ubd80\ubd84. \uc804\uccb4 \ud3c9\uade0\uc801\uc778 \ud6a8\uacfc\ub97c \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ub79c\ub364 \ud6a8\uacfc(Random Effects):<\/strong> \ub4a4\uc758 \ub300\uad04\ud638 \ubd80\ubd84. \ud559\uad50\ub9c8\ub2e4, \ud559\uc0dd\ub9c8\ub2e4 \ub2ec\ub77c\uc9c0\ub294 \uc624\ucc28(\ubcc0\ub3d9)\ub97c \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>WauriamL\uc758 \ud301:<\/strong> jamovi\ub098 R\uc744 \uc0ac\uc6a9\ud560 \ub54c\ub294 \uc774 \ubcf5\ud569 \ud45c\uae30\ubc95\uc758 \ub17c\ub9ac\ub97c \uc774\ud574\ud574\uc57c &#8220;\uc5b4\ub5a4 \ubcc0\uc218\ub97c Fixed\uc5d0 \ub123\uace0, \uc5b4\ub5a4 \ubcc0\uc218\ub97c Random\uc5d0 \ub123\uc744\uc9c0&#8221; \uacb0\uc815\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/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\">4. \ub2e8\uacc4\ubcc4 \ubd84\uc11d \ubc0f jamovi\/R \uc2e4\uc2b5<\/h2>\n\n\n\n<p>\ubd84\uc11d\uc740 \ubcf4\ud1b5 <strong>\ubb34\uc870\uac74 \ubaa8\ud615(\uae30\ucd08) <\/strong><math data-latex=\"\\to\"><semantics><mo lspace=\"0em\" rspace=\"0em\">\u2192<\/mo><annotation encoding=\"application\/x-tex\">\\to<\/annotation><\/semantics><\/math><strong> \ub79c\ub364 \uc808\ud3b8 \ubaa8\ud615 <\/strong><math data-latex=\"\\to\"><semantics><mo lspace=\"0em\" rspace=\"0em\">\u2192<\/mo><annotation encoding=\"application\/x-tex\">\\to<\/annotation><\/semantics><\/math><strong> \ub79c\ub364 \uae30\uc6b8\uae30 \ubc0f \uc0c1\ud638\uc791\uc6a9 \ubaa8\ud615<\/strong> \uc21c\uc11c\ub85c \uc9c4\ud589\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ub2e8\uacc4 1: \ubb34\uc870\uac74 \ud3c9\uade0 \ubaa8\ud615 (Unconditional Means Model)<\/h3>\n\n\n\n<p>\uc544\ubb34\ub7f0 \uc124\uba85 \ubcc0\uc218 \uc5c6\uc774, \uc131\uc801\uc758 \ubcc0\ub3d9\uc774 &#8220;\ud559\uad50 \uac04 \ucc28\uc774&#8221; \ub54c\ubb38\uc778\uc9c0 &#8220;\ud559\uc0dd \uac04 \ucc28\uc774&#8221; \ub54c\ubb38\uc778\uc9c0\ub9cc \ubd05\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>jamovi \uc2e4\uc2b5:<\/strong>\n<ol start=\"1\" class=\"wp-block-list\">\n<li><code>Analyses<\/code> > <code>Linear Models<\/code> > <code>Mixed Model<\/code> \uc120\ud0dd<\/li>\n\n\n\n<li>Dependent Variable: <code>math_score<\/code><\/li>\n\n\n\n<li>Cluster Variable: <code>school_id<\/code><\/li>\n\n\n\n<li>Random Effects: <code>Intercept | school_id<\/code> \uccb4\ud06c (\uae30\ubcf8\uac12)<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>R Code:<\/strong> <\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>R<code>model1 &lt;- lmer(math_score ~ 1 + (1 | school_id), data = data)<\/code>summary(model1)<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ud574\uc11d:<\/strong> \uacb0\uacfc\uc5d0\uc11c \uae09\ub0b4\uc0c1\uad00\uacc4\uc218(ICC)\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4. <br><math data-latex=\"\\rho = \\frac{\\sigma_{u0}^2}{\\sigma_{u0}^2 + \\sigma_{\\epsilon}^2}\"><semantics><mrow><mi>\u03c1<\/mi><mo>=<\/mo><mfrac><msubsup><mi>\u03c3<\/mi><mrow><mi>u<\/mi><mn>0<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>u<\/mi><mn>0<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>\u03c3<\/mi><mi>\u03f5<\/mi><mn>2<\/mn><\/msubsup><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\rho = \\frac{\\sigma_{u0}^2}{\\sigma_{u0}^2 + \\sigma_{\\epsilon}^2}<\/annotation><\/semantics><\/math>. \ub9cc\uc57d ICC\uac00 0.2(20%)\ub77c\uba74 \uc131\uc801 \ucc28\uc774\uc758 20%\ub294 \ud559\uad50 \ucc28\uc774\ub85c \uc124\uba85\ub41c\ub2e4\ub294 \ub73b\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ub2e8\uacc4 2: \ub79c\ub364 \uc808\ud3b8 \ubaa8\ud615 (Random Intercept Model)<\/h3>\n\n\n\n<p>\ud559\uc0dd \uc218\uc900\uc758 &#8216;\uc218\ud559 \ubd88\uc548&#8217;\uacfc \ud559\uad50 \uc218\uc900\uc758 &#8216;\uad50\uc0ac \uc9c0\uc9c0&#8217;\ub97c \ud22c\uc785\ud569\ub2c8\ub2e4. \ub2e8, \uc218\ud559 \ubd88\uc548\uc758 \ud6a8\uacfc(\uae30\uc6b8\uae30)\ub294 \ubaa8\ub4e0 \ud559\uad50\uc5d0\uc11c \ub3d9\uc77c\ud558\ub2e4\uace0 \uac00\uc815\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ud45c\uae30\ubc95\uc801 \uc758\ubbf8:<\/strong> \uc704\uacc4\uc801 \ud45c\uae30\ubc95\uc5d0\uc11c <math data-latex=\"\\beta_{1j} = \\gamma_{10}\"><semantics><mrow><msub><mi>\u03b2<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b3<\/mi><mn>10<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{1j} = \\gamma_{10}<\/annotation><\/semantics><\/math>\uc73c\ub85c \ub450\uc5b4 \ud559\uad50\ubcc4 \ucc28\uc774(<math data-latex=\"u_{1j}\"><semantics><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">u_{1j}<\/annotation><\/semantics><\/math>)\ub97c \uc5c6\uc564 \uac83\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>jamovi \uc2e4\uc2b5:<\/strong>\n<ol start=\"1\" class=\"wp-block-list\">\n<li>Covariates\uc5d0 <code>anxiety<\/code>, <code>support<\/code> \ucd94\uac00.<\/li>\n\n\n\n<li>Fixed Effects\uc5d0 <code>anxiety<\/code>, <code>support<\/code> \uc774\ub3d9.<\/li>\n\n\n\n<li>Random Effects\uc5d0\ub294 \uc5ec\uc804\ud788 <code>Intercept | school_id<\/code>\ub9cc \uc874\uc7ac.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\ubcc0\ub3d9\uc758 \uc124\uba85(Targeting Variance):<\/strong> &#8216;\uad50\uc0ac \uc9c0\uc9c0&#8217;\ub294 \ud559\uad50 \uc218\uc900 \ubcc0\uc218\uc774\ubbc0\ub85c \ud559\uad50 \uac04 \ubd84\uc0b0(<math data-latex=\"\\sigma_{u0}^2\"><semantics><msubsup><mi>\u03c3<\/mi><mrow><mi>u<\/mi><mn>0<\/mn><\/mrow><mn>2<\/mn><\/msubsup><annotation encoding=\"application\/x-tex\">\\sigma_{u0}^2<\/annotation><\/semantics><\/math>)\uc744 \uc904\uc774\uace0, &#8216;\uc218\ud559 \ubd88\uc548&#8217;\uc740 \ud559\uc0dd \uc218\uc900 \ubcc0\uc218\uc774\ubbc0\ub85c \uc794\ucc28 \ubd84\uc0b0(<math data-latex=\"\\sigma_{\\epsilon}^2\"><semantics><msubsup><mi>\u03c3<\/mi><mi>\u03f5<\/mi><mn>2<\/mn><\/msubsup><annotation encoding=\"application\/x-tex\">\\sigma_{\\epsilon}^2<\/annotation><\/semantics><\/math>)\uc744 \uc904\uc77c \uac83\uc73c\ub85c \uae30\ub300\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ub2e8\uacc4 3: \ub79c\ub364 \uae30\uc6b8\uae30 \ubc0f \uce35\uc704 \uac04 \uc0c1\ud638\uc791\uc6a9 \ubaa8\ud615 (Full Model)<\/h3>\n\n\n\n<p>\uc774\uc81c &#8220;\ud559\uad50\ub9c8\ub2e4 \uc218\ud559 \ubd88\uc548\uc758 \uc601\ud5a5\ub825\uc774 \ub2e4\ub97c \uc218 \uc788\ub2e4(<math data-latex=\"u_{1j}\"><semantics><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">u_{1j}<\/annotation><\/semantics><\/math>)&#8221;\ub294 \uac00\uc815\uacfc, &#8220;\uad50\uc0ac \uc9c0\uc9c0\uac00 \uadf8 \ucc28\uc774\ub97c \uc124\uba85\ud55c\ub2e4(\uc0c1\ud638\uc791\uc6a9)&#8221;\ub294 \uac00\uc124\uc744 \uac80\uc99d\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc218\uc2dd:<br><math data-latex=\"Y_{ij} = \\gamma_{00} + \\gamma_{01}Sup + \\gamma_{10}Anx + \\gamma_{11}(Sup \\times Anx) + u_{0j} + u_{1j}Anx + \\epsilon_{ij}\"><semantics><mrow><msub><mi>Y<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>\u03b3<\/mi><mn>00<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>01<\/mn><\/msub><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>10<\/mn><\/msub><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mo>+<\/mo><msub><mi>\u03b3<\/mi><mn>11<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>S<\/mi><mi>u<\/mi><mi>p<\/mi><mo>\u00d7<\/mo><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>u<\/mi><mrow><mn>0<\/mn><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><mi>A<\/mi><mi>n<\/mi><mi>x<\/mi><mo>+<\/mo><msub><mi>\u03f5<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_{ij} = \\gamma_{00} + \\gamma_{01}Sup + \\gamma_{10}Anx + \\gamma_{11}(Sup \\times Anx) + u_{0j} + u_{1j}Anx + \\epsilon_{ij}<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>jamovi \uc2e4\uc2b5:<\/strong>\n<ol start=\"1\" class=\"wp-block-list\">\n<li>Fixed Effects: <code>anxiety<\/code>, <code>support<\/code>, \uadf8\ub9ac\uace0 <code>anxiety * support<\/code> \uc0c1\ud638\uc791\uc6a9\ud56d \ucd94\uac00.<\/li>\n\n\n\n<li>Random Effects: <code>anxiety<\/code>\ub97c <code>school_id<\/code> \uc544\ub798\ub85c \uc774\ub3d9\uc2dc\ucf1c <strong>Random Slope<\/strong> \uc124\uc815. (\uc989, <math data-latex=\"u_{1j}\"><semantics><msub><mi>u<\/mi><mrow><mn>1<\/mn><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">u_{1j}<\/annotation><\/semantics><\/math> \ucd94\uac00).<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>R Code:<\/strong><\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>R<code>model3 &lt;- lmer(math_score ~ anxiety * support + (1 + anxiety | school_id), data = data) summary(model3)<\/code><\/code><\/pre>\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\uc758 \ud574\uc11d\uacfc \uc2dc\uac01\ud654<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">5.1. \uc8fc\uc694 \uacb0\uacfc \ud574\uc11d <\/h3>\n\n\n\n<p>\ubd84\uc11d \uacb0\uacfc\ud45c\ub97c \ubcfc \ub54c \uac00\uc7a5 \uc911\uc694\ud55c \uac83\uc740 <strong>\uace0\uc815 \ud6a8\uacfc\uc758 \uc720\uc758\uc131<\/strong>\uacfc <strong>\ub79c\ub364 \ud6a8\uacfc\uc758 \ubd84\uc0b0 \uc131\ubd84<\/strong>\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\uace0\uc815 \ud6a8\uacfc (Fixed Effects):<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Intercept (<\/strong><math data-latex=\"\\gamma_{00}\"><semantics><msub><mi>\u03b3<\/mi><mn>00<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\gamma_{00}<\/annotation><\/semantics><\/math><strong>):<\/strong> \ud3c9\uade0\uc801\uc778 \uc218\ud559 \uc131\ucde8\ub3c4<\/li>\n\n\n\n<li><strong>Support (<\/strong><math data-latex=\"\\gamma_{01}\"><semantics><msub><mi>\u03b3<\/mi><mn>01<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\gamma_{01}<\/annotation><\/semantics><\/math><strong>):<\/strong> \uad50\uc0ac \uc9c0\uc9c0\uac00 \ub192\uc744\uc218\ub85d \uc131\ucde8\ub3c4\uac00 \ub192\uc544\uc9c0\ub294\uac00? (\uc8fc\ud6a8\uacfc)<\/li>\n\n\n\n<li><strong>Anxiety (<\/strong><math data-latex=\"\\gamma_{10}\"><semantics><msub><mi>\u03b3<\/mi><mn>10<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\gamma_{10}<\/annotation><\/semantics><\/math><strong>):<\/strong> \ubd88\uc548\uc774 \ub192\uc744\uc218\ub85d \uc131\ucde8\ub3c4\uac00 \ub0ae\uc544\uc9c0\ub294\uac00? (\uc8fc\ud6a8\uacfc)<\/li>\n\n\n\n<li><strong>Interaction (<\/strong><math data-latex=\"\\gamma_{11}\"><semantics><msub><mi>\u03b3<\/mi><mn>11<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\gamma_{11}<\/annotation><\/semantics><\/math><strong>):<\/strong> \uad50\uc0ac \uc9c0\uc9c0\uac00 \ub192\uc740 \ud559\uad50\uc5d0\uc11c\ub294 \ubd88\uc548\uc774 \uc131\uc801\uc5d0 \ubbf8\uce58\ub294 \ubd80\uc815\uc801 \uc601\ud5a5\uc774 \uc904\uc5b4\ub4dc\ub294\uac00? (\uc870\uc808\ud6a8\uacfc)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\ub79c\ub364 \ud6a8\uacfc (Variance Components):<\/strong>\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\sigma_{u0}^2\"><semantics><msubsup><mi>\u03c3<\/mi><mrow><mi>u<\/mi><mn>0<\/mn><\/mrow><mn>2<\/mn><\/msubsup><annotation encoding=\"application\/x-tex\">\\sigma_{u0}^2<\/annotation><\/semantics><\/math> (Intercept Variance): \uad50\uc0ac \uc9c0\uc9c0\ub97c \uace0\ub824\ud558\uace0\ub3c4 \ub0a8\uc740 \ud559\uad50 \uac04 \uc131\uc801 \ucc28\uc774<\/li>\n\n\n\n<li><math data-latex=\"\\sigma_{u1}^2\"><semantics><msubsup><mi>\u03c3<\/mi><mrow><mi>u<\/mi><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><annotation encoding=\"application\/x-tex\">\\sigma_{u1}^2<\/annotation><\/semantics><\/math> (Slope Variance): \ud559\uad50\ub9c8\ub2e4 &#8216;\ubd88\uc548\uc758 \ud6a8\uacfc&#8217;\uac00 \uc5bc\ub9c8\ub098 \ub4e4\uc465\ub0a0\uc465\ud55c\uac00? \uc774 \uac12\uc774 \uc720\uc758\ud558\uba74 \ud559\uad50\ub9c8\ub2e4 \ubd88\uc548\uc5d0 \ub300\ucc98\ud558\ub294 \uc591\uc0c1\uc774 \ub2e4\ub974\ub2e4\ub294 \ub73b\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">5.2. \uc2dc\uac01\ud654 (R\uc744 \uc774\uc6a9\ud55c \uac1c\ub150\ub3c4)<\/h3>\n\n\n\n<p>\uacb0\uacfc\ub97c \uc774\ud574\ud558\uae30 \uc27d\uac8c \uc2dc\uac01\ud654\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc544\ub798 \uadf8\ub798\ud504\ub294 <strong>\uad50\uc0ac \uc9c0\uc9c0(Support)<\/strong>\uac00 \ub192\uace0 \ub0ae\uc740 \ub450 \ud559\uad50 \uc720\ud615\uc5d0\uc11c <strong>\uc218\ud559 \ubd88\uc548(Anxiety)<\/strong>\uacfc <strong>\uc131\ucde8\ub3c4(Math Score)<\/strong>\uc758 \uad00\uacc4\uac00 \uc5b4\ub5bb\uac8c \ub2e4\ub978\uc9c0\ub97c \ubcf4\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud544\uc694\ud55c \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nif(!require(ggplot2)) install.packages(\"ggplot2\")\nlibrary(ggplot2)\n\n# 1. \ub370\uc774\ud130 \uc0dd\uc131 (\uc55e\uc11c Python \ucf54\ub4dc\uc758 \ub85c\uc9c1\uc744 \uadf8\ub300\ub85c R\ub85c \uad6c\ud604)\nset.seed(2026)\n\n# X\ucd95 \ub370\uc774\ud130: \uc218\ud559 \ubd88\uc548 (Centered) -2\uc5d0\uc11c +2\uae4c\uc9c0 \uc0dd\uc131\nanxiety &lt;- seq(-2, 2, length.out = 100)\n\n# \uc2dc\ub098\ub9ac\uc624\uc5d0 \ub530\ub978 \uc608\uce21\uac12 \uc0dd\uc131\n# \ud559\uad50 A (\ub192\uc740 \uad50\uc0ac \uc9c0\uc9c0): \uae30\uc6b8\uae30 \uc644\ub9cc (-2), \uc808\ud3b8 \ub192\uc74c (55)\nscore_high_support &lt;- 55 - 2 * anxiety\n\n# \ud559\uad50 B (\ub0ae\uc740 \uad50\uc0ac \uc9c0\uc9c0): \uae30\uc6b8\uae30 \uae09\uaca9 (-8), \uc808\ud3b8 \ub0ae\uc74c (45)\nscore_low_support &lt;- 45 - 8 * anxiety\n\n# \uba54\uc778 \ud6a8\uacfc(\ub450 \ud559\uad50 \uc720\ud615)\ub97c \ub2f4\uc744 \ub370\uc774\ud130\ud504\ub808\uc784 \ub9cc\ub4e4\uae30\nmain_effects &lt;- data.frame(\n  anxiety = rep(anxiety, 2),\n  score = c(score_high_support, score_low_support),\n  support_type = rep(c(\"High Teacher Support\", \"Low Teacher Support\"), each = 100)\n)\n\n# \ub79c\ub364 \ud6a8\uacfc (\ubc30\uacbd\uc5d0 \uae54\ub9b4 20\uac1c \uac1c\ubcc4 \ud559\uad50\ub4e4\uc758 \ud68c\uadc0\uc120) \ub370\uc774\ud130 \uc0dd\uc131\nn_schools &lt;- 20\nrandom_lines &lt;- data.frame()\n\nfor(i in 1:n_schools) {\n  # Python \uc608\uc2dc\uc640 \ub3d9\uc77c\ud55c \ubd84\ud3ec \uc0ac\uc6a9: \uc808\ud3b8 ~ N(50, 5), \uae30\uc6b8\uae30 ~ N(-5, 2)\n  intercept &lt;- rnorm(1, 50, 5)\n  slope &lt;- rnorm(1, -5, 2)\n  \n  y_values &lt;- intercept + slope * anxiety\n  \n  temp_df &lt;- data.frame(\n    school_id = factor(i),\n    anxiety = anxiety,\n    score = y_values\n  )\n  random_lines &lt;- rbind(random_lines, temp_df)\n}\n\n# 2. ggplot2\ub97c \uc774\uc6a9\ud55c \uc2dc\uac01\ud654 \uadf8\ub9ac\uae30\nggplot() +\n  # &#91;Layer 1] \ubc30\uacbd: \uac1c\ubcc4 \ud559\uad50\ub4e4\uc758 \ud68c\uadc0\uc120 (\ub79c\ub364 \ud6a8\uacfc) - \ud68c\uc0c9\uc73c\ub85c \ud750\ub9ac\uac8c \ucc98\ub9ac\n  geom_line(data = random_lines, aes(x = anxiety, y = score, group = school_id), \n            color = \"gray\", alpha = 0.3) +\n  \n  # &#91;Layer 2] \uc804\uacbd: \uad50\uc0ac \uc9c0\uc9c0 \uc218\uc900\ubcc4 \ud3c9\uade0 \ud68c\uadc0\uc120 (\uace0\uc815 \ud6a8\uacfc + \uc0c1\ud638\uc791\uc6a9) - \uad75\uace0 \uc120\uba85\ud558\uac8c\n  geom_line(data = main_effects, aes(x = anxiety, y = score, color = support_type, linetype = support_type), \n            linewidth = 1.5) +\n  \n  # &#91;Layer 3] \uc0c9\uc0c1 \ubc0f \uc120 \uc2a4\ud0c0\uc77c \uc9c0\uc815 (\ud30c\ub780\uc0c9 \uc2e4\uc120 vs \ube68\uac04\uc0c9 \uc810\uc120)\n  scale_color_manual(values = c(\"blue\", \"red\")) +\n  scale_linetype_manual(values = c(\"solid\", \"dashed\")) +\n  \n  # &#91;Layer 4] \ub77c\ubca8 \ubc0f \uc81c\ubaa9 \uc124\uc815\n  labs(\n    title = \"Cross-Level Interaction: Teacher Support x Math Anxiety\",\n    subtitle = \"The moderating effect of teacher support on the anxiety-achievement relationship\",\n    x = \"Math Anxiety (Centered)\",\n    y = \"Math Achievement\",\n    color = \"School Context\",\n    linetype = \"School Context\"\n  ) +\n  \n  # &#91;Layer 5] \ud14c\ub9c8 \uc801\uc6a9 (\uae54\ub054\ud55c \ub17c\ubb38 \uc2a4\ud0c0\uc77c)\n  theme_bw() +\n  theme(\n    plot.title = element_text(size = 16, face = \"bold\", hjust = 0.5),\n    plot.subtitle = element_text(size = 12, hjust = 0.5, margin = margin(b = 20)),\n    legend.position = \"bottom\",\n    legend.title = element_text(face = \"bold\"),\n    axis.title = element_text(size = 12)\n  )\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"796\" height=\"547\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG02-1.png\" alt=\"\" class=\"wp-image-716\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG02-1.png 796w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG02-1-300x206.png 300w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG02-1-768x528.png 768w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG02-1-624x429.png 624w\" sizes=\"auto, (max-width: 796px) 100vw, 796px\" \/><\/figure>\n\n\n\n<p><em> High Support \ud559\uad50(\ud30c\ub780\uc120)\uc5d0\uc11c\ub294 \ubd88\uc548\uc774 \ub192\uc544\uc838\ub3c4 \uc131\uc801\uc774 \uc644\ub9cc\ud558\uac8c \ub5a8\uc5b4\uc9c0\uc9c0\ub9cc, Low Support \ud559\uad50(\ube68\uac04\uc120)\uc5d0\uc11c\ub294 \uae09\uaca9\ud558\uac8c \ub5a8\uc5b4\uc9c0\ub294 \uac83\uc744 \ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\uac83\uc774 \ubc14\ub85c <\/em><math data-latex=\"\\gamma_{11}\"><semantics><msub><mi>\u03b3<\/mi><mn>11<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\gamma_{11}<\/annotation><\/semantics><\/math><em> \uc0c1\ud638\uc791\uc6a9 \ud6a8\uacfc\uc785\ub2c8\ub2e4.<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">6. \uacb0\ub860 \ubc0f \uc694\uc57d<\/h2>\n\n\n\n<p>\uc624\ub298 \uc6b0\ub9ac\ub294 \ub2e4\uce35\ubaa8\ud615\uc758 \ud45c\uae30\ubc95\uacfc \ubd84\uc11d \ubc29\ubc95\uc744 &#8220;\ud589\ubcf5\ucd08\ub4f1\ud559\uad50&#8221; \uc608\uc2dc\ub97c \ud1b5\ud574 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \ud575\uc2ec\uc744 \uc815\ub9ac\ud574 \ub4dc\ub9bd\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\ud45c\uae30\ubc95\uc740 \uacb0\uad6d \ud558\ub098\ub2e4:<\/strong> \uc704\uacc4\uc801 \ud45c\uae30\ubc95(HLM)\uc740 \uad50\uc721\uc801 \uce35\uc704\ub97c \uc774\ud574\ud558\uae30 \uc88b\uace0, \ubcf5\ud569 \ud45c\uae30\ubc95(R, jamovi)\uc740 \uc218\ub9ac\uc801 \ubaa8\ub378\ub9c1\uc5d0 \ud3b8\ub9ac\ud569\ub2c8\ub2e4. \ub450 \uc2dd\uc740 \uc218\ud559\uc801\uc73c\ub85c \uc644\uc804\ud788 \ub3d9\uc77c\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ubd84\uc0b0\uc758 \uc124\uba85:<\/strong> \ud559\uad50 \ubcc0\uc218\ub294 \ud559\uad50 \uac04 \ubd84\uc0b0(<math data-latex=\"\\tau_{00}\"><semantics><msub><mi>\u03c4<\/mi><mn>00<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\tau_{00}<\/annotation><\/semantics><\/math>)\uc744, \ud559\uc0dd \ubcc0\uc218\ub294 \ud559\uc0dd \ub0b4 \ubd84\uc0b0(<math data-latex=\"\\sigma^2\"><semantics><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\sigma^2<\/annotation><\/semantics><\/math>)\uc744 \uc124\uba85\ud558\ub294 \uac83\uc744 \ubaa9\ud45c\ub85c \ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc18c\ud504\ud2b8\uc6e8\uc5b4 \ud65c\uc6a9:<\/strong> jamovi\ub098 R\uc740 \ubcf5\ud569 \ud45c\uae30\ubc95\uc744 \ub530\ub974\ubbc0\ub85c, \uace0\uc815 \ud6a8\uacfc\uc640 \ub79c\ub364 \ud6a8\uacfc\ub97c \uad6c\ubd84\ud558\uc5ec \uc785\ub825\ud558\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n\n\n\n<p>\ub2e4\uce35\ubaa8\ud615\uc740 \ubcf5\uc7a1\ud574 \ubcf4\uc774\uc9c0\ub9cc, <strong>&#8220;\ub9e5\ub77d(Context)\uc774 \uac1c\uc778(Individual)\uc5d0\uac8c \ubbf8\uce58\ub294 \uc601\ud5a5&#8221;<\/strong>\uc744 \ubd84\uc11d\ud558\ub294 \uac00\uc7a5 \uac15\ub825\ud55c \ub3c4\uad6c\uc785\ub2c8\ub2e4. \uc774 \uac15\uc758\uac00 \uc5ec\ub7ec\ubd84\uc758 \uc5f0\uad6c\uc5d0 \ub3c4\uc6c0\uc774 \ub418\uae30\ub97c \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>References<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Browne, W. J., Goldstein, H., &amp; Rasbash, J. (2001). Multiple membership multiple classification (MMMC) models. <em>Statistical Modelling, 1<\/em>(2), 103-124.<\/li>\n\n\n\n<li>Bryk, A. S., &amp; Raudenbush, S. W. (1992). <em>Hierarchical linear models: Applications and data analysis methods<\/em>. Sage.<\/li>\n\n\n\n<li>Fitzmaurice, G. M., Ware, J. H., &amp; Laird, N. M. (2004). <em>Applied longitudinal analysis<\/em>. Wiley-Interscience.<\/li>\n\n\n\n<li>Gelman, A., &amp; Hill, J. (2007). <em>Data analysis using regression and multilevel\/hierarchical models<\/em>. Cambridge University Press.<\/li>\n\n\n\n<li>Goldstein, H. (1995). <em>Multilevel statistical models<\/em>. Edward Arnold.<\/li>\n\n\n\n<li>Hox, J. (2002). <em>Multilevel analysis: Techniques and applications<\/em>. Erlbaum.<\/li>\n\n\n\n<li>Pinheiro, J. C., &amp; Bates, D. M. (2000). <em>Mixed-effects models in S and S-PLUS<\/em>. Springer.<\/li>\n\n\n\n<li>Scott, M. A., Shrout, P. E., &amp; Weinberg, S. L. (2013). Multilevel model notation: Establishing the commonalities. In <em>The SAGE Handbook of Multilevel Modeling<\/em> (pp. 21-38). Sage.<\/li>\n\n\n\n<li>Singer, J. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. <em>Journal of Educational and Behavioral Statistics, 23<\/em>(4), 323-355.<\/li>\n\n\n\n<li>Singer, J. D., &amp; Willett, J. B. (2003). <em>Applied longitudinal data analysis: Modeling change and event occurrence<\/em>. Oxford University Press.<\/li>\n\n\n\n<li>Snijders, T. A. B., &amp; Bosker, R. (1999). <em>Multilevel analysis: An introduction to basic and advanced multilevel modeling<\/em>. Sage.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 &#8220;\ub2e4\uce35\ubaa8\ud615\uc758 \ud45c\uae30\ubc95\uacfc \ubd84\uc11d(Multilevel Model Notation and Analysis)&#8221;\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. 1. \ub4e4\uc5b4\uac00\uba70: \ub2e4\uce35\ubaa8\ud615, \ub3c4\ub300\uccb4 \uc65c \ud45c\uae30\ubc95\uc774 \uc911\uc694\ud55c\uac00? \ub2e4\uce35\ubaa8\ud615(Multilevel Models, MLM)\uc740 <a class=\"read-more\" href=\"http:\/\/waurimal.kr\/?p=714\">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":[145,405,199,400],"class_list":["post-714","post","type-post","status-publish","format-standard","hentry","category-multilevel","tag-jamovi","tag-notation","tag-r","tag-400"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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