{"id":745,"date":"2026-01-20T18:55:07","date_gmt":"2026-01-20T09:55:07","guid":{"rendered":"http:\/\/waurimal.kr\/?p=745"},"modified":"2026-01-20T18:55:08","modified_gmt":"2026-01-20T09:55:08","slug":"chap08-%ec%9d%bc%eb%b0%98%ed%99%94-%ec%84%a0%ed%98%95-%ed%98%bc%ed%95%a9-%eb%aa%a8%ed%98%95","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=745","title":{"rendered":"Chap08. \uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc138\uc694!<\/p>\n\n\n\n<p>\uc624\ub298\uc740 <strong>\uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(Generalized Linear Mixed Models, GLMM)<\/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(GAMLj \ubaa8\ub4c8 \ud65c\uc6a9)\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. \uc11c\ub860: \uc65c &#8216;\uc77c\ubc18\ud654&#8217;\uc778\uac00\uc694?<\/h2>\n\n\n\n<p>\uc6b0\ub9ac\uac00 \uc9c0\uae08\uae4c\uc9c0 \ubc30\uc6b4 &#8216;\uc120\ud615 \ud63c\ud569 \ubaa8\ud615(LMM)&#8217;\uc740 \ub370\uc774\ud130\uac00 <strong>\uc815\uaddc\ubd84\ud3ec(Normal Distribution)<\/strong>\ub97c \ub530\ub978\ub2e4\uace0 \uac00\uc815\ud588\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \ud559\uc0dd\ub4e4\uc758 &#8216;\ud0a4&#8217;, &#8216;\uad6d\uc5b4 \uc810\uc218&#8217;, &#8216;\uc9c0\ub2a5 \uc9c0\uc218&#8217; \uac19\uc740 \uc5f0\uc18d\ud615 \ubcc0\uc218\ub4e4\uc774\uc8e0.<\/p>\n\n\n\n<p>\ud558\uc9c0\ub9cc \ud559\uad50 \ud604\uc7a5\uc758 \ub370\uc774\ud130\uac00 \ud56d\uc0c1 \uc608\uc05c \uc885 \ubaa8\uc591(\uc815\uaddc\ubd84\ud3ec)\uc744 \uadf8\ub9b4\uae4c\uc694? \ub2e4\uc74c\uc758 \uc608\ub97c \ubd05\uc2dc\ub2e4.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>[\uc0c1\ud669 A] \uc120\uc0dd\ub2d8\uc774 \ud55c \ud559\uae30 \ub3d9\uc548 \ud559\uc0dd\uc774 \uacfc\uc81c\ub97c \uc81c\ucd9c\ud588\ub294\uc9c0(1), \uc548 \ud588\ub294\uc9c0(0)\ub97c \ub9e4\uc8fc \uae30\ub85d\ud569\ub2c8\ub2e4. (\uc774\ud56d \ub370\uc774\ud130, Binary)<\/p>\n\n\n\n<p>[\uc0c1\ud669 B] \uc0c1\ub2f4 \uc120\uc0dd\ub2d8\uc774 \ud559\uae09 \ub0b4\uc5d0\uc11c \ubc1c\uc0dd\ud558\ub294 &#8216;\ub530\ub3cc\ub9bc \ud589\ub3d9 \ud69f\uc218&#8217;\ub97c \uad00\ucc30\ud569\ub2c8\ub2e4. 0\ud68c, 1\ud68c, 2\ud68c&#8230; (\uce74\uc6b4\ud2b8 \ub370\uc774\ud130, Count)<\/p>\n<\/blockquote>\n\n\n\n<p>\uc774\ub7f0 \ub370\uc774\ud130\ub294 \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub974\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc0c1\ud669 A<\/strong>\ub294 <strong>\uc774\ud56d\ubd84\ud3ec(Binomial Distribution)<\/strong>\ub97c \ub530\ub974\uba70, \uacb0\uacfc\uac00 0 \uc544\ub2c8\uba74 1\ub85c \ub531 \ub5a8\uc5b4\uc9d1\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc0c1\ud669 B<\/strong>\ub294 <strong>\ud3ec\uc544\uc1a1\ubd84\ud3ec(Poisson Distribution)<\/strong>\ub97c \ub530\ub974\uba70, \uc74c\uc218(-)\uac00 \ub098\uc62c \uc218 \uc5c6\uace0 \uc624\ub978\ucabd\uc73c\ub85c \uae34 \uaf2c\ub9ac\ub97c \uac00\uc9c8 \ud655\ub960\uc774 \ub192\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>\uc774\ucc98\ub7fc <strong>\uc815\uaddc\ubd84\ud3ec\uac00 \uc544\ub2cc \uc885\uc18d\ubcc0\uc218<\/strong>\ub97c \ub2e4\ub8e8\uba74\uc11c, \ub3d9\uc2dc\uc5d0 <strong>\ubc18\ubcf5\uce21\uc815<\/strong>\uc774\ub098 <strong>\ud559\uae09 \ub0b4 \ud559\uc0dd<\/strong>\ucc98\ub7fc \ub370\uc774\ud130\uac00 \uc704\uacc4\uc801(Hierarchical)\uc77c \ub54c \uc0ac\uc6a9\ud558\ub294 \ubd84\uc11d \ubc29\ubc95\uc774 \ubc14\ub85c <strong>\uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(GLMM)<\/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. \ubaa8\ud615\uc758 \uad6c\uc870: \uc5f0\uacb0 \uace0\ub9ac \ub9cc\ub4e4\uae30 (Link Function)<\/h2>\n\n\n\n<p>\uc77c\ubc18\uc801\uc778 \uc120\ud615 \ud68c\uadc0\uc2dd\uc740 <math data-latex=\"Y = X\\beta + e\"><semantics><mrow><mi>Y<\/mi><mo>=<\/mo><mi>X<\/mi><mi>\u03b2<\/mi><mo>+<\/mo><mi>e<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Y = X\\beta + e<\/annotation><\/semantics><\/math> \ud615\ud0dc\uc785\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \uacb0\uacfc\uac12 <math data-latex=\"Y\"><semantics><mi>Y<\/mi><annotation encoding=\"application\/x-tex\">Y<\/annotation><\/semantics><\/math>\uac00 0\uacfc 1 \uc0ac\uc774\uc758 \ud655\ub960(\uc2dc\ud5d8 \ud1b5\uacfc \uc5ec\ubd80)\uc774\uc5b4\uc57c \ud558\ub294\ub370, \uc6b0\ubcc0\uc758 <math data-latex=\"X\\beta\"><semantics><mrow><mi>X<\/mi><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X\\beta<\/annotation><\/semantics><\/math>\uac00 <math data-latex=\"-\\infty\"><semantics><mrow><mo>\u2212<\/mo><mi>\u221e<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">-\\infty<\/annotation><\/semantics><\/math>\uc5d0\uc11c <math data-latex=\"+\\infty\"><semantics><mrow><mo>+<\/mo><mi>\u221e<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">+\\infty<\/annotation><\/semantics><\/math>\uae4c\uc9c0 \uac12\uc744 \uac00\uc9c4\ub2e4\uba74 \ub9d0\uc774 \uc548 \ub418\uaca0\uc8e0?<\/p>\n\n\n\n<p>\uadf8\ub798\uc11c \uc6b0\ub9ac\ub294 <strong>\uc5f0\uacb0 \ud568\uc218(Link Function)<\/strong>\ub77c\ub294 \ud2b9\uc218\ud55c \uc7a5\uce58\ub97c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(1) \ub85c\uc9c0\uc2a4\ud2f1 \ud63c\ud569 \ubaa8\ud615 (Binary Data)<\/h3>\n\n\n\n<p>\uc2dc\ud5d8 \ud1b5\uacfc \uc5ec\ubd80(Pass\/Fail)\uc640 \uac19\uc740 \uc774\ud56d \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud560 \ub54c\ub294 \ub85c\uc9d3(Logit) \uc5f0\uacb0 \ud568\uc218\ub97c \uc501\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"\\ln\\left(\\frac{P_{ij}}{1-P_{ij}}\\right) = \\beta_0 + \\beta_1 Time_{ij} + u_{i0}\"><semantics><mrow><mrow><mi>ln<\/mi><mo>\u2061<\/mo><\/mrow><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mfrac><msub><mi>P<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mrow><mn>1<\/mn><mo>\u2212<\/mo><msub><mi>P<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>1<\/mn><\/msub><mi>T<\/mi><mi>i<\/mi><mi>m<\/mi><msub><mi>e<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mi>i<\/mi><mn>0<\/mn><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\ln\\left(\\frac{P_{ij}}{1-P_{ij}}\\right) = \\beta_0 + \\beta_1 Time_{ij} + u_{i0}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc5ec\uae30\uc11c <math data-latex=\"u_{i0}\"><semantics><msub><mi>u<\/mi><mrow><mi>i<\/mi><mn>0<\/mn><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">u_{i0}<\/annotation><\/semantics><\/math>\ub294 \ud559\uc0dd <math data-latex=\"i\"><semantics><mi>i<\/mi><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math> \uace0\uc720\uc758 \ub2a5\ub825(Random Intercept)\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(2) \ud3ec\uc544\uc1a1 \ud63c\ud569 \ubaa8\ud615 (Count Data)<\/h3>\n\n\n\n<p>\ud589\ub3d9 \ube48\ub3c4\uc640 \uac19\uc740 \uac00\uc0b0 \ub370\uc774\ud130\ub97c \ubd84\uc11d\ud560 \ub54c\ub294 \ub85c\uadf8(Log) \uc5f0\uacb0 \ud568\uc218\ub97c \uc501\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"\\ln(\\lambda_{ij}) = \\beta_0 + \\beta_1 Time_{ij} + u_{i0}\"><semantics><mrow><mrow><mi>ln<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bb<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><msub><mi>\u03b2<\/mi><mn>1<\/mn><\/msub><mi>T<\/mi><mi>i<\/mi><mi>m<\/mi><msub><mi>e<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>u<\/mi><mrow><mi>i<\/mi><mn>0<\/mn><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\ln(\\lambda_{ij}) = \\beta_0 + \\beta_1 Time_{ij} + u_{i0}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc5ec\uae30\uc11c <math data-latex=\"\\lambda_{ij}\"><semantics><msub><mi>\u03bb<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">\\lambda_{ij}<\/annotation><\/semantics><\/math>\ub294 \ud574\ub2f9 \uc2dc\uc810\uc5d0\uc11c\uc758 \ud3c9\uade0 \ubc1c\uc0dd \ud69f\uc218\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\">3. \uc2e4\uc2b5 1: \uc774\ud56d \uacb0\uacfc\ubcc0\uc218 (Binary Outcome) \ubd84\uc11d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\uc2dc\ub098\ub9ac\uc624: &#8220;\uae30\ucd08\ud559\ub825 \ud3c9\uac00 \ud1b5\uacfc \uc5ec\ubd80 \ucd94\uc801&#8221;<\/h3>\n\n\n\n<p>\uc5b4\ub290 \uad50\uc721\uccad\uc5d0\uc11c \ubc29\uacfc \ud6c4 \ubcf4\ucda9\uc218\uc5c5 \ud504\ub85c\uadf8\ub7a8\uc774 \ud559\uc0dd\ub4e4\uc758 <strong>\uae30\ucd08\ud559\ub825 \ud3c9\uac00 \ud1b5\uacfc(Pass=1, Fail=0)<\/strong>\uc5d0 \ubbf8\uce58\ub294 \uc601\ud5a5\uc744 \uc54c\uc544\ubcf4\uae30 \uc704\ud574, 100\uba85\uc758 \ud559\uc0dd\uc744 \ub300\uc0c1\uc73c\ub85c 4\ud559\uae30 \ub3d9\uc548 \ucd94\uc801 \uc870\uc0ac\ub97c \ud588\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc9d1\ub2e8:<\/strong> \uc2e4\ud5d8\uad70(\ubcf4\ucda9\uc218\uc5c5 O), \ub300\uc870\uad70(\ubcf4\ucda9\uc218\uc5c5 X)<\/li>\n\n\n\n<li><strong>\uc885\uc18d\ubcc0\uc218:<\/strong> \ud3c9\uac00 \ud1b5\uacfc \uc5ec\ubd80 (0, 1)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">[Step 1] R\uc744 \uc774\uc6a9\ud55c \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131<\/h3>\n\n\n\n<p>Jamovi\uc758 <code>Rj Editor<\/code>\ub098 R Studio\uc5d0\uc11c \ub2e4\uc74c \ucf54\ub4dc\ub97c \uc2e4\ud589\ud558\uc5ec \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>set.seed(1234)\nn_subjects &lt;- 100 # \ud559\uc0dd \uc218\nn_timepoints &lt;- 4 # 4\ud559\uae30 \uce21\uc815\n\n# \ub370\uc774\ud130 \ud504\ub808\uc784 \uc0dd\uc131\ndata_binary &lt;- data.frame(\n  student_id = rep(1:n_subjects, each = n_timepoints),\n  time = rep(0:3, n_subjects), # 0(\uae30\ucd08\uc120) ~ 3\ud559\uae30\n  group = rep(sample(c(\"Control\", \"Treatment\"), n_subjects, replace = T), each = n_timepoints)\n)\n\n# \ub79c\ub364 \ud6a8\uacfc (\ud559\uc0dd \uace0\uc720\uc758 \uae30\ucd08 \ud559\ub825 \uc218\uc900)\nrandom_intercept &lt;- rep(rnorm(n_subjects, mean = 0, sd = 1.5), each = n_timepoints)\n\n# \uace0\uc815 \ud6a8\uacfc \uc124\uc815\n# Intercept: -1 (\ucd08\uae30\uc5d4 \ud1b5\uacfc \ud655\ub960 \ub0ae\uc74c)\n# Time: 0.2 (\uc2dc\uac04\uc774 \uc9c0\ub0a0\uc218\ub85d \uc870\uae08\uc529 \ud5a5\uc0c1)\n# GroupTreatment: 0.5 (\uc2e4\ud5d8\uad70\uc774 \uc870\uae08 \ub354 \ub192\uc74c)\n# Time*Group: 0.4 (\uc2e4\ud5d8\uad70\uc758 \ud5a5\uc0c1 \uc18d\ub3c4\uac00 \ub354 \ube60\ub984)\nlogit_p &lt;- -1 + 0.2 * data_binary$time + \n           0.5 * (data_binary$group == \"Treatment\") + \n           0.4 * data_binary$time * (data_binary$group == \"Treatment\") + \n           random_intercept\n\n# \ud655\ub960 \uacc4\uc0b0 \ubc0f \uc774\ud56d \ub370\uc774\ud130 \uc0dd\uc131\nprob &lt;- exp(logit_p) \/ (1 + exp(logit_p))\ndata_binary$pass &lt;- rbinom(n = nrow(data_binary), size = 1, prob = prob)\n\nhead(data_binary)\n<\/code><\/pre>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-a4d1b801-0371-4dce-af18-d7f282fadf6c\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap08.csv\">chap08<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap08.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a4d1b801-0371-4dce-af18-d7f282fadf6c\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">[Step 2] Jamovi \ubd84\uc11d \uc808\ucc28 (GAMLj \ubaa8\ub4c8)<\/h3>\n\n\n\n<p>Jamovi\uc5d0\uc11c GLMM\uc744 \ubd84\uc11d\ud558\uae30 \uc704\ud574\uc11c\ub294 <strong>GAMLj<\/strong> \ubaa8\ub4c8 \uc124\uce58\uac00 \ud544\uc694\ud569\ub2c8\ub2e4. (Jamovi Library -&gt; GAMLj \ucd94\uac00)<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Analyses<\/strong> \ud0ed \ud074\ub9ad > <strong>GAMLj<\/strong> > <strong>Generalized Mixed Models<\/strong> \uc120\ud0dd<\/li>\n\n\n\n<li><strong>Dependent Variable<\/strong>: <code>pass<\/code> (\ud1b5\uacfc \uc5ec\ubd80)<\/li>\n\n\n\n<li><strong>Random Effect Grouping Factors<\/strong>: <code>student_id<\/code><\/li>\n\n\n\n<li><strong>Covariates<\/strong>: <code>time<\/code><\/li>\n\n\n\n<li><strong>Factors<\/strong>: <code>group<\/code><\/li>\n\n\n\n<li><strong>Model Definition<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Distribution: <strong>Binomial<\/strong><\/li>\n\n\n\n<li>Link Function: <strong>Logit<\/strong><\/li>\n\n\n\n<li>Fixed Effects: <code>time<\/code>, <code>group<\/code>, <code>time * group<\/code> (\uc0c1\ud638\uc791\uc6a9\ud56d)<\/li>\n\n\n\n<li>Random Effects: <code>student_id<\/code> (Intercept \uccb4\ud06c)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">[Step 3] \uacb0\uacfc \ud574\uc11d \ubc0f \uc2dc\uac01\ud654<\/h3>\n\n\n\n<p>\ubd84\uc11d \uacb0\uacfc, \uc0c1\ud638\uc791\uc6a9\ud56d(<code>time * group<\/code>)\uc774 \uc720\uc758\ud558\ub2e4\uba74 \ubcf4\ucda9\uc218\uc5c5 \uc9d1\ub2e8\uc774 \ub300\uc870\uad70\ubcf4\ub2e4 \uc2dc\uac04\uc774 \uc9c0\ub0a0\uc218\ub85d \ud1b5\uacfc \ud655\ub960\uc774 <strong>\ub354 \uac00\ud30c\ub974\uac8c \uc99d\uac00<\/strong>\ud55c\ub2e4\uace0 \ud574\uc11d\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc774\ub54c \uc8fc\uc758\ud560 \uc810\uc740 \uacc4\uc218(<math data-latex=\"\\beta\"><semantics><mi>\u03b2<\/mi><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math>)\uac00 &#8216;\ud655\ub960&#8217; \uadf8 \uc790\uccb4\uac00 \uc544\ub2c8\ub77c <strong>\ub85c\uadf8 \uc624\uc988(Log Odds)<\/strong>\uc758 \ubcc0\ud654\ub7c9\uc774\ub77c\ub294 \uc810\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\">4. \uc2e4\uc2b5 2: \uac00\uc0b0 \uacb0\uacfc\ubcc0\uc218 (Count Outcome) \ubd84\uc11d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\uc2dc\ub098\ub9ac\uc624: &#8220;\uc218\uc5c5 \uc911 \uc9c8\ubb38 \ud69f\uc218 \ubcc0\ud654&#8221;<\/h3>\n\n\n\n<p>\ud1a0\ub860\uc2dd \uc218\uc5c5(\uc2e4\ud5d8\uad70)\uc774 \ud559\uc0dd\ub4e4\uc758 <strong>\uc790\ubc1c\uc801 \uc9c8\ubb38 \ud69f\uc218<\/strong>\ub97c \ub298\ub9ac\ub294\uc9c0 \ud655\uc778\ud558\uae30 \uc704\ud574 10\uc8fc\uac04 \ub370\uc774\ud130\ub97c \uc218\uc9d1\ud588\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ub370\uc774\ud130 \ud2b9\uc131:<\/strong> \uc9c8\ubb38 \ud69f\uc218\ub294 0 \uc774\uc0c1\uc758 \uc815\uc218\uc774\uba70, \ub300\ubd80\ubd84 \uc801\uc740 \ud69f\uc218\uc5d0 \ubab0\ub824 \uc788\uc74c (\ud3ec\uc544\uc1a1 \ubd84\ud3ec \uac00\uc815).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">[Step 1] R\uc744 \uc774\uc6a9\ud55c \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>set.seed(5678)\n# \ub370\uc774\ud130 \ud504\ub808\uc784 \uc0dd\uc131 (\uad6c\uc870\ub294 \uc704\uc640 \ub3d9\uc77c)\ndata_count &lt;- data.frame(\n  student_id = rep(1:n_subjects, each = n_timepoints),\n  time = rep(0:3, n_subjects),\n  group = rep(sample(c(\"Lecture\", \"Discussion\"), n_subjects, replace = T), each = n_timepoints)\n)\n\n# \ub79c\ub364 \ud6a8\uacfc (\ud559\uc0dd\uc758 \uc801\uadf9\uc131)\nrandom_intercept_c &lt;- rep(rnorm(n_subjects, mean = 0, sd = 0.5), each = n_timepoints)\n\n# \uace0\uc815 \ud6a8\uacfc (\ub85c\uadf8 \uc2a4\ucf00\uc77c)\n# Discussion \uadf8\ub8f9\uc774 \uc2dc\uac04\uc774 \uc9c0\ub0a0\uc218\ub85d \uc9c8\ubb38\uc774 \uae09\uaca9\ud788 \ub298\uc5b4\ub098\ub3c4\ub85d \uc124\uc815\nlog_lambda &lt;- 0.5 + 0.1 * data_count$time + \n              0.2 * (data_count$group == \"Discussion\") + \n              0.3 * data_count$time * (data_count$group == \"Discussion\") + \n              random_intercept_c\n\n# \ud3ec\uc544\uc1a1 \ub370\uc774\ud130 \uc0dd\uc131\ndata_count$questions &lt;- rpois(n = nrow(data_count), lambda = exp(log_lambda))\n\nhead(data_count)\n\n# CSV\ub85c \uc800\uc7a5 (jamovi\uc5d0\uc11c \ubd88\ub7ec\uc624\uae30 \uc704\ud568)\nwrite.csv(data_count, \"chap08_2.csv\", row.names = FALSE)<\/code><\/pre>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-eb1fc8e8-9179-43d8-9996-3fc5a5d09e68\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap08_2.csv\">chap08_2<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap08_2.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-eb1fc8e8-9179-43d8-9996-3fc5a5d09e68\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">[Step 2] Jamovi \ubd84\uc11d \uc808\ucc28<\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>GAMLj<\/strong> > <strong>Generalized Mixed Models<\/strong><\/li>\n\n\n\n<li><strong>Dependent Variable<\/strong>: <code>questions<\/code><\/li>\n\n\n\n<li><strong>Model Definition<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Distribution: <strong>Poisson<\/strong><\/li>\n\n\n\n<li>Link Function: <strong>Log<\/strong><\/li>\n\n\n\n<li>\ub098\uba38\uc9c0 \uc124\uc815\uc740 \uc704\uc640 \ub3d9\uc77c.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">5. \uc2ec\ud654 \ubd84\uc11d: &#8220;\uac1c\ubcc4 \ud559\uc0dd&#8221; vs &#8220;\uc804\uccb4 \ud3c9\uade0&#8221;\uc758 \ud568\uc815<\/h2>\n\n\n\n<p>GLMM\uc5d0\uc11c \uac00\uc7a5 \uc911\uc694\ud55c \uac1c\ub150\uc774\uc790 \ud559\uc0dd\ub4e4\uc774 \uac00\uc7a5 \ub9ce\uc774 \ud5f7\uac08\ub9ac\ub294 \ubd80\ubd84\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p><strong>&#8220;\uac1c\ubcc4 \ud559\uc0dd\ub4e4\uc758 \uc131\uc7a5 \uace1\uc120\uc744 \ud3c9\uade0 \ub0b8 \uac83&#8221;<\/strong>\uacfc <strong>&#8220;\uc804\uccb4 \uc9d1\ub2e8\uc758 \ud3c9\uade0 \uc131\uc7a5 \uace1\uc120&#8221;<\/strong>\uc774 \uac19\uc744\uae4c\uc694?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc120\ud615 \ud63c\ud569 \ubaa8\ud615(LMM):<\/strong> \uac19\uc2b5\ub2c8\ub2e4. (<math data-latex=\"\\beta^{RE} = \\beta^M\"><semantics><mrow><msup><mi>\u03b2<\/mi><mrow><mi>R<\/mi><mi>E<\/mi><\/mrow><\/msup><mo>=<\/mo><msup><mi>\u03b2<\/mi><mi>M<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\beta^{RE} = \\beta^M<\/annotation><\/semantics><\/math>)<\/li>\n\n\n\n<li><strong>\uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(GLMM):<\/strong> <strong>\ub2e4\ub985\ub2c8\ub2e4!<\/strong> (<math data-latex=\"\\beta^{RE} \\neq \\beta^M\"><semantics><mrow><msup><mi>\u03b2<\/mi><mrow><mi>R<\/mi><mi>E<\/mi><\/mrow><\/msup><mo>\u2260<\/mo><msup><mi>\u03b2<\/mi><mi>M<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\beta^{RE} \\neq \\beta^M<\/annotation><\/semantics><\/math>)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\uc65c \ub2e4\ub97c\uae4c\uc694?<\/h3>\n\n\n\n<p>\ube44\uc120\ud615 \ud568\uc218(S\uc790 \uace1\uc120\uc778 \ub85c\uc9c0\uc2a4\ud2f1 \ub4f1)\ub97c \ud1b5\uacfc\ud558\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc218\uc2dd\uc73c\ub85c \ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \uad00\uacc4\uac00 \uc131\ub9bd\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"E(y) \\neq \\frac{\\exp(X\\beta)}{1+\\exp(X\\beta)}\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>y<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2260<\/mo><mfrac><mrow><mrow><mi>exp<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>X<\/mi><mi>\u03b2<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mrow><mi>exp<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>X<\/mi><mi>\u03b2<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">E(y) \\neq \\frac{\\exp(X\\beta)}{1+\\exp(X\\beta)}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc624\ud788\ub824, \uc8fc\ubcc0(Marginal) \ud6a8\uacfc\ub294 \uac1c\ubcc4(Subject-specific) \ud6a8\uacfc\ubcf4\ub2e4 <strong>\uc808\ub313\uac12\uc774 \uc791\uac8c(\uc644\ub9cc\ud558\uac8c)<\/strong> \ub098\ud0c0\ub0a9\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">R\ub85c \uc2dc\uac01\ud654\ud558\uc5ec \uc774\ud574\ud558\uae30<\/h3>\n\n\n\n<p>\uc774 \ucc28\uc774\ub97c \ub208\uc73c\ub85c \ud655\uc778\ud574 \ubd05\uc2dc\ub2e4. \uac1c\ubcc4 \ud559\uc0dd\ub4e4\uc758 \uace1\uc120(\ud68c\uc0c9)\uacfc \uadf8 \ud3c9\uade0(\ube68\uac04\uc0c9, \ud30c\ub780\uc0c9)\uc744 \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># \uc2dc\uac01\ud654 \ucf54\ub4dc\nlibrary(ggplot2)\n\n# \uc608\uce21\uac12 \uc0dd\uc131 (\uac1c\ubcc4 \ud6a8\uacfc \ud3ec\ud568)\n# *\uc8fc\uc758: \uc2e4\uc81c GLMM \uc608\uce21\uc740 \ubcf5\uc7a1\ud558\uc9c0\ub9cc, \uc5ec\uae30\uc11c\ub294 \uac1c\ub150 \uc124\uba85\uc744 \uc704\ud574 \ub2e8\uc21c\ud654\ud558\uc5ec \uc2dc\uac01\ud654\ud569\ub2c8\ub2e4.\ndata_binary$pred_prob &lt;- predict(glm(pass ~ time * group, data=data_binary, family=binomial), type=\"response\") \n\n# \uadf8\ub798\ud504 \uadf8\ub9ac\uae30\nggplot(data_binary, aes(x = time, y = pred_prob, group = student_id)) +\n  # \uac1c\ubcc4 \ud559\uc0dd\ub4e4\uc758 \uc131\uc7a5 \uace1\uc120 (\ud68c\uc0c9, \uc587\uac8c)\n  geom_line(alpha = 0.2, color = \"gray\") + \n  \n  # \uc9d1\ub2e8 \ud3c9\uade0 \uc131\uc7a5 \uace1\uc120 (\uc0c9\uc0c1, \uad75\uac8c)\n  # *\ubcc0\uacbd\uc0ac\ud56d: size = 1.5 -> linewidth = 1.5\n  stat_summary(aes(group = group, color = group), fun = mean, geom = \"line\", linewidth = 1.5) + \n  \n  # \ub77c\ubca8 \ubc0f \ud14c\ub9c8 \uc124\uc815\n  labs(title = \"\uac1c\ubcc4 \ud559\uc0dd \uc131\uc7a5 \uace1\uc120(\ud68c\uc0c9) vs \uc9d1\ub2e8 \ud3c9\uade0 \uace1\uc120(\uc0c9\uc0c1)\",\n       y = \"\ud1b5\uacfc \ud655\ub960 (Probability)\", x = \"\uc2dc\uac04 (\ud559\uae30)\") +\n  theme_minimal()\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"821\" height=\"765\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG08-1.png\" alt=\"\" class=\"wp-image-748\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG08-1.png 821w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG08-1-300x280.png 300w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG08-1-768x716.png 768w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/FIG08-1-624x581.png 624w\" sizes=\"auto, (max-width: 821px) 100vw, 821px\" \/><\/figure>\n\n\n\n<p><\/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<\/h2>\n\n\n\n<p>\uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(GLMM)\uc740 \ud604\uc2e4 \uc138\uacc4\uc758 \ubcf5\uc7a1\ud55c \ub370\uc774\ud130(O\/X, \ud69f\uc218 \ub4f1)\ub97c \ud1b5\uacc4\uc801\uc73c\ub85c \uc5c4\ubc00\ud558\uac8c \ub2e4\ub8f0 \uc218 \uc788\ub294 \uac15\ub825\ud55c \ub3c4\uad6c\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>\ub370\uc774\ud130\uac00 \uc815\uaddc\ubd84\ud3ec\uac00 \uc544\ub2d0 \ub54c(\uc774\ud56d, \ud3ec\uc544\uc1a1 \ub4f1) \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc5f0\uacb0 \ud568\uc218(Link Function)<\/strong>\ub97c \ud1b5\ud574 \uc120\ud615 \uc608\uce21\uc2dd\uacfc \uacb0\uacfc\ub97c \uc5f0\uacb0\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uac1c\ubcc4 \ub300\uc0c1(Subject-specific)<\/strong>\uc758 \ubcc0\ud654\uc5d0 \ucd08\uc810\uc744 \ub9de\ucd94\ubbc0\ub85c, \uc804\uccb4 \ud3c9\uade0(Population-averaged) \ud574\uc11d \uc2dc \uc8fc\uc758\uac00 \ud544\uc694\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n\n\n\n<p>\ud559\uad50 \ud604\uc7a5\uc5d0\uc11c &#8220;\uc6b0\ub9ac \ubc18 \uc544\uc774\ub4e4\uc758 \uc219\uc81c \uc81c\ucd9c \uc5ec\ubd80&#8221;\ub098 &#8220;\ubb38\uc81c \ud589\ub3d9 \ud69f\uc218&#8221;\ub97c \uc885\ub2e8\uc801\uc73c\ub85c \uc5f0\uad6c\ud558\uace0 \uc2f6\ub2e4\uba74, GLMM\uc774 \uac00\uc7a5 \uc801\ud569\ud55c \uce5c\uad6c\uac00 \ub418\uc5b4\uc904 \uac83\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ucc38\uace0\ubb38\ud5cc<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Breslow, N. E., &amp; Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. <em>Journal of the American Statistical Association<\/em>, <em>88<\/em>(421), 9-25.<\/li>\n\n\n\n<li>Diggle, P. J., Heagerty, P., Liang, K. Y., &amp; Zeger, S. L. (2002). <em>Analysis of longitudinal data<\/em> (2nd ed.). Oxford University Press.<\/li>\n\n\n\n<li>Faught, E., Wilder, B. J., Ramsay, R. E., Reife, R. A., Kramer, L. D., Pledger, G. W., &amp; Karim, R. M. (1996). Topiramate placebo-controlled dose-ranging trial in refractory partial epilepsy using 200-, 400-, and 600-mg daily dosages. <em>Neurology<\/em>, <em>46<\/em>(6), 1684-1690.<\/li>\n\n\n\n<li>Liang, K. Y., &amp; Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. <em>Biometrika<\/em>, <em>73<\/em>(1), 13-22.<\/li>\n\n\n\n<li>Molenberghs, G., &amp; Verbeke, G. (2005). <em>Models for discrete longitudinal data<\/em>. Springer.<\/li>\n\n\n\n<li>Verbeke, G., &amp; Molenberghs, G. (2000). <em>Linear mixed models for longitudinal data<\/em>. Springer.<\/li>\n\n\n\n<li>Verbeke, G., &amp; Molenberghs, G. (n.d.). Generalized Linear Mixed Models &#8211; Overview. In <em>The SAGE Handbook of Multilevel Modeling<\/em> (Chapter 8).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ud615(Generalized Linear Mixed Models, GLMM)\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(GAMLj \ubaa8\ub4c8 \ud65c\uc6a9)\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. \uc11c\ub860: \uc65c &#8216;\uc77c\ubc18\ud654&#8217;\uc778\uac00\uc694? \uc6b0\ub9ac\uac00 \uc9c0\uae08\uae4c\uc9c0 \ubc30\uc6b4 <a class=\"read-more\" href=\"http:\/\/waurimal.kr\/?p=745\">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":[420,145,199,400,421],"class_list":["post-745","post","type-post","status-publish","format-standard","hentry","category-multilevel","tag-glmm","tag-jamovi","tag-r","tag-400","tag-421"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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