{"id":1923,"date":"2019-08-05T20:22:08","date_gmt":"2019-08-05T11:22:08","guid":{"rendered":"http:\/\/141.164.34.82\/?p=1923"},"modified":"2019-08-05T21:28:41","modified_gmt":"2019-08-05T12:28:41","slug":"fixed-effects-vs-random-effects","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=1923","title":{"rendered":"\uace0\uc815\ud6a8\uacfc(fixed effect)\uc640 \uc784\uc758\ud6a8\uacfc(random effect)"},"content":{"rendered":"<h2>\ub2e4\ub978 \ubd84\uc57c, \ub2e4\ub978 \uc2dc\uae30, \ub2e4\ub978 \uc6a9\uc5b4<\/h2>\n<p><strong>\uc6a9\uc5b4<\/strong>\ub780 \ubd84\uc57c, \uc2dc\uae30\ub9c8\ub2e4 \ub2e4\ub974\uac8c \uc0ac\uc6a9\ub418\uae30 \ub9c8\ub828\uc774\ub2e4. \ub530\ub77c\uc11c \uac19\uc740 \uc6a9\uc5b4\uac00 \ub2e4\ub978 \ubd84\uc57c\uc5d0\uc11c\ub3c4 <strong>\ub2f9\uc5f0\ud788<\/strong> \uac19\uc740 \uc758\ubbf8\ub97c \uac00\uc9c4\ub2e4\uace0 \uc0dd\uac01\ud558\ub294 \uac83\uc740 \uc2ac\uae30\ub86d\uc9c0 \ubabb\ud558\ub2e4. \uc61b\ub9d0\ub85c <strong>\uc5b4\ub9ac\ub2e4<\/strong>. (\u2018\uc2ac\uae30\ub86d\uc9c0 \ubabb\ud558\uace0 \ub454\ud558\ub2e4\u2019\ub780 \ub73b\uc744 \uac00\uc9c4 \u2018\uc5b4\ub9ac\uc11d\ub2e4\u2019\ub780 \ub2e8\uc5b4\uac00 \uc0dd\uae30\uae30 \uc774\uc804\uc5d0\ub294 <strong>\u2018\uc5b4\ub9ac\ub2e4\u2019<\/strong>\uac00 \u2018\uc5b4\ub9ac\uc11d\ub2e4\u2019\uc758 \uc758\ubbf8\ub97c \uc9c0\ub2c8\uace0 \uc788\uc5c8\ub2e4.<sup>[1]<\/sup> )<\/p>\n<p><sup>[1]<sup>:<\/sup><\/sup> <a href=\"https:\/\/www.korean.go.kr\/nkview\/nknews\/200503\/80_1.html\">https:\/\/www.korean.go.kr\/nkview\/nknews\/200503\/80_1.html<\/a><\/p>\n<h2>\ud1b5\uacc4\ud559\uc5d0\uc11c\uc758 \uc784\uc758 \ud6a8\uacfc<\/h2>\n<p>\ud1b5\uacc4\ud559\uc5d0\uc11c <strong>\uc784\uc758 \ud6a8\uacfc(random effect)<\/strong>\ub294 sampling of sampling\uc758 \ub9e5\ub77d\uc5d0\uc11c \uc4f0\uc778\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4 \ubcf4\uc790. \uc5b4\ub5a4 \ud55c \uc9d1\ub2e8(\ubaa8\uc9d1\ub2e8\uc758 \ud06c\uae30\uac00 \ubb34\ud55c\ud558\ub2e4\uace0 \ud558\uc790)\uc758 \ud0a4 \ud3c9\uade0(\ubaa8\ud3c9\uade0)\uc744 \uad6c\ud558\uae30 \uc704\ud574 \uc0ac\ub78c\uc758 \ud0a4\ub97c \uc784\uc758\ub85c \ud45c\uc9d1(sampling)\ud558\uc5ec \ud0a4 \ud3c9\uade0\uc744 \ucd94\uc815\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\ud558\uc9c0\ub9cc \ud0a4\ub97c \uce21\uc815\ud558\ub294 \ub3c4\uad6c\uac00 \ub9e4\uc6b0 \uc870\uc7a1\ud574\uc11c \uce21\uc815\ub41c \ud0a4\uc758 \ud45c\uc900\uc624\ucc28\uac00 \\(10\\) cm \ub77c\uace0 \uac00\uc815\ud574\ubcf4\uc790. \uc774\ub54c \uce21\uc815\uc5d0 \ub530\ub978 \uc624\ucc28\uac00 \uc11c\ub85c \ub3c5\ub9bd\uc774\ub77c\uba74, \uce21\uc815\uc758 \uc815\ud655\uc131\uc744 \ub192\uc774\ub294 \uac83\uc740 \uc5ec\ub7ec\ubc88 \uce21\uc815\ud558\ub294 \uac83\uc774\ub2e4. <\/p>\n<ul>\n<li>\\(Y_{ij}\\) : \\(i\\) \ubc88\uc9f8 \uc0ac\ub78c\uc758 \\(j\\) \ubc88\uc9f8 \ud0a4 \uce21\uc815 \uacb0\uacfc <\/li>\n<li>\n<p>\\(e_{ij}\\) : \\(i\\) \ubc88\uc9f8 \uc0ac\ub78c\uc758 \\(j\\) \ubc88\uc9f8 \ud0a4 \uce21\uc815\uc5d0\uc11c \uc624\ucc28<\/p>\n<\/li>\n<li>\n<p>\\(\\mu\\) : \ubaa8\ud3c9\uade0(\ud0a4)<\/p>\n<\/li>\n<li>\n<p>\\(\\mu_i\\) : \\(i\\) \ubc88\uc9f8 \uc0ac\ub78c\uc758 \uc2e4\uc81c \ud0a4<\/p>\n<\/li>\n<li>\n<p>\\(Y_{ij} = \\mu_i + e_{ij} = \\mu + u_i + e_{ij}\\) ( \\(\\mu\\) : \uc804\uccb4 \ud3c9\uade0, \\(u_i = \\mu_i &#8211; \\mu\\) : \\(i\\) \ubc88\uc9f8 \uc0ac\ub78c \uc2e4\uc81c \ud0a4\uc640 \uc804\uccb4 \ud3c9\uade0\uc758 \ucc28\uc774)<\/p>\n<\/li>\n<\/ul>\n<p>\ub370\uc774\ud130\uac00 \uc5b4\ub5bb\uac8c \uc0dd\uc131\ub418\ub294 \uc0b4\ud3b4\ubcf4\uc790. \uba3c\uc800 \\(n\\) \uba85\uc758 \ud0a4 \uce21\uc815 \uc790\ub8cc\ub97c \ud65c\uc6a9\ud55c\ub2e4\uba74,<\/p>\n<pre><code class=\"r\">sNum = 4\nset.seed(sNum)\nmuAll = 175; sigmaAll = 15\nn = 10\nmu = rnorm(n, muAll, sigmaAll) # n \uba85\uc758 \ud45c\ubcf8 \ucd94\ucd9c\n\nt.test(mu)\n<\/code><\/pre>\n<pre>## \n##  One Sample t-test\n## \n## data:  mu\n## t = 36.936, df = 9, p-value = 3.874e-11\n## alternative hypothesis: true mean is not equal to 0\n## 95 percent confidence interval:\n##  172.2595 194.7364\n## sample estimates:\n## mean of x \n##  183.4979\n<\/pre>\n<p>\ubaa8\ud3c9\uade0\uc740 183(95% \uc2e0\ub8b0\uad6c\uac04 172.9-194)\uc73c\ub85c \ucd94\uc815\ub418\uc5c8\ub2e4. \ub9cc\uc57d \uc5ec\ub7ec \ubc88 \uce21\uc815\ud560 \uc218 \uc788\ub2e4\uba74,<\/p>\n<pre><code class=\"r\">sNum = 5\nset.seed(sNum)\nmuAll = 175; sigmaAll = 15\nn = 10;\nns = sample(5:10,n,replace=TRUE)\nmu = rnorm(n, muAll, sigmaAll) # n \uba85 \ud45c\ubcf8 \ucd94\ucd9c\n# \ud0a4 \ubc18\ubcf5 \uce21\uc815(\ud69f\uc218, ns)\ny &lt;- g &lt;- mus &lt;-  vector(&quot;list&quot;, n)\nfor (i in 1:length(mus)) {\n  mus[[i]] &lt;- rep(mu[i], each=ns[i])\n  y[[i]] &lt;- rnorm(ns[i], mu[i], 10) # ns[i] \ubc88 \ubc18\ubcf5 \uce21\uc815\n  g[[i]] &lt;- rep(i, each=ns[i]) \n}\ny &lt;- unlist(y)\ng &lt;- factor(unlist(g))\nmus &lt;- unlist(mus)\ndat &lt;- data.frame(mus, g, y)\nhead(dat)\n<\/code><\/pre>\n<pre>##        mus g        y\n## 1 165.9564 1 164.5665\n## 2 165.9564 1 159.9832\n## 3 165.9564 1 144.1167\n## 4 165.9564 1 168.3646\n## 5 165.9564 1 163.3628\n## 6 165.9564 1 174.9615\n<\/pre>\n<pre><code class=\"r\"># This is the title image.\n#ggplot(dat, aes(x=g, y=y)) + \n#   geom_hline(yintercept=175, linetype=&#39;dotted&#39;) + \n#   geom_boxplot() + \n#   geom_point(alpha=0.2)\n<\/code><\/pre>\n<p>\ub370\uc774\ud130\ub294 \uc704\uc640 \uac19\uc740 \uad6c\uc870\ub97c \uac00\uc9c0\uac8c \ub41c\ub2e4.<\/p>\n<p>\uc774\ub54c \uc774\ub7f0 \uad6c\uc870\ub97c \uace0\ub824\ud558\uc9c0 \uc54a\uace0 \ubaa8\ud3c9\uade0\uc744 \ucd94\uc815\ud55c\ub2e4\uba74, \ub2e4\uc74c\uacfc \uac19\ub2e4. \ud3c9\uade0 \\(\\mu\\) \uac00 \\(175\\) \uc640 \ub2e4\ub978\uc9c0 \uac80\uc815\ud55c\ub2e4\uba74, 95% \uc2e0\ub8b0\uad6c\uac04\uc73c\ub85c \ubcf4\uc544 \uc601\uac00\uc124( \\(\\mu = 175\\) )\ub294 \uae30\uac01\ub41c\ub2e4. <\/p>\n<pre><code class=\"r\">t.test(dat$y, mu=175)\n<\/code><\/pre>\n<pre>## \n##  One Sample t-test\n## \n## data:  dat$y\n## t = -2.8967, df = 76, p-value = 0.004924\n## alternative hypothesis: true mean is not equal to 175\n## 95 percent confidence interval:\n##  166.9416 173.5081\n## sample estimates:\n## mean of x \n##  170.2248\n<\/pre>\n<p>\ub9cc\uc57d Random-effect \ubaa8\ud615\uc744 \uc0ac\uc6a9\ud55c\ub2e4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uc6b0\ub9ac\ub294 \uc804\uccb4 \ud3c9\uade0( \\(\\mu\\) )\uc774 \\(175\\) \uc640 \ub2e4\ub978\uc9c0 \ud655\uc778\ud558\ub824\uba74 \ub450 \ubc88\uc9f8 \ubc29\ubc95\uc73c\ub85c \uc190\uc27d\uac8c \uac80\uc815\ud560 \uc218 \uc788\ub2e4. \uacb0\uacfc\ub294 \uae30\uac01\ud560 \uc218 \uc5c6\ub2e4. <\/p>\n<pre><code class=\"r\">#library(lme4)\nlibrary(lmerTest)\n(lmerMod &lt;- lmer(y ~ 1|g, data=dat))\n<\/code><\/pre>\n<pre>## Linear mixed model fit by REML [&#39;lmerModLmerTest&#39;]\n## Formula: y ~ 1 | g\n##    Data: dat\n## REML criterion at convergence: 588.7467\n## Random effects:\n##  Groups   Name        Std.Dev.\n##  g        (Intercept) 10.896  \n##  Residual              9.865  \n## Number of obs: 77, groups:  g, 10\n## Fixed Effects:\n## (Intercept)  \n##       169.7\n<\/pre>\n<pre><code class=\"r\">summary(lmerMod)\n<\/code><\/pre>\n<pre>## Linear mixed model fit by REML. t-tests use Satterthwaite&#39;s method [\n## lmerModLmerTest]\n## Formula: y ~ 1 | g\n##    Data: dat\n## \n## REML criterion at convergence: 588.7\n## \n## Scaled residuals: \n##      Min       1Q   Median       3Q      Max \n## -2.28259 -0.47224  0.04513  0.70982  2.27324 \n## \n## Random effects:\n##  Groups   Name        Variance Std.Dev.\n##  g        (Intercept) 118.72   10.896  \n##  Residual              97.32    9.865  \n## Number of obs: 77, groups:  g, 10\n## \n## Fixed effects:\n##             Estimate Std. Error      df t value Pr(&gt;|t|)    \n## (Intercept)  169.679      3.635   9.093   46.67 3.85e-12 ***\n## ---\n## Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1\n<\/pre>\n<pre><code class=\"r\">(lmerMod2 &lt;- lmer(I(y-175) ~ 1|g, data=dat))\n<\/code><\/pre>\n<pre>## Linear mixed model fit by REML [&#39;lmerModLmerTest&#39;]\n## Formula: I(y - 175) ~ 1 | g\n##    Data: dat\n## REML criterion at convergence: 588.7467\n## Random effects:\n##  Groups   Name        Std.Dev.\n##  g        (Intercept) 10.896  \n##  Residual              9.865  \n## Number of obs: 77, groups:  g, 10\n## Fixed Effects:\n## (Intercept)  \n##      -5.321\n<\/pre>\n<pre><code class=\"r\">summary(lmerMod2)\n<\/code><\/pre>\n<pre>## Linear mixed model fit by REML. t-tests use Satterthwaite&#39;s method [\n## lmerModLmerTest]\n## Formula: I(y - 175) ~ 1 | g\n##    Data: dat\n## \n## REML criterion at convergence: 588.7\n## \n## Scaled residuals: \n##      Min       1Q   Median       3Q      Max \n## -2.28259 -0.47224  0.04513  0.70982  2.27324 \n## \n## Random effects:\n##  Groups   Name        Variance Std.Dev.\n##  g        (Intercept) 118.72   10.896  \n##  Residual              97.32    9.865  \n## Number of obs: 77, groups:  g, 10\n## \n## Fixed effects:\n##             Estimate Std. Error     df t value Pr(&gt;|t|)\n## (Intercept)   -5.321      3.635  9.093  -1.464    0.177\n<\/pre>\n<p>\ub9c8\uc9c0\ub9c9 \ubc29\ubc95\uc740 \uac00\uc911\uce58\ub97c \ud65c\uc6a9\ud558\uc5ec WLS\ub97c \uc2e4\uc2dc\ud558\ub294 \uac83\uc774\ub2e4. \uac19\uc740 \ud53c\ud5d8\uc790\uc758 \ud0a4\ub97c 4\ubc88 \uce21\uc815\ud55c \uacbd\uc6b0\uc640 1\ubc88\ub9cc \uce21\uc815\ud55c \uacbd\uc6b0, 4\ubc88 \uce21\uc815\ud55c \ud53c\ud5d8\uc790\uc758 \ud0a4\uc5d0 \ub300\ud55c \uac00\uc911\uce58\ub97c \\(&frac14;\\) \ub85c \ub0ae\ucdb0 \uc8fc\ub294 \uac83\uc774\ub2e4. (\uc774\uc5d0 \ube44\ud574 \uc704\uc758 <code>t.test<\/code>\ub294 \ubaa8\ub4e0 \uac00\uc911\uce58\ub97c 1\ub85c \uc8fc\ub294 \uacbd\uc6b0\uc774\ub2e4.) \uc55e\uc758 Mixed effect \ubaa8\ud615\uacfc \uc57d\uac04 \ub2e4\ub974\uc9c0\ub9cc \ube44\uc2b7\ud55c \uacb0\uacfc\ub97c \ubcf4\uc5ec\uc900\ub2e4.<\/p>\n<pre><code class=\"r\">library(dplyr)\nnewdat &lt;- dat %&gt;% group_by(g) %&gt;% summarise(y = mean(y), n=n())\n\nlmMod &lt;- lm(y ~ 1, weights=n, data=newdat)\nsummary(lmMod)\n<\/code><\/pre>\n<pre>## \n## Call:\n## lm(formula = y ~ 1, data = newdat, weights = n)\n## \n## Weighted Residuals:\n##    Min     1Q Median     3Q    Max \n## -35.53 -27.70   1.19  12.24  70.87 \n## \n## Coefficients:\n##             Estimate Std. Error t value Pr(&gt;|t|)    \n## (Intercept)  170.225      3.679   46.27 5.14e-12 ***\n## ---\n## Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1\n## \n## Residual standard error: 32.28 on 9 degrees of freedom\n<\/pre>\n<pre><code class=\"r\">#summary(lmMod)\nconfint(lmMod)\n<\/code><\/pre>\n<pre>##                2.5 %   97.5 %\n## (Intercept) 161.9033 178.5464\n<\/pre>\n<pre><code class=\"r\">lmMod2 &lt;- lm(I(y-175) ~ 1, weights=n, data=newdat)\nsummary(lmMod2)\n<\/code><\/pre>\n<pre>## \n## Call:\n## lm(formula = I(y - 175) ~ 1, data = newdat, weights = n)\n## \n## Weighted Residuals:\n##    Min     1Q Median     3Q    Max \n## -35.53 -27.70   1.19  12.24  70.87 \n## \n## Coefficients:\n##             Estimate Std. Error t value Pr(&gt;|t|)\n## (Intercept)   -4.775      3.679  -1.298    0.227\n## \n## Residual standard error: 32.28 on 9 degrees of freedom\n<\/pre>\n<pre><code class=\"r\">#summary(lmMod)\nconfint(lmMod2)\n<\/code><\/pre>\n<pre>##                2.5 %   97.5 %\n## (Intercept) -13.0967 3.546356\n<\/pre>\n<h2>\uacc4\ub7c9\uacbd\uc81c\ud559\uc5d0\uc11c\uc758 \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc<\/h2>\n<p>&lt;\ucd5c\uadfc \ud328\ub110\uc790\ub8cc \uc5f0\uad6c\uc758 \ub3d9\ud5a5&gt;<sup>[2]<\/sup> \uc5d0\uc11c\ub294 \uc784\uc758\ud6a8\uacfc\uc640 \uace0\uc815\ud6a8\uacfc\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc124\uba85\ud55c\ub2e4.<\/p>\n<p>\ubb38: \uc784\uc758\ud6a8\uacfc (random effects)\uc640 \uace0\uc815\ud6a8\uacfc (fixed effects)\ub780?<\/p>\n<p>\ub2f5: \uc624\ucc28\ud56d\uc774 \\(v_{it} = u_i +\u03b5_{it}\\) \uc77c \ub54c, \uc774 \uc911 \uac1c\uccb4\ubcc4 \ud6a8\uacfc( \\(u_i\\) )\uac00 \uc5b4\ub5a0\ud55c \uac83\uc778\uc9c0 \uc9c0\uce6d\ud558\ub294 \uc6a9\uc5b4\uc774\ub2e4. \\(u_i\\) \uac00 \ub3c5\ub9bd\ubcc0\uc218\ub4e4\uacfc \uc0c1\uad00( \\(i\\) \uc5d0 \uac78\uce5c \uc0c1\uad00)\ub418\uc5b4 \uc788\uc73c\uba74 \uc774 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\ub97c <strong>\uace0\uc815\ud6a8\uacfc<\/strong>\ub77c \ud55c\ub2e4. \ub3c5\ub9bd\ubcc0\uc218\ub4e4\uacfc \uc0c1\uad00\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc740 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\ub97c <strong>\uc784\uc758\ud6a8\uacfc<\/strong>\ub77c \ud55c\ub2e4. \\(u_i\\) \ub97c \ub450\uace0 \u201c\uace0\uc815\ud6a8\uacfc\u201d\uc774\uac70\ub098 \u201c\uc784\uc758\ud6a8\uacfc\u201d\ub77c\uace0 \ud558\ub294 \uac83\uc740 \uc801\uc808\ud558\uc9c0\ub9cc, \ubaa8\ud615\uc774 \uace0\uc815\ud6a8\uacfc\ub77c\uac70\ub098 \uc784\uc758\ud6a8\uacfc\ub77c\uace0 \ud558\ub294 \uac83\uc740 \ud0c0\ub2f9\ud558\uc9c0 \uc54a\ub2e4. \ud558\uc9c0\ub9cc \\(u_i\\) \uac00 \uc784\uc758\ud6a8\uacfc(\uace0\uc815\ud6a8\uacfc)\ub85c \uac04\uc8fc\ub418\ub294 \ubaa8\ud615\uc774\ub77c\ub294 \ub73b\uc5d0\uc11c \u201c\uc784\uc758\ud6a8\uacfc \ubaa8\ud615(\uace0\uc815\ud6a8\uacfc \ubaa8\ud615)\u201d\uc774\ub77c\uace0 \ud558\ub294 \uac83\uc740 \uc801\uc808\ud558\ub2e4.<\/p>\n<p><sup>[2]<sup>:<\/sup><\/sup> <a href=\"https:\/\/www.kli.re.kr\/klips\/downloadCnfrncSjIemFile.do?iemNo=480\">https:\/\/www.kli.re.kr\/klips\/downloadCnfrncSjIemFile.do?iemNo=480<\/a><\/p>\n<p>\ub2e4\uc74c \ub178\ud2b8\uc758 \uc815\uc758\ub294 \uc880 \ub354 \ud765\ubbf8\ub86d\ub2e4.<sup>[3]<\/sup> \ud2b9\ud788 random effect\uc640 fixed effect\ub97c \ubaa8\ub450 <strong>random<\/strong> variable\uc774\ub77c\uace0 \uc124\uba85\ud558\uace0 \uc788\ub2e4.<\/p>\n<p><sup>[3]<sup>:<\/sup><\/sup> <a href=\"https:\/\/www.schmidheiny.name\/teaching\/panel2up.pdf\">https:\/\/www.schmidheiny.name\/teaching\/panel2up.pdf<\/a><\/p>\n<p>In the random effects model, the individual-specific effct is a <strong>random<\/strong> variable that is uncorrelated with the explanatory variables.<\/p>\n<p>In the fixed effects model, the individual-specific effect is a <strong>random<\/strong> variable that is allowed to be correlated with the explanatory variables.<\/p>\n<p>\uc5ec\uae30\uc11c <strong>the individual-specific effect<\/strong>\ub780 \uc704\uc5d0\uc11c \uac1c\uccb4\ubcc4 \ud6a8\uacfc\ub77c\uace0 \uce6d\ud55c \ub2e4\uc74c \uc2dd\uc758 \\(u_i\\) \uc5d0 \ud574\ub2f9\ud55c\ub2e4. <\/p>\n<p>\\[Y_{ij} = \\beta_0 + x_{ij} \\beta_1 + u_i + e_{ij}\\]<\/p>\n<p>\uc774 \ubaa8\ud615\uc5d0\uc11c \uc124\uba85\ubcc0\uc218\uc758 \uac2f\uc218\ub97c \ub298\ub9ac\uba74 \ub2e4\uc74c\uacfc \ud45c\uae30\ud560 \uc218 \uc788\ub2e4. <\/p>\n<p>\\[Y_{ij} = \\beta_0 + x_{1ij} \\beta_1 + x_{2ij} \\beta_2 + \\cdots + u_i + e_{ij}\\]<\/p>\n<p>\uc774\ub54c <strong>\uac1c\uccb4\ubcc4 \ud6a8\uacfc<\/strong>\uc5d0 \ub300\ud574 \uc880 \ub354 \uc0dd\uac01\ud574\ubcf4\uc790. \uc5b4\ub5a4 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \uace0\uc815 \ud6a8\uacfc\uc778\uc9c0 \uc544\ub2cc\uc9c0\ub294 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \ub3c5\ub9bd\ubcc0\uc218\uc640 \uc0c1\uad00\uc774 \uc788\ub294\uc9c0 \uc544\ub2cc\uc9c0\uc5d0 \uc758\ud574 \uacb0\uc815\ub41c\ub2e4. \uadf8\ub7f0\ub370 <strong>\ub3c5\ub9bd\ubcc0\uc218\ub780 \ubaa8\ud615\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c0\uac8c \ub9c8\ub828\uc774\ub2e4.<\/strong> \ub530\ub77c\uc11c <strong>\uac1c\uccb4\ubcc4 \ud6a8\uacfc<\/strong>\uac00 \uace0\uc815\ud6a8\uacfc\uc778\uc9c0 \uc544\ub2cc\uc9c0\ub294 \uac1c\uccb4\ubcc4 \ud6a8\uacfc \uc790\uccb4\uc758 \uc131\uc9c8\uc774\ub77c\uae30 \ubcf4\ub2e4\ub294 \ubaa8\ud615\uc5d0 \uc758\ud574 \uacb0\uc815\ub418\ub294 \uac83\uc774\ub77c\uace0 \ubcfc \uc218 \uc788\ub2e4!<\/p>\n<p>\uc5b4\uca0b\ub4e0 (\uc804\ud1b5\uc801\uc778?) \ud1b5\uacc4\ud559\uacfc \uacc4\ub7c9\ud1b5\uacc4\ud559(\ub610\ub294 \uacbd\uc81c\ud1b5\uacc4\ud559)\uc5d0\uc11c \uc774\ub807\uac8c \ub2e4\ub978 \uc758\ubbf8\ub85c \uc6a9\uc5b4\ub97c \uc0ac\uc6a9\ud558\uace0 \uc788\uc74c\uc5d0\ub3c4 \uad50\uc721\uc790\ub4e4\uc740 \uc774\ub97c \ubb34\uc2dc\ud558\uace0 \uc788\ub2e4. \uc194\uc9c1\ud788 \uc774\uac74 \uad50\uc721\uc790\uc758 \uc798\ubabb\uc774\ub77c\uace0 \uc0dd\uac01\ud55c\ub2e4. \uc790\uae30 \ubd84\uc57c\uc5d0\uc11c \uc4f0\uc774\ub294 \uc758\ubbf8\ub9cc\uc744 \uac00\ub974\uce58\ub294 \uac83\uc740 \ud559\uc0dd\ub4e4\uc758 \uc774\ud574\ub97c \uc800\ud574\ud558\uace0, \uc624\ud574\ub97c \uc99d\uc9c4\uc2dc\ud0a4\uace0, \ud559\ubb38\uac04\uc758 \ud611\ub825\uc744 \uc5b4\ub835\uac8c \ud558\uace0, \ud559\ubb38\uc758 \ubc1c\uc804\uc744 \ub354\ub514\uac8c \ud55c\ub2e4. \uc790\uc138\ud788 \uc124\uba85\ud560 \uc2dc\uac04\uc774 \uc5c6\ub354\ub77c\ub3c4 \ub2e4\ub978 \ubd84\uc57c(\uc194\uc9c1\ud788 \uacc4\ub7c9 \uacbd\uc81c\ud559\uacfc \uc804\ud1b5\uc801\uc778 \ud1b5\uacc4\ud559\uc774 \uadf8\ub807\uac8c \uba3c \ubd84\uc57c\ub3c4 \uc544\ub2c8\ub2e4!)\uc5d0\uc11c\ub294 \uc5b4\ub5bb\uac8c \uc4f0\uc774\ub294\uc9c0 \uc5b8\uae09\uc774\ub77c\ub3c4 \ud574\uc57c \ud558\uc9c0 \uc54a\uaca0\ub294\uac00?<\/p>\n<p>\uadf8\ub9ac\uace0 \uacc4\ub7c9\uacbd\uc81c\ud559\uc5d0\uc11c \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc\ub97c \uc800\ub807\uac8c \uc124\uba85\ud558\ub294 \uac83\ub3c4 \uc194\uc9c1\ud788 \uc870\uae08 \ub9d8\uc5d0 \uc640 \ub2ff\uc9c0 \uc54a\ub294\ub2e4. <a href=\"http:\/\/141.164.34.82\/?p=1867\">\ub0b4\uc0dd\uc131 \ud3ec\uc2a4\ud305<\/a>\uc5d0\uc11c \uc5b8\uae09\ud588\uc9c0\ub9cc, \ucd94\uc815\uac12\uc758 \uc758\ubbf8\uac00 \ubb34\uc5c7\uc778\uc9c0, \uadf8\ub9ac\uace0 \uadf8\uac83\uc774 \uc815\ud655\ud55c \ubc29\ubc95\uc778\uc9c0\ub294 \uc5b4\ub5a4 \ubaa8\ud615\uc744 \uc0ac\uc6a9\ud588\ub294\uc9c0\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c4\ub2e4. \uc784\uc758\ud6a8\uacfc \ubaa8\ud615\uc740 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uc640 \uc624\ucc28\ud56d\uc774 \ub3c5\ub9bd\uc774\ub77c\ub294 \uac00\uc815\uc774 \ub4e4\uc5b4\uac00 \uc788\uae30 \ub54c\ubb38\uc5d0 \uac00\uc815\uc774 \uc131\ub9bd\ud558\ub294 \uc0c1\ud669\uc5d0\uc11c\ub9cc \ud6a8\uacfc \ucd94\uc815\ub7c9\uc5d0 \ud3b8\uc774\uac00 \uc5c6\ub2e4. \ubc18\uba74 \uace0\uc815\ud6a8\uacfc \ubaa8\ud615\uc740 \uadf8\ub7f0 \uac00\uc815\uc774 \uc5c6\uae30 \ub54c\ubb38\uc5d0 \uadf8\ub7f0 \uac00\uc815\uc774 \uc5c6\ub294 \uacbd\uc6b0\uc5d0\ub3c4 \ucd94\uc815\ub7c9\uc5d0 \ud3b8\uc774\uac00 \uc5c6\ub2e4. <\/p>\n<p>\ub530\ub77c\uc11c \uace0\uc815 \ud6a8\uacfc\ub780 \uace0\uc815 \ud6a8\uacfc \ubaa8\ud615\uc744 \uc368\uc57c \ud3b8\ud5a5\uc774 \uc5c6\uc774 \ucd94\uc815\uac12\uc744 \uad6c\ud560 \uc218 \uc788\ub294 \ud6a8\uacfc\uc774\uace0, \uc784\uc758 \ud6a8\uacfc\ub780 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uc640 \uc624\ucc28\ud56d\uc774 \ub3c5\ub9bd\uc774\uc5b4\uc11c \uc784\uc758 \ud6a8\uacfc \ubaa8\ud615\uc744 \uc368\ub3c4 \ud3b8\ud5a5 \uc5c6\uc774 \ucd94\uc815\uac12\uc744 \uad6c\ud560 \ud6a8\uacfc\ub77c\uace0 \uc124\uba85\ud558\ub294\uac8c \ub0ab\uc9c0 \uc54a\uc744\uae4c? <\/p>\n<h3>\uc608\uc2dc : \uc778\uacfc\uad00\uacc4 \ucd94\uc815(\uacc4\ub7c9\uacbd\uc81c\ud559)\uc5d0\uc11c \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758 \ud6a8\uacfc \uad6c\ubd84\uc774 \uc911\uc694\ud55c \uc774\uc720<\/h3>\n<p>\ub2e4\uc74c\uc740 \uc0ac\ub78c\ub4e4\uc758 \ud0a4\uc640 \uccb4\uc911\uc758 \uad00\uacc4\ub97c \ubcf4\uc5ec\uc900\ub2e4. <\/p>\n<p>\\[ \\textrm{weight}_{ij} = \\beta_0 + \\beta_{1} \\textrm{gender}_i + \\beta_2 \\textrm{height}_{ij} + u_{i} + e_{ij} \\]<\/p>\n<p>\uccb4\uc911\uc740 \ud3c9\uade0\uc801\uc73c\ub85c \ud0a4\uac00 1 \uc99d\uac00\ud560 \ub54c \\(\\beta_2\\) \ub9cc\ud07c \uc99d\uac00\ud55c\ub2e4. (\uc5ec\uae30\uc11c\ub294 \ud0a4\uac00 \ubcc0\ud560 \uc218 \uc788\ub2e4\uace0 \uac00\uc815\ud588\ub2e4. \uc544\ub2c8\uba74, \ud0a4\uac00 \uc131\uc7a5\ud558\uace0 \uc788\ub294 \uccad\uc18c\ub144 \ub370\uc774\ud130\ub77c\uace0 \uc0dd\uac01\ud574\ub3c4 \ubb34\ubc29\ud558\ub2e4.) <\/p>\n<p>\uc774\ub54c \\(\\textrm{height}\\) \uc640 \\(\\textrm{gender}\\) \uc5d0 \uc0c1\uad00\uad00\uacc4\uac00 \uc788\ub2e4. (\ubcf4\ud1b5 \ub0a8\uc790\uc758 \ud0a4\uac00 \uc5ec\uc790\ubcf4\ub2e4 \ud06c\ub2e4.) \ud558\uc9c0\ub9cc \\(\\textrm{height}_i\\) \uc640 \\(u_i\\) (\uac1c\uccb4\ubcc4 \ud6a8\uacfc)\uc5d0 \uc0c1\uad00\uc774 \uc5c6\ub2e4\uba74 \uc784\uc758 \ud6a8\uacfc \ubaa8\ud615\uc73c\ub85c \\(\\beta_2\\) \ub97c \ucd94\uc815\ud574\ub3c4 \\(\\beta_2\\) \uc758 \ucd94\uc815\ub7c9\uc740 \ube44\ud3b8\ud5a5(unbiased)\uc774\ub2e4. <\/p>\n<p>\ud558\uc9c0\ub9cc \uc704\uc758 \ubaa8\ud615\uc5d0\uc11c \\(\\textrm{gender}_i\\) \ub97c \uc81c\uac70\ud55c\ub2e4\uba74, \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ubcc0\ud55c\ub2e4.<\/p>\n<p>\\[ \\textrm{weight}_{ij} = \\beta_0 + \\beta_2 \\textrm{height}_{ij} + (\\beta_{1} \\textrm{gender}_i + u_{i}) + e_{ij} = \\beta_0 + \\beta_2 \\textrm{height}_{ij} + u_i&#8217; + e_{ij} \\]<\/p>\n<p>\uc0c8\ub85c\uc6b4 \uac1c\uccb4\ubcc4 \ud6a8\uacfc \\(u_i&#8217;\\) \ub294 \\(u_i&#8217; = \\beta_{1} \\textrm{gender}_i + u_{i}\\) \uc774\ubbc0\ub85c, \uc0c8\ub85c\uc6b4 \uac1c\uccb4\ubcc4 \ud6a8\uacfc \\(u_i&#8217;\\) \uc640 \\(\\textrm{height}_{ij}\\) \ub294 \uc0c1\uad00\uc774 \uc788\ub2e4. <\/p>\n<p>\ub530\ub77c\uc11c \uc774 \uac04\ub2e8\ud55c(reduced) \ubaa8\ud615\uc5d0\uc11c \uc784\uc758 \ud6a8\uacfc \ubaa8\ud615\uc73c\ub85c \\(\\beta_2\\) \ub97c \ucd94\uc815\ud558\uba74, \ucd94\uc815\ub7c9\uc740 \ud3b8\ud5a5\uc774 \uc0dd\uae34\ub2e4. \uc774\ub7f0 \uacbd\uc6b0\uc5d0 \uacc4\ub7c9\uacbd\uc81c\ud559\uc740 FE(fixed effects) \ubaa8\ud615\uc744 \uc4f0\ub77c\uace0 \uac00\ub974\ud0a8\ub2e4. \ub2e4\uc74c\uc758 \uc2dc\ubbac\ub808\uc774\uc158\uc740 \uac01\uac01\uc758 \ubaa8\ud615\uc5d0\uc11c \\(\\beta_2\\) \uc758 \ubd84\ud3ec\ub97c \ubcf4\uc5ec\uc900\ub2e4.<\/p>\n<ul>\n<li>RE(Random effects) full \ubaa8\ud615( \\(\\textrm{weight}_{ij} = \\beta_0 + \\beta_{1} \\textrm{gender}_i + \\beta_2 \\textrm{height}_{ij} + u_{i} + e_{ij}\\ \\ (u_i \\sim \\mathcal{N}(0, \\sigma_u^2))\\) )<\/li>\n<li>RE(Random effects) reduced \ubaa8\ud615( \\(\\beta_0 + \\beta_2 \\textrm{height}_{ij} + u_i&#8217; + e_{ij}\\ \\ (u_i&#8217; \\sim \\mathcal{N}(0, \\sigma_u^2))\\) )<\/li>\n<li>FE(Fixed effects) \ubaa8\ud615( \\(\\beta_0 + \\beta_2 \\textrm{height}_{ij} + u_i&#8217; + e_{ij}\\) )<\/li>\n<\/ul>\n<pre><code class=\"r\"># SIMULATION\nsNum = 11\nset.seed(sNum)\n\n# set nexp here ex) nexp=5000\n\nres &lt;- matrix(NA, nexp, 3)\nres2 &lt;- matrix(NA, nexp, 3)\ncolnames(res) &lt;- c(&quot;random_full&quot;, &quot;random_reduced&quot;, &quot;fixed&quot;)\ncolnames(res2) &lt;- c(&quot;random_full&quot;, &quot;random_reduced&quot;, &quot;fixed&quot;)\n\nfor (iexp in 1:nexp) {\n\n  n =50;\n  ns = sample(3:5, n, replace = TRUE) # length(ns)\n  gender = sample(0:1, n, replace = TRUE) # length(gender)\n  height = rnorm(n, 160, 10) + gender*10 # length(height)\n  u = rnorm(n, 0, 5)  # u_i\n  # length(weight)\n\n  us &lt;- weights &lt;- heights &lt;- genders &lt;- g &lt;-  vector(&quot;list&quot;, n)\n\n  for (i in 1:n) {\n    heights[[i]] &lt;- rnorm(ns[[i]], height[i], 5)\n    weights[[i]] &lt;- rnorm(ns[[i]], -20 + 0.8*heights[[i]] + gender[i]*10+ u[i], 5)  # e_ij\n\n    g[[i]] &lt;- rep(i, each=ns[i]) \n    genders[[i]] &lt;- rep(gender[i], each=ns[i])\n    us[[i]] &lt;- rep(u[i], each=ns[i])\n  }\n\n  heights &lt;- unlist(heights)\n  g &lt;- factor(unlist(g))\n  genders &lt;- factor(unlist(genders))\n  weights &lt;- unlist(weights)\n  us &lt;- unlist(us)\n\n  dat &lt;- data.frame(weights, heights, genders, g, us)\n\n  library(nlme)\n  lmeMod &lt;- lme(weights ~ genders + heights, random=~1|g, data= dat)\n  lmeMod2 &lt;- lme(weights ~ heights, random = ~1|g, data= dat)\n  lmeMod3 &lt;- lme(weights ~ genders, random = ~1|g, data= dat)\n\n  contrasts(dat$g) &lt;- contr.treatment(nlevels(g))\n  lmMod &lt;- lm(weights ~ heights + g, data= dat)\n  lmMod2 &lt;- lm(weights ~ genders + g, data= dat)\n\n  res[iexp, ] = c(coef(lmeMod)[1,&quot;heights&quot;],\n                  coef(lmeMod2)[1,&quot;heights&quot;],\n                  coef(lmMod)[&quot;heights&quot;])\n\n  res2[iexp, ] = c(coef(lmeMod)[1,&quot;genders1&quot;],\n                   coef(lmeMod3)[1,&quot;genders1&quot;],\n                   coef(lmMod2)[&quot;genders1&quot;])\n}\n<\/code><\/pre>\n<pre><code class=\"r\">#dfRes &lt;- as.data.frame(res)\napply(res, 2, function(x) { paste0(round(mean(x),02),&quot;(&quot;, round(sd(x),02),&quot;)&quot;) })\n<\/code><\/pre>\n<pre>##    random_full random_reduced          fixed \n##    &quot;0.8(0.06)&quot;   &quot;0.88(0.06)&quot;    &quot;0.8(0.08)&quot;\n<\/pre>\n<pre><code class=\"r\">library(ggplot2)\n#library(tidyr)\ndfRes &lt;- data.frame(value=c(res), cond = rep(colnames(res), each=nrow(res)))\nggplot(dfRes, aes(x=value, col=cond, fill=cond)) + \n  geom_density(alpha=0.2) + \n  geom_vline(xintercept=0.8, linetype=&#39;dotted&#39;) +\n  scale_x_continuous(name=&#39;estimated coefficient of `height`&#39;) \n<\/code><\/pre>\n<p><img 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alt=\"plot of chunk unnamed-chunk-7\"\/><\/p>\n<p>\uc704\uc758 \uc2dc\ubbac\ub808\uc774\uc158 \uacb0\uacfc\ub97c \ubcf4\uba74 \ub3c5\ub9bd\ubcc0\uc218\uc640 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uc5d0 \uc0c1\uad00\uc774 \uc788\uc744 \ub54c, RE \ubaa8\ud615\uc744 \uc4f0\uba74 \ud0a4\uc758 \uace0\uc815\ud6a8\uacfc\ub97c \uacfc\ub300 \ucd94\uc815\ud558\uac8c \ub428\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4. <\/p>\n<pre><code class=\"r\">#dfRes2 &lt;- as.data.frame(res2)\napply(res2, 2, function(x) { paste0(round(mean(x),02),&quot;(&quot;, round(sd(x),02),&quot;)&quot;) })\n<\/code><\/pre>\n<pre>##    random_full random_reduced          fixed \n##      &quot;10(1.7)&quot;     &quot;18(2.83)&quot;    &quot;17.83(14)&quot;\n<\/pre>\n<pre><code class=\"r\">library(ggplot2)\n#library(tidyr)\ndfRes2 &lt;- data.frame(value=c(res2), cond = rep(colnames(res2), each=nrow(res2)))\nggplot(dfRes2, aes(x=value, col=cond, fill=cond)) + \n  geom_density(alpha=0.2) + \n  geom_vline(xintercept=10, linetype=&#39;dotted&#39;) +\n  scale_x_continuous(name=&#39;estimated coefficient of `gender`&#39;) \n<\/code><\/pre>\n<p><img src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAH4CAMAAACR9g9NAAABOFBMVEUAAAAAADoAAGYAOmYAOpAAZmYAZrYAujgTtGAzMzM6AAA6ADo6AGY6OgA6Ojo6OmY6OpA6ZmY6ZrY6kLY6kNtNTU1NTW5NTY5NbqtNjshhnP9mAABmADpmAGZmOgBmOpBmZgBmZmZmkJBmtttmtv9uTU1uTY5uq+SOTU2OTY6ObquOjsiOq+SOyP+QOgCQOjqQOmaQkDqQtpCQ2\/+q09Krbk2rxcKr5P+yiYG2ZgC2Zjq2kDq2tma2z82225C2\/7a2\/\/+84ce+z7PC583GhGLIjk3Ijm7IyP\/I\/\/\/L3MDM8dfP2+\/SydvV4fXaforbkDrbtmbb25Db\/7bb\/\/\/f1ujf6\/\/kq27kq47k\/\/\/r6+vu1NLz2df4dm3+5OL\/tmb\/yI7\/25D\/29v\/5Kv\/\/7b\/\/8j\/\/9v\/\/+T\/\/\/+rYkHbAAAACXBIWXMAAAsSAAALEgHS3X78AAAVwElEQVR4nO3cjX\/bRhkHcDWUeMmAZRCP1dnGW0agWzogtCXAWDuaUsogdBltCMYxTVL9\/\/8Bp5NkyXo53T3So\/Nj\/X6fLbGVJ9b1vnl0cqw4CJFBJvA9AMRPAD\/QAH6gAfxA4wD\/76Y0VzhXNhYGHvftXFhVyUdrjnR48fvmozUH8J73zUdrDuA975uP1hzp8FjjiZEOL37ffLTmAN7zvvlozQG8533z0ZojHR5rPDHS4cXvm4\/WHMB73jcfrTmA97xvPlpzpMNjjSdGOrz4ffPRmgN4z\/vmozUH8J73zUdrjnR4rPHESIcXv28+WnMA73nffLTmAN7zvvlozZEOjzWeGOHwI4\/7di8EPOCzTZ4iHT6VB7xjpMNjjSdGOjw6nhjA91gIeMBnmzxFOjzWeGKkw6PjiZENP3oMeGIA32Mh4LuDxxpPjHR4dDwxgO+xEPCAzzZ5inR4rPHESIdPWx7wjgF8j4WAB3y2yVNkv8Hh6Hkw8j0GoUHH91gotON5J4BUCHhyxMMn8oB3jHT4APC0SIdHxxMjGj5yBzwtgO+xEPDdwWONJ0Y6PDqeGMD3WAh4wGebPEU6PNZ4YqTDo+OJkQ8fywPeMYDvsRDwXa7xgCdFOjw6nhjA91gIeMBnmzxFOjzWeGKkw6PjiQF8j4WAB3y2yVOkw2ONJ0Y6PDqeGMD3WAh4wGebPEU6PNZ4YqTDo+OJAXyPhYDvFF7LA94x0uEDwNMiHR4dTwzgeywEPOCzTZ4iHR5rPDHS4dHxxAC+x0LAAz7b5CnS4bHGEyMdHh1PTBX8m\/vjO9Hn61+Mf\/gsvQP49oWrDn95EJ4cqs8vD8OXB+kdwLcvXHX4Vw8je53Lw+TO1tZWj6OyzOj58+D58+cj3+OQmCr4pwv467vn2R3en3xKITqeHmPHX\/\/yWa79eSeAUgh4ekxr\/OufP8vuAL594arD6xN5dZQ\/GY\/HByt+Vo\/n8cTgeXyPhYAHfLbJUwDfYyHgscZnmzxFOjw6nhjA91gIeMBnmzxFOjzWeGIkwycND3hKAN9jIeABn23yFOnwWOOJkQ6PjicG8D0WAh7w2SZPkQ6PNZ4Y6fDoeGIA32Mh4AGfbfIU6fBY44mRDo+OJwbwPRYCHvDZJk+RDo81nhjp8Oh4YgDfYyHgAZ9t8hTp8FjjiZEOj44nBvA9FgIe8NkmT5EOjzWeGOnw6HhiAN9jIeABn23yFOnwWOOJkQ6PjicG8D0WAh7w2SZPkQ6PNZ4YB\/iVy+h5nJHvgUiM9I7HoZ4YwPdYCHis8dkmT5EOj44nBvA9FgIe8NkmT5EOjzWeGOnw6HhiAN9jIeABn23yFOnwWOOJkQ6ftjzgHQP4HgsBD\/hsk6dIhw8AT4t0eHQ8MYDvsRDwgM82eYp0eKzxxEiHR8cTA\/geCwHfyZwu3AFPiHR4rPHESIdHxxMD+B4LAQ\/4bJOnSIfHGk+MdHh0PDGA77EQ8IDPNnmKdHis8cRIh0fHEwP4HgsBD\/hsk6dIh8caT4x0eHQ8MYDvsRDwgM82eYp0eKzxxEiHR8cTA\/geCwEP+GyTp1TBv7k\/vhPfenkY3Xnvob7DOwHuhVjj26QK\/vIgPDmMbpyMD8PrT9LNvBPgXoiOb5Mq+FcPI\/swvP6L6vjXH4\/fPw\/Dra2tnkfWmPQ9jPEuxpRUwT9N4PWhXt16\/am+w\/uT716Ijm8TU8dr+DBM7\/BOgHNh7I41nhjjGh\/BR00f3+GdAOfCrOEBT0jtWf313fP0rD45xeedAOdCwLeK3OfxgG8V6fBY44mRDo+OJwbwPRYCHvDZJk+RDo81nhjp8Oh4YgDfYyHgAZ9t8hTp8FjjiZEOj44nBvA9FgIe8NkmT5EOjzWeGOnw6HhiAN9jIeABn23yFOnwWOOJkQ5f2\/GTCeO+iYWA54ef\/O1vNfKA1wE8Zd\/EQsDzr\/GAb4h0+IF0\/M29fZpvbdYYvkYe8DprCh+5S4Wfbwcbj8LTINgN5+\/uBZuhuv2tjwCfxrjGC4a\/+uAoPN2cf+eRuhF9\/PCR+jjfBnya5o6vll91+PnOmfo4U41+vK9u33x2dLob3e7OXAfwlH0TCwEP+GxTMdGhfnb7RXyo1\/DRAX8P8GlMa3zsLhM+O7nbD2N4dfvWdwGfJtfxSn6N4PsJ4Cn7JhYCHvDZJk+RDh8Anhbp8Oh4YtYavlIe8DqAZx1kc2VpmqfFdKidywL+am+3oZR3ApwLLdZ4mfD\/WQ43fBi\/HmQI7wQ4F65tx\/cOH4bxr4vqwjsBzoWAb5Uc\/Czq+KsPH\/HsqPNk72Fcfhfjyb\/iTHwMrGX6hr\/a22wo5f3Jdy7EGt8qOKtnHWRzZWma6+Dn27uz5XOw0zYv3GQdHx3jjQd63glwLhwafJm5C\/ibe4HO7bO1gq+SFwo\/3751NNs93gyPN6\/2lJP68L3uOt4Y3glwLjSs8Qv3NYKP+lsd6o9\/shnfUh9aXZUTpOxf7EUdv7EWh\/o1hp+\/fRQeK6jN3x91tMY3h3cCnAsHCX\/z2W92zjR4Rx0fRpf3qWXD9FC8E+BamHcfDPwP7u2Gp7e\/Vgfn3c7W+Ohqzs34Ck9J8A1rfIW8VPiOkz+5O94V9HTOruMBX5es43\/1hb6ct76UdwJcCwHfLrk1Prj99QdHhlLeCXAtXF\/4nl+Pbw7vBLgWru0a31My+FNZz+PXtuNHxTCoh\/mTO+NhPgrvBLgWri\/8n5cz6lg8idhf2S7BPx4B3jHZob7x90C8E+BauLTG18OX5QGvk7sQQ\/AaD3jnSD+rBzwxGbxq+Z99JvR5\/ADhK1+am2\/H1+jMihfrGOBv7u3rd2AQBj\/YNb4SPt3oAh\/9rn5f6u\/ql+Hz7msDP\/vexp+2g1tHs+hETL80d3MvuH02e3d744\/pqVl8lY7id+74mZxLrwYHvxn+7ywyja7A0S\/GnyriXSV2urno9PhiDTd4fVpvOqkHfOvCVvC7+sLIfQ2rL79RH+bfV3f1lhbwjeGdANdCwxq\/rvBK+jiGz3V8BfyxA3z8LH5NnsevK7xa3n+yq5lza3wRXn\/JqeOj39zNTH9NwzsBroVDg+86Yv+gAvD5zLfV4fpW08tslfD6\/ZHlndU3rvEl+bWEd8\/yWb3JfTXhGzteHHxPkX5WXwG\/7C4OflJMh9q5AJ5zkBaVpWme\/H05gF9O\/RoPeJtIh0fHEwN4zkFaVJamGfDmQsC3i3T4wa7xDX8jXfXlpW3S4Qfb8YBvgi\/KC4W3uRBD1XyxeJsU\/dqNqtHV5bdOATznIC0qreEtLsSY5d8mJXlhXm2sfOsU6fDNa\/y6wFtciBG9Fr94m5T0hfuw+q1TpMMPp+MtLsRIb6Udrz\/Md\/5Q9dYpVfBv7o\/vxLdeHubu8E6Aa+EA4RsvxFC3rhZvkxIv6sfqtOCq6q1TquAvD8KTw+jGyfgwuwP41oWr\/jz+1cOIOwyv\/6I6PrmztbXFMwBqkvcwDsrvYpy+g\/G\/ZL6TMQm+xYUYuTxN4PWhPrvD+5PvWoiObxdTx2v4V4DvrHDVX4\/PlvWXWOO7LFz1K3D0ifz13XMJZ\/Xl5\/FFd8BXZv2exwPeKoDnHKRFJR+tOYDnHKRFJR+tOdLhscYTIx0eHU8M4DkHaVHJR2sO4DkHaVHJR2uOdHis8cRIh0fHEwN4zkFaVPLRmrMm8I9Hiy8A3irS4YNm+II84HWkwhcaHvCuATzjIG0q+WjNATzjIG0q+WjNkQ6PNZ4Y6fDoeGIAzzhIm0o+WnPWDr7sDviqSIcvrfGAt4t0eHQ8MYBnHKRNJR+tOYBnHKRNJR+tOdLhscYTIx0eHU8M4BkHaVPJR2sO4BkHaVPJR2uOdHis8cRIhy92fIU74KsCeMZB2lTy0ZoDeMZB2lTy0ZojHb64xgPeMtLhbTp+WR7wOoBnHKRNJR+tOYBnHKRNJR+tOdLhbdZ4wFdEOjw6nhjAMw7SppKP1hyh8EV3wLtGOjzWeGIc4FcpyVsYZxklXyi+g7HEtzHuJdI73upQv9Ty6HgdwPMN0qqSj9Yc6fBWazzgy5EOj44nBvB8g7Sq5KM1B\/B8g7Sq5KM1Rzo81nhipMOneZ7IA94yawZf7Q74cgDPN0irSj5ac6TDB4CnRTo8Op4YwPMN0qqSj9YcwPMN0qqSj9Yc6fBY44mRDo+OJwbwfIO0quSjNWcY8Hl5wOtIh7db4wFfinR4dDwxgOcbpFUlH605gOcbpFUlH6050uEXa3z8ijzgbSMd\/jHgaQE83yCtKvlozQE83yCtKvlozZEOjzWeGOnwyx1f5w74UgDPN0irSj5acwDPN0irSj5ac6TDB4CnRTo8Op4YwPMN0qqSj9YcwPMN0qqSj9Yc6fBY44mRDm\/Z8Tl5wOsAnm+QVpV8tOasFXy9O+CLkQ4fAJ4WmfClhge8awDPNki7Sj5acwDPNki7Sj5ac6rg39wf31l8Vh\/ee6g3806AU2EGjzWemCr4y4Pw5DD9fP1Jupl3ApwK0fGtUwX\/6mFknnx+\/fH4\/fMw3Nra6nlkppTewzh+G+PKdzDG+xhXpgr+aQKvP6tbrz\/Vm3l\/8p0K3Ts+a3l0vE5jx4dh\/GFF4W3XeMAX0rjGvzwMLw\/1Zt4JcCpEx7dO7Vn99d3z9Kz+TryZdwKcCgHfOkN5Hg\/4QqTDY40nRjo8Op4YwLMN0q6Sj9ac9YFX8oC3j3T4IAdvcgd8IdLhHwOeFsCzDdKuko\/WHMCzDdKuko\/WHOnwWOOJkQ6PjicG8GyDtKvkozUH8GyDtKvkozVHOnxujTe6A74Q6fCPAU\/LYOAX8oDXATzbIO0q+WjNkQ5vvcYDfjki4csND3jXAJ5rkJaVfLTmAJ5rkJaVfLTmSIfHGk+MdHh0PDGA5xqkZSUfrTnDgU\/lAa8jHd5+jQf8UqTDo+OJATzXIC0r+WjNWR\/4yVuAd4hE+Lx7AHhapMOj44kBPNMgbSv5aM0BPNMgbSv5aM2RDp9b43+byf9DB\/CGSId\/XICPyb\/SKegDPp+1gs\/MF8nZAz6fNYL\/3VtF9dQe8OVIh0\/X+CdPJg\/eqnSP2z6TB7yOdPhE\/clfJw\/q4RN6wOeyBvCK\/csvG+A1PeBzcYBfmSy9hbFqdp3J55+\/9Y05k+nU99BXJ8I7\/knwZZzGjleZXExV0PE6ouH1QT6OcreAV4ns+xikbSUfrTmC4TN1F\/iL\/2p89kHaVvLRmiMWfondEf7Cyh7wSXgnwKFwlHMPcvBN8nl4C3vAJ+GdAIfCUbHdafBN9IBPwjsB9oWjJ2V3GnxEzzRI60o+WnNEwpfY7eBj+SV4Ez3gk\/BOgG3hdDrKgydr\/ORzKnz98R7wSXgnwLJwOr0YVTU8Hb626QGfhHcCrAoV+0X38DXygE\/COwE2hdqdAb6aHvBJeCfAonAaI9HXeC1fCV8lD\/gkvBPQWDhN3Ft0vAG+gh7wSXgnoKkwZa907wK+JA\/4JLwTYC5ctHtNwz\/oAL5ID\/gkvBNgLJzmdJbhgy7hl+UBn4R3AgyF07w7Z8cv0wM+Ce8E1BdOl2l44RU9aZDkSj5ac1Yeflpwr4KfPOgQftH0gE\/COwHVKbFXrvEpvNVvcBrhU3rAJ+GdgKpMpxVKho63ankL+Fge8El4J6CcqWp3T\/CaHvBJeCegFH2U9wZ\/wXEdNuCbK5PFvRHebY13gDdfndPdv5uP1pzVhF+c05WVqp\/NJfA2Z3fW8P+1vQIf8G0mIJfcqbwVfHTZFQe8bdMDvs0EZJkuT75PeDt6wLeZgDTLz9wb4QM3eCXvBt\/pX14Avray+AubrjveHf6iuesB32YCdEq\/qFsJ+CZ6wLeZgH9X\/n7WBl5fUm8L\/9WEAm8+4AO+zQRUsdut8X3AX3TylxeAL1VOK9mtOl67p\/AWx3oqfH3bA544AdM69orJrznS9wJfRw94ygQY1K3gY3d7+ORPJ2nwF+2uwwZ8eimdEd0KPnjQM3xF2wPeaQKa1Ssmv67hHeC\/mVjS168JhffRAbz1BFih28Cn7i7wX1nKN12VucAHvDW6nToFvln+G3W0t6K3uDhv6napzjDhp0ms5rRm8svuxTXeCt5uobe9VGc6rT7Zlwf\/5v74zuJzeocKP82Du81poXCkUtPvOfhGeQ1vc7h3e\/02i1z4y4Pw5DD9nN5xgs\/PQ9s5XaTU7jl3Z3gLefqv+EoRAv\/qYWSefE7ubG1tFaomCC3splapgn+awOvP6R3ffy1bk8Djvp0LJXZ8uKLw4vfdo\/VSeNb4zioBz5Xas\/rru+ednNW3qwQ8V7y\/SNOyEGs8MdLhxe+bj9YcwHveNx+tOYD3vG8+WnOkw2ONJ0Y6vPh989GaA3jP++ajNQfwnvfNR2uOdHis8cRIhxe\/bz5acwDved98tOYA3vO++WjNkQ6PNZ4Y6fDi981Haw7gPe+bj9YcwHveNx+tOdLhscYT4wDfmOJ1uEN5SIZB8gfwq\/iIPaRLeERQAD\/QAH6gAfxAA\/iBpiv461+Mf\/jszf3xew87esAwzP0tR0fpfpD6wTofZx\/pCv7lYfjy4PqTjh4tTvbXWx2l+0HqB+t8nH2kw0P95eHrj8fvn3f3gNnfa3aXjgepH4xjnOzpDv767rn657\/+tLMHDJ92P6FdD1I\/GMM4+dMJ\/In6sb\/+5bPoZpcz0H0nMQxy6S\/JBaWrjn\/982d6Db3scLHrfO3sfpD6wQa9xp+Mx+ODjk9vOz9b7n6Qhb8kFxQ8jx9oAD\/QAH6gAfxAA\/iBZgXhr350Nt85K25a3L65t1\/9fTf3gn31\/0+T711+jPwj6EpV8J1HdQ+U20NtlfCsIHxRvbCpFj4qqvjeigdN7sx2q2uX91BXJTyrAj8Lgs2oE4Nd9eH2i50X73wU\/OBesBueqi9Em850hbr7rY80y3w72HgUfXU3+earvWDjC\/X\/n3bO9NeUrt4+f3cveYQwjOujykeL\/W78ej\/MCtM9xFve+WhjPft9ZeCjHjzenym+DyOx+c6Lt4\/m6r+dFztn6aaoQh1459sR\/NUHR+HpprqrbsRfSjt+vvN1\/LXoe+NviR8h1Mft6Buz9lf3rvb25\/lCvYdky9tHHueENysCrxpM9aLq1M0wxnuhqee6e28dxd2rKk5Vfx9H8LGd+kmJfl70lzL4FzHyzj\/jB905u\/nsKF+fg09+4HKF8R4WW7zNCHdWBX4z\/qyY95fg\/7mR9HRcUQ0ff3MZfjPZ3AifK0zg0y39TUHPWRF4dVBVp1SnkcvuMvxmONMdH1dEh+O99FA\/u\/0iPtTrLy0f6mfReUL8LTn4ukN9vlDvYbHF45zwZkXg45Op8DhQ52BXexFaAv\/1XvDtvX21aXFyd+u7yyd3++k3L+ALJ3faM3qEMEzqc6Dq5O7H6amcLkz2kG7xNiHcWRV4f4mwB5iBw6tndsF6Pk9vysDhhxvADzSAH2gAP9AAfqD5P2w3eXyS\/TbjAAAAAElFTkSuQmCC\" alt=\"plot of chunk unnamed-chunk-8\"\/><\/p>\n<p>\ud558\uc9c0\ub9cc FE\ub97c \uc4f4\ub2e4\uace0 \uc5b8\uc81c\ub098 \ube44\ud3b8\ud5a5\uc801\uc778 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc704\uc758 \uacb0\uacfc\ub97c \ubcf4\uba74 <code>gender<\/code> \uacc4\uc218\uc758 \uacbd\uc6b0\ub294 FE\ub97c \uc368\ub3c4 \ucd94\uc815\ub7c9\uc740 \ud3b8\ud5a5\uc774 \uc788\ub2e4. \uc774\ub294 \ubb3c\ub860 <code>gender<\/code>\uc640 \uc624\ucc28\ud56d <code>e_{ij}<\/code>\uc758 \uc0c1\uad00(\ub0b4\uc0dd\uc131)\uc5d0 \uc758\ud55c \uac83\uc774\ub2e4. (\uc704\uc758 \uadf8\ub798\ud504\ub97c \ubcf4\uba74 \uc704\uc758 \uc0c1\ud669\uc5d0\uc11c RE\uac00 \uc544\ub2c8\ub77c \ubc18\ub4dc\uc2dc FE\ub97c \uc368\uc57c \ud55c\ub2e4\ub294 \uc8fc\uc7a5\uc5d0 \uace0\uac1c\ub97c \uc57d\uac04 \uac38\uc6b0\ub6b1\ud560 \uc218\ub3c4 \uc788\uc744 \uac83\uc774\ub2e4. RE\uc774 \ube44\ud574 FE\uac00 \uc800\ub807\uac8c\ub098 \ubd84\uc0b0\uc774 \ud070\ub370?)<\/p>\n<p>\uc704\uc758 \uadf8\ub798\ud504\uc5d0\uc11c \uac01 \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. <\/p>\n<ul>\n<li>RE(Random effects) full \ubaa8\ud615( \\(\\textrm{weight}_{ij} = \\beta_0 + \\beta_{1} \\textrm{gender}_i + \\beta_2 \\textrm{height}_{ij} + u_{i} + e_{ij}\\ \\ (u_i \\sim \\mathcal{N}(0, \\sigma_u^2))\\) )<\/li>\n<li>RE(Random effects) reduced \ubaa8\ud615( \\(\\beta_0 + \\beta_2 \\textrm{gender}_{i} + u_i&#8217; + e_{ij}\\ \\ (u_i&#8217; \\sim \\mathcal{N}(0, \\sigma_u^2))\\) )<\/li>\n<li>FE(Fixed effects) \ubaa8\ud615( \\(\\beta_0 + \\beta_2 \\textrm{gender}_{i} + u_i&#8217; + e_{ij}\\) )<\/li>\n<\/ul>\n<h2>\ub2e4\uc2dc \ud1b5\uacc4\ud559\uc758 \uace0\uc815 \ud6a8\uacfc\uc640 \uc784\uc758 \ud6a8\uacfc<\/h2>\n<p>\uc0ac\uc2e4 \uc218\uc2dd\uc73c\ub85c \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc\ub97c \uc368\ubcf4\uba74 \uc774 \ub458\uc758 \ucc28\uc774\uac00 \ubaa8\ud638\ud558\ub2e4. \ub2e4\uc74c\uc758 \uc218\uc2dd\uc5d0\uc11c \\(\\vec{\\beta}\\) \ub294 \uace0\uc815 \ud6a8\uacfc, \\(\\vec{u}\\) \ub294 \uc784\uc758 \ud6a8\uacfc\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\\[\\vec{y} = \\mathbb{X} \\vec{\\beta} + \\mathbb{Z} \\vec{u} + \\vec{\\epsilon}\\]<\/p>\n<p>\uadf8\ub7f0\ub370 \ub2e4\uc74c\ucc98\ub7fc \ud589\ub82c \\(\\mathbb{X}\\) \uc640 \\(\\mathbb{Z}\\) \ub97c \ud569\uce58\uace0, \ud589\ubca1\ud130 \\(\\vec{\\beta}\\) \uc640 \\(\\vec{u}\\) \ub97c \ud569\uccd0\uc11c \uc4f8 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n<p><img src=\"http:\/\/141.164.34.82\/wp-content\/uploads\/2019\/08\/term_fixed_and_random_01.png\" alt=\"\"\/><\/p>\n<p>\uad6c\uccb4\uc801\uc778 \uc608\ub85c \ub2e4\uc74c\uacfc \uac19\uc740 \uacbd\uc6b0\ub97c \ub4e4 \uc218 \uc788\ub2e4. <\/p>\n<p><img src=\"http:\/\/141.164.34.82\/wp-content\/uploads\/2019\/08\/term_fixed_and_random_02.png\" alt=\"\"\/><\/p>\n<p>\uadf8\ub807\ub2e4\uba74 \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc\uc758 \ucc28\uc774\ub294 \ubb34\uc5c7\uc778\uac00?<\/p>\n<p>\uc774 \ub458\uc758 \ucc28\uc774\ub294 \uace0\uc815 \ud6a8\uacfc\uc5d0 \ub300\ud574\uc11c\ub294 \ud2b9\ubcc4\ud55c \uac00\uc815\uc774 \ub4e4\uc5b4\uac00\uc9c0 \uc54a\uc9c0\ub9cc \uc784\uc758 \ud6a8\uacfc \\(\\vec{u} = (u_1, u_2, \\cdots, u_g)^T\\) \uc5d0 \ub300\ud574\uc11c\ub294 \ubd84\ud3ec \uac00\uc815 \\(u_i \\sim \\mathcal{N}(0, \\sigma_u^2)\\) \uc744 \ud558\uace0, \\(u_i\\) \ub97c \uac01\uac01 \ucd94\uc815\ud558\uc9c0 \uc54a\uace0, \ub300\uc2e0 \ub2e8 \ud558\ub098\uc758 \ubaa8\uc218 \\(\\sigma_u^2\\) \ub97c \ucd94\uc815\ud55c\ub2e4\ub294 \ucc28\uc774\uac00 \uc788\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(u_i\\) \ub97c \uacc4\ub7c9 \uacbd\uc81c\ud559\uc5d0\uc11c \ub9d0\ud558\ub294 \uace0\uc815\ud6a8\uacfc \ubaa8\ud615\uc73c\ub85c \ucd94\uc815\ud55c\ub2e4\uba74 \uc704\uc758 \ubaa8\ud615\uc5d0\uc11c &ldquo;\ubd84\ud3ec \uac00\uc815 \\(u_i \\sim \\mathcal{N}(0, \\sigma_u^2)\\) &quot;\ub97c \uc81c\uac70\ud574 \uc8fc\uae30\ub9cc \ud558\uba74 \ub41c\ub2e4.<\/p>\n<p>\ub530\ub77c\uc11c \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc\uc758 \ucc28\uc774\ub294 \ud6a8\uacfc(\uc5ec\uae30\uc11c\ub294 \\(\\vec{\\beta}\\) \ub610\ub294 \\(\\vec{u}\\) \ub85c \ub098\ud0c0\ub098\ub294 \uacc4\uc218)\ub97c \uc5b4\ub5a4 \ubaa8\ud615 \ub610\ub294 \uc5b4\ub5a4 \uac00\uc815\uc744 \ud1b5\ud574 \ucd94\uc815\ud558\ub290\ub0d0\uc758 \ucc28\uc774\ub9cc \uc788\uc744 \ubfd0\uc774\ub2e4.<\/p>\n<p>\uacc4\ub7c9 \uacbd\uc81c\ud559\uc5d0\uc11c \uace0\uc815\ud6a8\uacfc\uc640 \uc784\uc758\ud6a8\uacfc\uc758 \uad6c\ubd84\uc774 \ud544\uc694\ud55c \uc774\uc720\ub294 \ub0b4\uc0dd\uc131\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uac83\ucc98\ub7fc \uc778\uacfc \uad00\uacc4 \ucd94\uc815\uc744 \uc704\ud574\uc11c\ub294 \uc815\ud655\ud55c \ubaa8\ud615\uc744 \uc0ac\uc6a9\ud574\uc57c \ud558\uae30 \ub54c\ubb38\uc774\ub2e4. <\/p>\n<p>\uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \uc124\uba85\ubcc0\uc218\uc640 \uc0c1\uad00\uc774 \uc788\uc74c\uc5d0\ub3c4 \ubd88\uad6c\ud558\uace0, \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \uc124\uba85\ubcc0\uc218\uc640 \ub3c5\ub9bd\uc774\ub77c\ub294 \uac00\uc815\uc744 \uac00\uc9c0\uace0 \uc788\ub294 \uc784\uc758 \ud6a8\uacfc \ubaa8\ud615\uc744 \uc4f4\ub2e4\uba74 \uc124\uba85\ubcc0\uc218\uc758 <strong>\uc778\uacfc \uad00\uacc4<\/strong> \uacc4\uc218 \ucd94\uc815\ub7c9\uc774 \ud3b8\ud5a5(bias)\uc744 \uac00\uc9c0\uac8c \ub41c\ub2e4. <\/p>\n<p>\ud558\uc9c0\ub9cc \uc778\uacfc\uad00\uacc4\ub97c \ucd94\uc815\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74 \uc784\uc758\ud6a8\uacfc \ubaa8\ud615\ub3c4 \uad1c\ucc2e\ub2e4. \uc608\uce21 \ubaa8\ud615\uc73c\ub85c\ub294 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \uc124\uba85\ubcc0\uc218\uc640 \uc0c1\uad00\uc774 \uc788\uc5b4\ub3c4 \ud070 \ubb38\uc81c\uac00 \uc5c6\ub2e4. <\/p>\n<p>\uc624\ud788\ub824 \ub354 \uc911\uc694\ud55c \ubb38\uc81c\ub294 \uacfc\uc5f0 \uc784\uc758 \ud6a8\uacfc\uac00 \uac00\uc815\ud55c \uac83\ucc98\ub7fc \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub978\ub2e4\uace0 \ud560 \uc218 \uc788\ub294\uc9c0\uac00 \ub420 \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc \uba87\uba87 \uc5f0\uad6c\ub4e4\uc740 \uc784\uc758 \ud6a8\uacfc\uac00 \uc815\ub9d0 \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub974\uc9c0 \uc54a\ub294\ub2e4\uace0 \ud574\ub3c4 \ud070 \ubb38\uc81c\uac00 \uc5c6\ub2e4\uace0 \ubcf4\uace0\ud558\uc600\ub2e4(\ucc38\uace0\uc790\ub8cc 3). <\/p>\n<p>\uc2e4\ud5d8 \uc790\ub8cc\ub97c \ubd84\uc11d\ud558\ub294 \uacbd\uc6b0\uc5d0 \uac1c\uccb4\ubcc4 \ud6a8\uacfc\uac00 \uc815\ub9d0 \uc815\uaddc\ubd84\ud3ec\uc640 \uc720\uc0ac\ud558\ub2e4\uba74 random effects model\uc744 \uc4f0\uc9c0 \uc54a\uc744 \uc774\uc720\uac00 \uc5c6\uc5b4 \ubcf4\uc778\ub2e4. \uc2e4\ud5d8 \uc870\uac74\uc744 fixed effect\ub85c \ub450\uace0, group\uc744 random effects\ub85c \uc0ac\uc6a9\ud55c\ub2e4\uba74, \ud3c9\uade0\uc801\uc73c\ub85c fixed effect\uc640 random effects\uc5d0 \uc0c1\uad00\uc774 \uc5c6\ub2e4. (\ubb3c\ub860 group\uc758 \uac2f\uc218\uac00 \uc791\uc744 \uacbd\uc6b0\uc5d0\ub294 \uc6b0\uc5f0\ud788 \uc0dd\uae38 \uc218\ub3c4 \uc788\uc73c\ubbc0\ub85c fixed effects model\ub97c \uc0ac\uc6a9\ud574\uc57c \ud560 \uac83\uc774\ub2e4.) \uadf8\ub9ac\uace0 \ub2e4\ub978 \ud1b5\uc81c \ubcc0\uc218\uc758 \uacbd\uc6b0\ub294 \uadf8 \ubcc0\uc218\uc758 \uacc4\uc218\ub97c <strong>\uc778\uacfc \uad00\uacc4\ub85c \ud574\uc11d<\/strong>\ud558\uc9c0 \uc54a\ub294 \uc774\uc0c1 \uad1c\ucc2e\uc744 \uac83 \uac19\ub2e4. <\/p>\n<h2>\uc5b4\uca0b\ub4e0 \uc815\ub9ac<\/h2>\n<p><strong>\uc5b4\uca43\ub4e0 \uc815\ub9ac<\/strong>\ub97c \ud574\ubcf4\uc790\uba74, \uc804\ud1b5\uc801\uc778(?) \ud1b5\uacc4\ud559\uc5d0\uc11c fixed effect\uc640 random effect\uc758 \ucc28\uc774\ub294 \uacc4\uc218\uc758 \ubd84\ud3ec\uc5d0 \ub300\ud55c \uac00\uc815\uc774 \uc788\uc73c\ub0d0 \uc5c6\ub290\ub0d0\uc758 \ucc28\uc774\uc774\ub2e4. \uadf8\ub9ac\uace0 \ucd94\uc815\uc744 \ud560 \ub54c fixed effect\ub294 \ubaa8\uc218\ub97c \uba85\uc2dc\uc801\uc73c\ub85c \ucd94\uc815\ud558\uace0, random effect\uc758 \uacbd\uc6b0\ub294 \ubd84\ud3ec\uc5d0 \ub300\ud55c \ubaa8\uc218(\uc608. \ubd84\uc0b0)\uc744 \ucd94\uc815\ud55c\ub2e4\ub294 \ucc28\uc774\uac00 \uc788\ub2e4.<\/p>\n<p>\uacc4\ub7c9 \uacbd\uc81c\ud559\uc5d0\uc11c \uc784\uc758 \ud6a8\uacfc\ub294 \uc784\uc758\ud6a8\uacfc \ubaa8\ud615(RE model)\uc73c\ub85c \ucd94\uc815\ud574\ub3c4 \uc778\uacfc\uad00\uacc4\ub97c \ube44\ud3b8\ud5a5\uc801\uc73c\ub85c \ucd94\uc815\ud560 \uc218 \uc788\ub294 \ud6a8\uacfc\uc774\uace0, \uace0\uc815 \ud6a8\uacfc\ub294 \uc784\uc758\ud6a8\uacfc \ubaa8\ud615\uc73c\ub85c \ucd94\uc815\ud558\uba74 \ud3b8\ud5a5\uc774 \uc0dd\uae30\uae30 \ub54c\ubb38\uc5d0 \uace0\uc815\ud6a8\uacfc \ubaa8\ud615\uc744 \uc0ac\uc6a9\ud558\uc5ec \ucd94\uc815\ud574\uc57c \uc778\uacfc\uad00\uacc4 \uacc4\uc218\ub97c \ube44\ud3b8\ud5a5\uc801\uc73c\ub85c \ucd94\uc815\ud560 \uc218 \uc788\ub294 \ud6a8\uacfc\uc774\ub2e4. (\uacc4\uc218\ub97c \ube44\ud3b8\ud5a5\uc801\uc73c\ub85c \ucd94\uc815\ud55c\ub2e4. = \uacc4\uc218 \ucd94\uc815\ub7c9\uc774 \ube44\ud3b8\ud5a5\uc801\uc774\ub2e4.) \ub2e4\uc2dc \ub9d0\ud574 \uc784\uc758 \ud6a8\uacfc\ub294 \uc124\uba85\ubcc0\uc218\uc640 \ub3c5\ub9bd\uc778 \uacbd\uc6b0\uc774\uace0, \uace0\uc815 \ud6a8\uacfc\ub294 \uc124\uba85\ubcc0\uc218\uc640 \ub3c5\ub9bd\uc774 \uc544\ub2cc \uacbd\uc6b0\uc774\ub2e4. <\/p>\n<p>\uacb0\uad6d \ubca0\uc774\uc9c0\uc548\uc758 \uad00\uc810\uc5d0\uc11c \ubcfc \ub54c, \uc784\uc758\ud6a8\uacfc\ub294 \uc0ac\uc804 \ubd84\ud3ec\uac00 \uc8fc\uc5b4\uc9c4 \uac83\uc73c\uace0, \uace0\uc815\ud6a8\uacfc\ub294 \uc0ac\uc804\ubd84\ud3ec\uac00 uniform\ud55c \uacbd\uc6b0\ub85c \uc0dd\uac01\ud560 \uc218 \uc788\uc9c0 \uc54a\uc744\uae4c? <\/p>\n<p>\ub2e4\uc74c\uc758 \uae00\uc740 \uacc4\ub7c9\uc0dd\ubb3c\ud559(biometrics) \ub610\ub294 \uc0dd\ubb3c\ud1b5\uacc4\ud559(biostatistics) \uad00\uc810\uc744 \ub2e4\ub8e8\uace0 \uc788\ub2e4. (\uc194\uc9c1\ud788 \uc790\uc138\ud788 \uc77d\uc5b4\ubcf4\uc9c4 \uc54a\uc558\uc9c0\ub9cc, \uc9d1\ub2e8\ub4e4\uc774 \ubaa8\uc9d1\ub2e8 \uc804\uccb4\ub97c \ub098\ud0c0\ub0b4\ub290\ub0d0 \uadf8\ub807\uc9c0 \uc54a\ub290\ub0d0\uc758 \uad6c\ubd84\uc740 \uc911\uc694\ud574 \ubcf4\uc778\ub2e4.)<\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/rlbarter.github.io\/Practical-Statistics\/2017\/03\/03\/fixed-mixed-and-random-effects\/\">https:\/\/rlbarter.github.io\/Practical-Statistics\/2017\/03\/03\/fixed-mixed-and-random-effects\/<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/www.stats.ox.ac.uk\/%7Esnijders\/FixedRandomEffects.pdf\">https:\/\/www.stats.ox.ac.uk\/~snijders\/FixedRandomEffects.pdf<\/a><\/p>\n<\/li>\n<\/ul>\n<h2>\ucc38\uace0 \uc790\ub8cc<\/h2>\n<ul>\n<li>\n<p><a href=\"https:\/\/stats.stackexchange.com\/questions\/4700\/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode\/188559#188559\">https:\/\/stats.stackexchange.com\/questions\/4700\/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode\/188559#188559<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"http:\/\/support.sas.com\/documentation\/cdl\/en\/statug\/63033\/HTML\/default\/viewer.htm#statug_intromod_a0000000337.htm\">http:\/\/support.sas.com\/documentation\/cdl\/en\/statug\/63033\/HTML\/default\/viewer.htm#statug_intromod_a0000000337.htm<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/arxiv.org\/pdf\/1201.1980.pdf\">McCulloch and Neuhaus(2011). Misspecifying the Shape of a Random Effects Distribution<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/stats.stackexchange.com\/questions\/25308\/distribution-of-random-effects\">STACKEXCHANGE: Distribution of random effects<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/statmodeling.stat.columbia.edu\/2005\/01\/25\/why_i_dont_use\/\">https:\/\/statmodeling.stat.columbia.edu\/2005\/01\/25\/why_i_dont_use\/<\/a><\/p>\n<\/li>\n<\/ul>\n<hr\/>\n<h3>\ubd80\ub85d: JAGS\ub97c \ud65c\uc6a9\ud55c \ubca0\uc774\uc9c0\uc548 \ubd84\uc11d\uacfc <code>lme<\/code> \ub610\ub294 <code>lm<\/code>\uc744 \ud65c\uc6a9\ud55c \uc784\uc758\ud6a8\uacfc\/\uace0\uc815\ud6a8\uacfc \ubaa8\ud615\uc758 \ube44\uad50<\/h3>\n<h4>Data generation<\/h4>\n<pre><code class=\"r\">  n =50;\n  ns = sample(3:5, n, replace = TRUE) # length(ns)\n  gender = sample(0:1, n, replace = TRUE) # length(gender)\n  height = rnorm(n, 160, 10) + gender*10 # length(height)\n  u = rnorm(n, 0, 5)  # u_i\n  # length(weight)\n\n  us &lt;- weights &lt;- heights &lt;- genders &lt;- g &lt;-  vector(&quot;list&quot;, n)\n\n  for (i in 1:n) {\n    heights[[i]] &lt;- rnorm(ns[[i]], height[i], 5)\n    weights[[i]] &lt;- rnorm(ns[[i]], -20 + 0.8*heights[[i]] + gender[i]*10+ u[i], 5)  # e_ij\n\n    g[[i]] &lt;- rep(i, each=ns[i]) \n    genders[[i]] &lt;- rep(gender[i], each=ns[i])\n    us[[i]] &lt;- rep(u[i], each=ns[i])\n  }\n\n  heights &lt;- unlist(heights)\n  g &lt;- factor(unlist(g))\n  genders &lt;- factor(unlist(genders))\n  weights &lt;- unlist(weights)\n  us &lt;- unlist(us)\n\n  dat &lt;- data.frame(weights, heights, genders, g, us)\n\n  library(nlme)\n  lmeMod &lt;- lme(weights ~ genders + heights, random=~1|g, data= dat)\n  lmeMod2 &lt;- lme(weights ~ heights, random = ~1|g, data= dat)\n  lmeMod3 &lt;- lme(weights ~ genders, random = ~1|g, data= dat)\n<\/code><\/pre>\n<h4>\uc784\uc758 \ud6a8\uacfc \ubaa8\ud615<\/h4>\n<ul>\n<li>JAGS<\/li>\n<\/ul>\n<pre><code class=\"r\">model &lt;- &#39;\n\nmodel {\n    # model\n    for (i in 1:N) {\n        #predW[i] &lt;- beta0 + beta1*genders[i] + beta2*heights[i] + groupmean[g[i]]\n        predW[i] &lt;- beta0 + beta2*heights[i] + groupmean[g[i]]\n        weights[i] ~ dnorm(predW[i], tauE)\n    }\n\n    # priors\n    for (igroup in 1:G) {\n        groupmean[igroup] ~ dnorm(0, tauG)\n    }\n\n    tauE &lt;- pow(sigmaE, -2)\n    tauG &lt;- pow(sigmaG, -2)\n\n    #beta0 ~ dnorm(0, 0.01)\n    #beta1 ~ dnorm(0, 0.01)\n    #beta2 ~ dnorm(0, 0.01)\n    beta0 ~ dunif(-100,100)\n    #beta1 ~ dunif(-100,100)\n    beta2 ~ dunif(-1000,1000)\n    sigmaE ~ dunif(0,1000)\n    sigmaG ~ dunif(0,1000)\n}\n&#39;\ncat(model, file=&quot;currentModel.j&quot;)\n\nrequire(rjags)\nmyj &lt;- jags.model(&#39;currentModel.j&#39;,\n                  data = list(&#39;weights&#39; = weights-mean(weights), \n                              &#39;heights&#39; = heights-mean(heights),\n                              &#39;genders&#39;= genders,\n                              &#39;N&#39; = length(weights),\n                              &#39;G&#39; = nlevels(g),\n                              &#39;g&#39; = as.numeric(as.character(g))),\n                  n.chains = 3)\n\n# set n.iter here ex. n.iter =5000\nupdate(myj, n.iter = n.iter)\nn.thin=1\nmcmcsamp &lt;- \n  coda.samples(myj, \n               c(&#39;beta0&#39;, &#39;beta1&#39;, &#39;beta2&#39;, &#39;sigmaE&#39;, &#39;sigmaG&#39;), \n               n.iter*n.thin, thin=n.thin)\n<\/code><\/pre>\n<pre><code class=\"r\">summary(mcmcsamp)\n<\/code><\/pre>\n<pre>## \n## Iterations = 6001:11000\n## Thinning interval = 1 \n## Number of chains = 3 \n## Sample size per chain = 5000 \n## \n## 1. Empirical mean and standard deviation for each variable,\n##    plus standard error of the mean:\n## \n##            Mean      SD  Naive SE Time-series SE\n## beta0  0.001029 0.91480 0.0074693       0.029572\n## beta2  0.827124 0.05655 0.0004618       0.001270\n## sigmaE 4.826100 0.28072 0.0022921       0.003521\n## sigmaG 5.927431 0.73537 0.0060043       0.010025\n## \n## 2. Quantiles for each variable:\n## \n##           2.5%     25%       50%    75%  97.5%\n## beta0  -1.7909 -0.5963 0.0000117 0.5947 1.8332\n## beta2   0.7162  0.7896 0.8265548 0.8653 0.9395\n## sigmaE  4.3096  4.6331 4.8124548 5.0065 5.4091\n## sigmaG  4.6327  5.4101 5.8738156 6.3918 7.5322\n<\/pre>\n<pre><code class=\"r\">plot(mcmcsamp)\n<\/code><\/pre>\n<p><img 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\" alt=\"plot of chunk unnamed-chunk-12\"\/><\/p>\n<pre><code class=\"r\">print(mean(weights))\n<\/code><\/pre>\n<pre>## [1] 119.3505\n<\/pre>\n<ul>\n<li><code>lme<\/code><\/li>\n<\/ul>\n<pre><code class=\"r\">lmeMod &lt;- lme(weights ~ genders + heights, random=~1|g, data= dat)\nlmeMod2 &lt;- lme(weights ~ heights, random=~1|g, data= dat)\n#summary(lmeMod)\nintervals(lmeMod2)\n<\/code><\/pre>\n<pre>## Approximate 95% confidence intervals\n## \n##  Fixed effects:\n##                   lower        est.      upper\n## (Intercept) -37.4291885 -19.2095342 -0.9898798\n## heights       0.7230944   0.8318989  0.9407034\n## attr(,&quot;label&quot;)\n## [1] &quot;Fixed effects:&quot;\n## \n##  Random Effects:\n##   Level: g \n##                    lower     est.    upper\n## sd((Intercept)) 4.559427 5.777233 7.320309\n## \n##  Within-group standard error:\n##    lower     est.    upper \n## 4.272828 4.783595 5.355418\n<\/pre>\n<h4>\uace0\uc815\ud6a8\uacfc \ubaa8\ud615<\/h4>\n<ul>\n<li>JAGS<\/li>\n<\/ul>\n<pre><code class=\"r\">model &lt;- &#39;\n\nmodel {\n    # model\n    for (i in 1:N) {\n        #predW[i] &lt;- beta0 + beta1*genders[i] + beta2*heights[i] + groupmean[g[i]]\n        predW[i] &lt;- beta0 + beta2*heights[i] + groupmean[g[i]]\n        weights[i] ~ dnorm(predW[i], tauE)\n    }\n\n    # priors\n    groupmean[1] ~ dnorm(0, 100000)I(-0.005,0.005) # dummy coding\n    for (igroup in 2:G) {\n        #groupmean[igroup] ~ dnorm(0, tauG)\n        groupmean[igroup] ~ dunif(-100,100)\n    }\n\n    tauE &lt;- pow(sigmaE, -2)\n    tauG &lt;- pow(sigmaG, -2)\n\n    #beta0 ~ dnorm(0, 0.01)\n    #beta1 ~ dnorm(0, 0.01)\n    #beta2 ~ dnorm(0, 0.01)\n    beta0 ~ dunif(-100,100)\n    #beta1 ~ dunif(-100,100)\n    beta2 ~ dunif(-1000,1000)\n    sigmaE ~ dunif(0,1000)\n    sigmaG ~ dunif(0,1000)\n}\n&#39;\ncat(model, file=&quot;currentModel.j&quot;)\n\nrequire(rjags)\nmyj &lt;- jags.model(&#39;currentModel.j&#39;,\n                  data = list(&#39;weights&#39; = weights-mean(weights), \n                              &#39;heights&#39; = heights-mean(heights),\n                              &#39;genders&#39;= genders,\n                              &#39;N&#39; = length(weights),\n                              &#39;G&#39; = nlevels(g),\n                              &#39;g&#39; = as.numeric(as.character(g))),\n                  n.chains = 3)\n\nupdate(myj, n.iter = n.iter)\n\nn.thin=1\nmcmcsamp &lt;- \n  coda.samples(myj, \n               c(&#39;beta0&#39;, &#39;beta2&#39;, &#39;sigmaE&#39;, &#39;sigmaG&#39;), \n               n.iter*n.thin, thin=n.thin)\n<\/code><\/pre>\n<pre><code class=\"r\">summary(mcmcsamp)\n<\/code><\/pre>\n<pre>## \n## Iterations = 6001:11000\n## Thinning interval = 1 \n## Number of chains = 3 \n## Sample size per chain = 5000 \n## \n## 1. Empirical mean and standard deviation for each variable,\n##    plus standard error of the mean:\n## \n##            Mean        SD  Naive SE Time-series SE\n## beta0   -1.0553   2.14677 0.0175283       0.192093\n## beta2    0.7781   0.07624 0.0006225       0.002680\n## sigmaE   4.8235   0.27971 0.0022838       0.003784\n## sigmaG 495.8028 287.72874 2.3492953       2.376685\n## \n## 2. Quantiles for each variable:\n## \n##           2.5%     25%      50%      75%    97.5%\n## beta0  -5.0352  -2.561  -1.0240   0.4047   3.2214\n## beta2   0.6291   0.726   0.7777   0.8303   0.9281\n## sigmaE  4.3193   4.631   4.8078   5.0003   5.4234\n## sigmaG 23.9875 245.228 492.5443 744.7671 973.1308\n<\/pre>\n<pre><code class=\"r\">plot(mcmcsamp)\n<\/code><\/pre>\n<p><img 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alt=\"plot of chunk unnamed-chunk-16\"\/><\/p>\n<pre><code class=\"r\">print(mean(weights))\n<\/code><\/pre>\n<pre>## [1] 119.3505\n<\/pre>\n<ul>\n<li><code>lm<\/code><\/li>\n<\/ul>\n<pre><code class=\"r\">lmMod &lt;- lm(weights ~ heights + g, data= dat)\nconfint(lmMod, &quot;heights&quot;)\n<\/code><\/pre>\n<pre>##             2.5 %    97.5 %\n## heights 0.6290757 0.9264142\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\ub2e4\ub978 \ubd84\uc57c, \ub2e4\ub978 \uc2dc\uae30, \ub2e4\ub978 \uc6a9\uc5b4 \uc6a9\uc5b4\ub780 \ubd84\uc57c, \uc2dc\uae30\ub9c8\ub2e4 \ub2e4\ub974\uac8c \uc0ac\uc6a9\ub418\uae30 \ub9c8\ub828\uc774\ub2e4. \ub530\ub77c\uc11c \uac19\uc740 \uc6a9\uc5b4\uac00 \ub2e4\ub978 \ubd84\uc57c\uc5d0\uc11c\ub3c4 \ub2f9\uc5f0\ud788 \uac19\uc740 \uc758\ubbf8\ub97c \uac00\uc9c4\ub2e4\uace0 \uc0dd\uac01\ud558\ub294 \uac83\uc740 \uc2ac\uae30\ub86d\uc9c0 \ubabb\ud558\ub2e4. \uc61b\ub9d0\ub85c \uc5b4\ub9ac\ub2e4. (\u2018\uc2ac\uae30\ub86d\uc9c0 \ubabb\ud558\uace0 \ub454\ud558\ub2e4\u2019\ub780 \ub73b\uc744 \uac00\uc9c4 \u2018\uc5b4\ub9ac\uc11d\ub2e4\u2019\ub780 \ub2e8\uc5b4\uac00 \uc0dd\uae30\uae30 \uc774\uc804\uc5d0\ub294 \u2018\uc5b4\ub9ac\ub2e4\u2019\uac00 \u2018\uc5b4\ub9ac\uc11d\ub2e4\u2019\uc758 \uc758\ubbf8\ub97c \uc9c0\ub2c8\uace0 \uc788\uc5c8\ub2e4.[1] ) [1]: https:\/\/www.korean.go.kr\/nkview\/nknews\/200503\/80_1.html \ud1b5\uacc4\ud559\uc5d0\uc11c\uc758 \uc784\uc758 \ud6a8\uacfc \ud1b5\uacc4\ud559\uc5d0\uc11c \uc784\uc758 \ud6a8\uacfc(random effect)\ub294 sampling of sampling\uc758 \ub9e5\ub77d\uc5d0\uc11c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1928,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[146,319],"tags":[334,362,360,365,321,359,364,363,361],"jetpack_featured_media_url":"http:\/\/ds.sumeun.org\/wp-content\/uploads\/2019\/08\/term_random_fixed_effects.png","_links":{"self":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1923"}],"collection":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1923"}],"version-history":[{"count":9,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1923\/revisions"}],"predecessor-version":[{"id":1933,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1923\/revisions\/1933"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/media\/1928"}],"wp:attachment":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1923"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1923"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1923"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}