{"id":1867,"date":"2019-06-27T02:25:54","date_gmt":"2019-06-26T17:25:54","guid":{"rendered":"http:\/\/141.164.34.82\/?p=1867"},"modified":"2019-07-19T00:36:33","modified_gmt":"2019-07-18T15:36:33","slug":"%eb%b2%a0%ec%9d%b4%ec%a7%80%ec%95%88-%ea%b2%bd%eb%a1%9c-%eb%b6%84%ec%84%9d","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=1867","title":{"rendered":"\ub0b4\uc0dd\uc131: \ubca0\uc774\uc9c0\uc548 \ubd84\uc11d"},"content":{"rendered":"

\ubd88\ud655\uc2e4\uc744 \uac10\uc548\ud55c \ubd84\uc11d<\/h2>\n
set.seed(1)\nN <- 1000\ngene <- rnorm(N)\npower <- gene + (e1 = rnorm(N))\nheight <- 180 + 5*gene + (e2 = rnorm(N))\nability <- power + height\/10 + (e3 = rnorm(N))\nsummary(lm(ability ~ height)) # \uc608\uce21 \ubaa8\ud615\n<\/code><\/pre>\n
## \n## Call:\n## lm(formula = ability ~ height)\n## \n## Residuals:\n##     Min      1Q  Median      3Q     Max \n## -5.1616 -1.0461 -0.0145  1.0365  5.0071 \n## \n## Coefficients:\n##              Estimate Std. Error t value Pr(>|t|)    \n## (Intercept) -35.56398    1.59503  -22.30   <2e-16 ***\n## height        0.29756    0.00886   33.59   <2e-16 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n## \n## Residual standard error: 1.491 on 998 degrees of freedom\n## Multiple R-squared:  0.5306, Adjusted R-squared:  0.5301 \n## F-statistic:  1128 on 1 and 998 DF,  p-value: < 2.2e-16\n<\/pre>\n
summary(lm(ability ~ height + power)) # \uc6d0\uc778 \uacb0\uacfc \ubaa8\ud615\n<\/code><\/pre>\n
## \n## Call:\n## lm(formula = ability ~ height + power)\n## \n## Residuals:\n##     Min      1Q  Median      3Q     Max \n## -3.2322 -0.7124 -0.0099  0.7173  3.0623 \n## \n## Coefficients:\n##              Estimate Std. Error t value Pr(>|t|)    \n## (Intercept) -0.372789   1.551017   -0.24     0.81    \n## height       0.102167   0.008614   11.86   <2e-16 ***\n## power        1.013926   0.031168   32.53   <2e-16 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n## \n## Residual standard error: 1.039 on 997 degrees of freedom\n## Multiple R-squared:  0.7723, Adjusted R-squared:  0.7718 \n## F-statistic:  1691 on 2 and 997 DF,  p-value: < 2.2e-16\n<\/pre>\n
cov(height, power + e3)\n<\/code><\/pre>\n
## [1] 5.604122\n<\/pre>\n
\"\"\/<\/p>\n
\uc55e\uc758 \uc608\uc5d0\uc11c \\(\\mathbb{C}\\textrm{ov}(x, e)\\) \uc744 \uc815\ud655\ud558\uac8c \ubaa8\ub978\ub2e4\uba74, \uc5ec\ub7ec \uac00\uc9c0 \uac00\ub2a5\ud55c \uac12\uc744 \ub300\uc785\ud55c \ud6c4, \uc778\uacfc\uad00\uacc4 \uacc4\uc218\ub97c \uc0b4\ud3b4\ubcfc \uc218 \uc788\uc744 \uac83\uc774\ub2e4.[1]<\/sup><\/p>\n
[1]<\/sup> : \ud754\ud788 \uc774\ub807\uac8c \uac00\uc815\uc774 \ub2ec\ub77c\uc9d0\uc5d0 \ub530\ub77c \ubd84\uc11d \uacb0\uacfc \uc5b4\ub5bb\uac8c \ub2ec\ub77c\uc9c0\ub294\uc9c0\ub97c \ud655\uc778\ud558\ub294 \uacfc\uc815\uc744 \ubbfc\uac10\ub3c4 \ubd84\uc11d(Sensitivity Analysis)\ub77c\uace0 \ud55c\ub2e4. <\/p>\n
\\(\\mathbb{C}\\textrm{ov}(x, e)\\) \uac00 4 \ub610\ub294 5 \ub610\ub294 6\uc77c\uc9c0 \ubaa8\ub978\ub2e4\uba74,<\/p>\n
library(lavaan)\n<\/code><\/pre>\n
causalModel <- '\nability ~ height\nability ~~ b4*height\nb4 == 4'\n\ndat = data.frame(gene=gene, power=power, height=height, ability=ability)\nfit <- sem(causalModel, data=dat)\ncoef(fit)\n<\/code><\/pre>\n
##   ability~height               b4 ability~~ability   height~~height \n##            0.156            4.000            2.784           28.338\n<\/pre>\n
causalModel <- '\nability ~ height\nability ~~ b4*height\nb4 == 5'\n\ndat = data.frame(gene=gene, power=power, height=height, ability=ability)\nfit <- sem(causalModel, data=dat)\n#fit <- sem(causalModel, data=dat, estimator='GLS')\ncoef(fit)\n<\/code><\/pre>\n
##   ability~height               b4 ability~~ability   height~~height \n##            0.121            5.000            3.102           28.338\n<\/pre>\n
causalModel <- '\nability ~ height\nability ~~ b4*height\nb4 == 6'\n\ndat = data.frame(gene=gene, power=power, height=height, ability=ability)\n#fit <- sem(causalModel, data=dat)\nfit <- sem(causalModel, data=dat, estimator='GLS')\n#fit <- sem(causalModel, data=dat, estimator='WLS')\ncoef(fit)\n<\/code><\/pre>\n
##   ability~height               b4 ability~~ability   height~~height \n##            0.086            6.000            3.491           28.366\n<\/pre>\n
\uc778\uacfc\uad00\uacc4 \uacc4\uc218\ub294 0.15 \ub610\ub294 0.12 \ub610\ub294 0.09\ub85c \ucd94\uc815\ub418\uc5c8\ub2e4. \uadf8\ub7f0\ub370 \uc774\ub807\uac8c\ub9cc \ub9d0\ud558\uace0 \ub05d\ub0b4\uae30\uac00 \uaebc\ub9bc\uce59\ud55c\ub370 \uc65c\ub0d0\ud558\uba74 \uc774 \ucd94\uc815\uac12\uc5d0\ub294 \ud45c\uc900\uc624\ucc28\ub3c4 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n
\ubca0\uc774\uc9c0\uc548 \ubd84\uc11d\uc740 \ubaa8\ud615\uc774 \uc874\uc7ac\ud55c\ub2e4\uba74, \ubaa8\uc218\uc758 \ubd88\ud655\uc2e4\uc131\uc744 \uac10\uc548\ud558\uc5ec \ubd84\uc11d\uc744 \uc9c4\ud589\ud560 \uc218 \uc788\ub2e4. <\/p>\n
\ubca0\uc774\uc9c0\uc548 \ubd84\uc11d<\/h2>\n
\uc608\ub97c \ub4e4\uc5b4 \\(\\mathbb{C}\\textrm{ov}(x, e)\\) \uc758 \uc815\ud655\ud55c \uac12\uc744 \uc54c\uc9c0 \ubabb\ud558\uc9c0\ub9cc, \uadf8\ub807\ub2e4\uace0 \uc544\uc608 \uc5b4\ub5a4 \uac12\uc778\uc9c0 \ubaa8\ub974\ub294 \uac83\ub3c4 \uc544\ub2c8\ub77c\uba74 \uc5b4\ub5a8\uae4c? \uc774\ub97c\ud14c\uba74 5\ub97c \uc911\uc2ec\uc73c\ub85c \uadf8 \uadfc\ucc98\uc77c \uac00\ub2a5\uc131\uc774 \ud06c\uace0, \uc774\ub97c \ud655\ub960\ubd84\ud3ec\ub85c \ud3c9\uade0 5\uc774\uace0, \ud45c\uc900\ud3b8\ucc28 1\uc778 \uc815\uaddc\ubd84\ud3ec\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4\uace0 \ud558\uc790.<\/p>\n
\uadf8\ub9ac\uace0 \uc624\ucc28 \\(e\\) \ub294 \\(x\\) \uc5d0 \ub530\ub978 \uc870\uac74\ubd80 \ud3c9\uade0\uc774 \\(\\rho (x-\\bar{x})\\) \uc774\uace0, \ubd84\uc0b0\uc774 \\(1\/\\tau^2\\) \uc778 \uc815\uaddc\ubd84\ud3ec\ub97c \ub748\ub2e4\uace0 \uac00\uc815\ud574\ubcf4\uc790. \\(e\\) \uc758 \ubd84\ud3ec\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. ( \\(\\mathbb{C}\\textrm{ov}(x, e)\\) \uc774 \uc591\uc774\uace0, \\(x\\) \uc640 \\(e\\) \uac00 \uc120\ud615\uc801 \uad00\uacc4\ub97c \uac00\uc815\ud588\ub2e4.) <\/p>\n
\\(e|x \\sim \\mathcal{N}(\\rho \\cdot (x-\\bar{x}), 1\/\\tau^2)\\)<\/p>\n
\uc804\uccb4 \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n
\\[y = \\beta_0 + \\beta_1 x + e, \\ \\ e \\sim \\mathcal{N}(\\rho \\cdot (x-\\bar{x}), 1\/\\tau^2)\\]<\/p>\n
(\uc774\ub54c \\(\\mathbb{V}ar(e) = \\rho^2 \\mathbb{V}\\textrm{ar}(x) + 1\/\\tau^2, \\mathbb{C}\\textrm{ov}(x,e) = \\rho\\mathbb{V}\\textrm{ar}(x)\\) \uc774 \ub41c\ub2e4.)<\/p>\n
\uc5ec\uae30\uc11c \\(x\\) \ub97c \uc8fc\uc5b4\uc9c4 \uac12\uc73c\ub85c \uc0dd\uac01\ud558\uba74, \\(\\mathbb{E}(x)\\) \uc640 \\(\\mathbb{V}\\textrm{ar}(x)\\) \uc5ed\uc2dc \uc8fc\uc5b4\uc9c4 \\(x\\) \uc5d0\uc11c \uacc4\uc0b0\ud560 \uc218 \uc788\ub294 \uc0c1\uc218\uc774\uace0, \\(\\rho\\) \ub294 \\(\\mathbb{C}\\textrm{ov}(x,e)\/\\mathbb{V}\\textrm{ar}(x)\\) \uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\n
\uc790\ub8cc\ub294 \\(x\\) \uc640 \\(y\\) (\ud0a4\uc640 \uae30\ub7c9)\uc774\uace0 \ubaa8\uc218\ub294 \\(\\beta_0, \\beta_1, \\sigma^2 = \\tau^2, \\mathbb{C}\\textrm{ov}(e,x)\\) \uc774\uace0, \uc774\ub4e4 \ubaa8\uc218\ub97c \ud1b5\ud574 \\(\\rho = \\mathbb{C}\\textrm{ov}(x,e)\/\\mathbb{V}\\textrm{ar}(x), \\mathbb{V}ar(e) = \\rho^2 \\mathbb{V}\\textrm{ar}(x) + 1\/\\tau^2\\) \uc744 \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\n
\uc774 \ubaa8\ud615\uc744 JAGS\ub97c \ud65c\uc6a9\ud558\uc5ec \ubd84\uc11d\ud574\ubcf4\uc790.<\/p>\n
JAGS<\/h3>\n
JAGS\ub294 J<\/strong>ust A<\/strong>nother G<\/strong>ibbs S<\/strong>ampler\uc758 \uc57d\uc790\ub85c, \ub2e4\uc74c\uc758 \ub9c1\ud06c\uc5d0\uc11c \ub2e4\uc6b4 \ubc1b\uc744 \uc218 \uc788\ub2e4.<\/p>\n