{"id":925,"date":"2026-03-01T23:40:09","date_gmt":"2026-03-01T14:40:09","guid":{"rendered":"http:\/\/waurimal.kr\/?p=925"},"modified":"2026-03-01T23:40:11","modified_gmt":"2026-03-01T14:40:11","slug":"chap31-%ec%a0%90-%ec%b0%b8%ec%a1%b0-%ea%b3%b5%ea%b0%84-%eb%aa%a8%eb%8d%b8%eb%a7%81point-referenced-spatial-modeling","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=925","title":{"rendered":"Chap31. \uc810-\ucc38\uc870 \uacf5\uac04 \ubaa8\ub378\ub9c1(Point-Referenced Spatial Modeling)"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc138\uc694!<\/p>\n\n\n\n<p>\uc624\ub298\uc740 <strong>\uc810-\ucc38\uc870 \uacf5\uac04 \ubaa8\ub378\ub9c1(Point-Referenced Spatial Modeling)<\/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 jamovi\uc758 \uc0ac\uc6a9\ubc95\uc744 \uc124\uba85\ud558\ub418, jamovi\uc758 \uae30\ubc18\uc774 \ub418\ub294 R \ucf54\ub4dc\ub97c \ud568\uaed8 \uc81c\uc2dc\ud558\uc5ec \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131\ubd80\ud130 \ubd84\uc11d, \uc2dc\uac01\ud654\uae4c\uc9c0 \uc644\ubcbd\ud558\uac8c \uad6c\ud604\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. \ucd08\ub4f1\ud559\uc0dd\ub3c4 \uc774\ud574\ud558\ub294 &#8216;\uacf5\uac04 \ubaa8\ub378\ub9c1&#8217; \uc774\uc57c\uae30<\/h2>\n\n\n\n<p>\ucd08\ub4f1\ud559\uad50 \uad50\uc2e4\uc744 \ub5a0\uc62c\ub824 \ubcfc\uae4c\uc694? \uad50\uc2e4\uc5d0\uc11c \uc5b4\ub5a4 \uce5c\uad6c\uac00 \uc9c0\uc6b0\uac1c \uac00\ub8e8\ub97c \ubd88\uba70 \uc7a5\ub09c\uc744 \uce69\ub2c8\ub2e4. \uc774 \uc7a5\ub09c\uafb8\ub7ec\uae30 \uce5c\uad6c \ubc14\ub85c \uc606\uc5d0 \uc549\uc740 \uc9dd\uafcd\uc740 \uc9c0\uc6b0\uac1c \uac00\ub8e8\ub97c \ub9ce\uc774 \ub4a4\uc9d1\uc5b4\uc4f0\uaca0\uc9c0\ub9cc, \uad50\uc2e4 \ub9e8 \ub4a4\uc5d0 \uc549\uc740 \uce5c\uad6c\ub294 \uac70\uc758 \ud53c\ud574\uac00 \uc5c6\uc744 \uac70\uc608\uc694. \uc989, <strong>&#8220;\uac70\ub9ac\uac00 \uac00\uae4c\uc6b8\uc218\ub85d \uc11c\ub85c\uc5d0\uac8c \ubbf8\uce58\ub294 \uc601\ud5a5\uc774 \ud06c\uace0, \uba40\uc5b4\uc9c8\uc218\ub85d \uadf8 \uc601\ud5a5\uc774 \uc904\uc5b4\ub4e0\ub2e4&#8221;<\/strong>\ub294 \uc0ac\uc2e4\uc744 \uc6b0\ub9ac\ub294 \uc9c1\uad00\uc801\uc73c\ub85c \uc54c\uace0 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-19\">\uacf5\uac04 \ubaa8\ub378\ub9c1\ub3c4 \uc774\uc640 \ub611\uac19\uc2b5\ub2c8\ub2e4! \uae30\uc874\uc758 \ub2e4\uce35\ubaa8\ud615(MLM)\uc774 \uc8fc\ub85c \ud559\uc0dd\ub4e4\uc744 \ud559\uae09\uc774\ub098 \ud559\uad50\ub77c\ub294 &#8216;\uadf8\ub8f9&#8217;\uc73c\ub85c \ubb36\uc5b4\uc11c \uad00\ucc30\ud558\ub294 \ubc29\uc2dd\uc774\ub77c\uba74 , <strong>\uc810-\ucc38\uc870 \uacf5\uac04 \ubaa8\ub378\ub9c1<\/strong>\uc740 \uac01 \ub370\uc774\ud130\uac00 \uc874\uc7ac\ud558\ub294 &#8216;\uc815\ud655\ud55c \uc9c0\ub9ac\uc801 \uc88c\ud45c(\uc608: \uc704\ub3c4\uc640 \uacbd\ub3c4)&#8217;\ub97c \ubc14\ud0d5\uc73c\ub85c \ubd84\uc11d\uc744 \uc9c4\ud589\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc774 \ubd84\uc11d\uc5d0\uc11c\ub294 \ub450 \uac00\uc9c0 \uc911\uc694\ud55c \uad00\uacc4(\uc5f0\uad00\uc131)\ub97c \uc0b4\ud3b4\ubd05\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\uccab \ubc88\uc9f8 \uad00\uacc4:<\/strong> \uc11c\ub85c \ub2e4\ub978 \uc704\uce58(\ud559\uad50)\uc5d0 \uc788\ub294 &#8216;\uac19\uc740&#8217; \ubcc0\uc218 \uac04\uc758 \uad00\uacc4\uc785\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, A\ud559\uad50\uc758 \uc218\ud559 \uc131\uc801\uc740 \ubc14\ub85c \uc606\ub3d9\ub124 B\ud559\uad50\uc758 \uc218\ud559 \uc131\uc801\uacfc \ube44\uc2b7\ud560 \ud655\ub960\uc774 \ub192\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ub450 \ubc88\uc9f8 \uad00\uacc4:<\/strong> \uac19\uc740 \uc704\uce58(\ud559\uad50) \ub0b4\uc5d0 \uc788\ub294 &#8216;\uc11c\ub85c \ub2e4\ub978&#8217; \ubcc0\uc218 \uac04\uc758 \uad00\uacc4\uc785\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, A\ud559\uad50 \ud559\uc0dd\ub4e4\uc758 &#8216;\uc218\ud559 \uc131\uc801&#8217;\uacfc &#8216;\ud589\ubcf5\ub3c4&#8217; \uc0ac\uc774\uc758 \uad00\uacc4\ub97c \ub73b\ud569\ub2c8\ub2e4.<\/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\">2. \uc218\ub9ac\uc801 \ubaa8\ub378\uc758 \uc774\ud574: \ub2e8\ubcc0\ub7c9 \ubc0f \ub2e4\ubcc0\ub7c9 \uacf5\uac04 \ud68c\uadc0\ubaa8\ud615<\/h2>\n\n\n\n<p>\uc774\uc81c \ub300\ud559\uc6d0\uc0dd \ubaa8\ub4dc\ub85c \uc804\ud658\ud558\uc5ec \uc870\uae08 \ub354 \uc218\ub9ac\uc801\uc73c\ub85c \uc5c4\ubc00\ud558\uac8c \uc811\uadfc\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \ub2e8\ubcc0\ub7c9 \uacf5\uac04 \ud68c\uadc0\ubaa8\ud615 (Univariate Spatial Regression)<\/h3>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-22\">\uc9c0\ub9ac\uc801 \uc704\uce58 <math data-latex=\"s\"><semantics><mi>s<\/mi><annotation encoding=\"application\/x-tex\">s<\/annotation><\/semantics><\/math>\uc5d0 \uc704\uce58\ud55c \ud559\uad50\uc758 \uc131\uacfc(\uc608: \uc218\ud559 \uc131\uc801)\ub97c <math data-latex=\"y(s)\"><semantics><mrow><mi>y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y(s)<\/annotation><\/semantics><\/math>\ub77c\uace0 \ud560 \ub54c, \uc774\ub97c \uc124\uba85\ud558\ub294 \ud68c\uadc0 \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"y(s) = x(s)'\\beta + u(s) + \\epsilon(s)\"><semantics><mrow><mi>y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>x<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><\/msup><mi>\u03b2<\/mi><mo>+<\/mo><mi>u<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>\u03f5<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y(s) = x(s)&#8217;\\beta + u(s) + \\epsilon(s)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"x(s)'\\beta\"><semantics><mrow><mi>x<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><\/msup><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x(s)&#8217;\\beta<\/annotation><\/semantics><\/math>: \ud559\uad50\uc758 \uad50\uc721\uc608\uc0b0\uc774\ub098 \uc9c0\uc5ed\uc758 \uc0ac\ud68c\uacbd\uc81c\uc801 \ubc30\uacbd(SES)\ucc98\ub7fc \uc6b0\ub9ac\uac00 \uce21\uc815\ud55c \uc124\uba85 \ubcc0\uc218\ub4e4\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><math data-latex=\"u(s)\"><semantics><mrow><mi>u<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">u(s)<\/annotation><\/semantics><\/math>: \uacf5\uac04 \ud655\ub960 \ud6a8\uacfc(Spatial random effects)\uc785\ub2c8\ub2e4. \uc6b0\ub9ac\uac00 \ubbf8\ucc98 \uce21\uc815\ud558\uc9c0 \ubabb\ud588\uc9c0\ub9cc \uacf5\uac04\uc801 \ud328\ud134\uc744 \uac00\uc9c4 \uc694\uc778\ub4e4(\uc608: \uc778\uadfc \uc9c0\uc5ed\uc758 \uad50\uc721\uc5f4)\uc744 \uc7a1\uc544\ub0c5\ub2c8\ub2e4. \uac00\uc6b0\uc2a4 \uacfc\uc815(Gaussian process)\uc73c\ub85c \ubaa8\ud615\ud654\ub429\ub2c8\ub2e4.<\/li>\n\n\n\n<li><math data-latex=\"\\epsilon(s)\"><semantics><mrow><mi>\u03f5<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon(s)<\/annotation><\/semantics><\/math>: \ub3c5\ub9bd\uc801\uc778 \ubc31\uc0c9 \uc7a1\uc74c(white-noise process)\uc73c\ub85c, \uc21c\uc218\ud55c \uce21\uc815 \uc624\ucc28\ub098 \uc544\uc8fc \ubbf8\uc2dc\uc801\uc778 \ubcc0\ub3d9\uc131\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4. \ud754\ud788 &#8216;\ub108\uac9f(nugget)&#8217;\uc774\ub77c\uace0 \ubd80\ub985\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \ub300\uaddc\ubaa8 \ub370\uc774\ud130\uc758 \ud55c\uacc4\uc640 \uc608\uce21 \ud504\ub85c\uc138\uc2a4 \ubaa8\ud615 (Predictive Process Models)<\/h3>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-26\">\ud559\uad50 \uc218\uac00 10,000\uac1c\ucc98\ub7fc \uc5c4\uccad\ub098\uac8c \ub9ce\uc544\uc9c0\uba74 \uc5b4\ub5bb\uac8c \ub420\uae4c\uc694? \uacf5\uac04 \ubd84\uc11d\uc5d0\uc11c\ub294 \ub370\uc774\ud130 \uac1c\uc218(<math data-latex=\"n\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math>)\uc758 \uc138\uc81c\uacf1\uc778 <math data-latex=\"O(n^3)\"><semantics><mrow><mi>O<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mn>3<\/mn><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n^3)<\/annotation><\/semantics><\/math> \uc218\uc900\uc73c\ub85c \uacc4\uc0b0\uc774 \ubcf5\uc7a1\ud574\uc9c0\ub294 \uc774\ub978\ubc14 &#8216;Big <math data-latex=\"n\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math>&#8216; \ubb38\uc81c\uac00 \ubc1c\uc0dd\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-27\">\uc774\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uc804\uccb4 \ud559\uad50 \uc911 \ub300\ud45c\uc131\uc744 \ub760\ub294 \uc18c\uc218\uc758 \uc9c0\uc810(\ub9e4\ub4ed, knots)\ub9cc\uc744 \uc120\ud0dd\ud558\uc5ec \ucc28\uc6d0\uc744 \ucd95\uc18c\ud558\ub294 <strong>\uc608\uce21 \ud504\ub85c\uc138\uc2a4 \ubaa8\ud615(Predictive process models)<\/strong>\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4. \uc774\ub294 \ub370\uc774\ud130\uc758 \uacf5\uac04\uc801 \uc815\ubcf4\ub97c \uc783\uc9c0 \uc54a\uc73c\uba74\uc11c\ub3c4 \uacc4\uc0b0 \uc18d\ub3c4\ub97c \ud68d\uae30\uc801\uc73c\ub85c \ub192\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 \ub2e4\ubcc0\ub7c9 \uacf5\uac04 \ud68c\uadc0\ubaa8\ud615 (Multivariate Spatial Regression)<\/h3>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-28\">\ub9cc\uc57d \uc218\ud559 \uc131\uc801(<math data-latex=\"y_1\"><semantics><msub><mi>y<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">y_1<\/annotation><\/semantics><\/math>)\uacfc \ud559\uc0dd \ud589\ubcf5\ub3c4(<math data-latex=\"y_2\"><semantics><msub><mi>y<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">y_2<\/annotation><\/semantics><\/math>)\ub77c\ub294 \ub2e4\uc218\uc758 \uacb0\uacfc \ubcc0\uc218\ub97c \ub3d9\uc2dc\uc5d0 \ubd84\uc11d\ud558\uace0 \uc2f6\ub2e4\uba74 \ub2e4\ubcc0\ub7c9 \ubaa8\ud615\uc744 \ud655\uc7a5\ud558\uc5ec \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"y(s) = X(s)'\\beta + u(s) + \\epsilon(s)\"><semantics><mrow><mi>y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>X<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo lspace=\"0em\" rspace=\"0em\" class=\"tml-prime\">\u2032<\/mo><\/msup><mi>\u03b2<\/mi><mo>+<\/mo><mi>u<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>\u03f5<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y(s) = X(s)&#8217;\\beta + u(s) + \\epsilon(s)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-29\">\uc774\ub54c \uad6c\uc870\ub294 \ub3d9\uc77c\ud558\uc9c0\ub9cc, <math data-latex=\"y(s)\"><semantics><mrow><mi>y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y(s)<\/annotation><\/semantics><\/math>, <math data-latex=\"u(s)\"><semantics><mrow><mi>u<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">u(s)<\/annotation><\/semantics><\/math>, <math data-latex=\"\\epsilon(s)\"><semantics><mrow><mi>\u03f5<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon(s)<\/annotation><\/semantics><\/math>\uac00 \ub2e8\uc77c \uc22b\uc790\uac00 \uc544\ub2cc \ubca1\ud130(vector) \ud615\ud0dc\uac00 \ub418\uba70, \ubcc0\uc218\ub4e4 \uac04\uc758 \uad50\ucc28-\uacf5\ubd84\uc0b0(cross-covariance)\uc744 \uace0\ub824\ud558\uac8c \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p id=\"p-rc_eec79db64ea504fa-30\"><strong>\ud83d\udca1 \uba74\uc801 \ub370\uc774\ud130(Areal Data)\uc640\uc758 \ucc28\uc774\uc810<\/strong> \uad50\uc721\uccad\uc5d0\uc11c \uac1c\uc778\uc815\ubcf4 \ubcf4\ud638\ub97c \uc704\ud574 \uac1c\ubcc4 \ud559\uad50\uc758 \uc704\uce58\ub97c \uc228\uae30\uace0 &#8220;\uc218\uc6d0\uc2dc \uc7a5\uc548\uad6c \uc804\uccb4 \ud3c9\uade0 \uc131\uc801&#8221;, &#8220;\uad8c\uc120\uad6c \uc804\uccb4 \ud3c9\uade0 \uc131\uc801&#8221;\ucc98\ub7fc \ud589\uc815 \uad6c\uc5ed \ub2e8\uc704\ub85c \ubb36\uc5b4\uc11c \ubc1c\ud45c\ud560 \ub54c\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ucc98\ub7fc \ubd88\uc5f0\uc18d\uc801\uc774\uace0 \uc774\uc6c3\ud55c &#8216;\uad6c\uc5ed&#8217; \uac04\uc758 \uc778\uc811\uc131(adjacency)\uc744 \ubc14\ud0d5\uc73c\ub85c \ubd84\uc11d\ud558\ub294 \uac83\uc744 <strong>\uba74\uc801 \ubaa8\ud615(CAR, SAR \ub4f1)<\/strong>\uc774\ub77c\uace0 \ud569\ub2c8\ub2e4. \ubc18\uba74 \uc624\ub298 \uc6b0\ub9ac\uac00 \ub2e4\ub8e8\ub294 \uc810-\ucc38\uc870 \ubaa8\ud615\uc740 \uacf5\uac04 \uc0c1\uc758 \uc5b4\ub290 \uc9c0\uc810\uc5d0\uc11c\ub4e0 \uc5f0\uc18d\uc801\uc73c\ub85c \uc608\uce21\ud560 \uc218 \uc788\ub2e4\ub294 \uc810\uc5d0\uc11c \uadfc\ubcf8\uc801\uc778 \ucc28\uc774\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. \ud559\uad50 \ud604\uc7a5 \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131 \ubc0f \uc2a4\ud1a0\ub9ac\ud154\ub9c1<\/h2>\n\n\n\n<p><strong>[\uac00\uc0c1\uc758 \uc2dc\ub098\ub9ac\uc624]<\/strong><\/p>\n\n\n\n<p>\uacbd\uae30\ub3c4 K\uc2dc\uc758 \uad50\uc721\uac10\uc740 \uad00\ub0b4 100\uac1c \ucd08\ub4f1\ud559\uad50\ub97c \ub300\uc0c1\uc73c\ub85c <strong>&#8220;\uad50\uc721 \uc608\uc0b0(Budget) \ud22c\uc785\uc774 \ud559\uad50\ubcc4 \ud3c9\uade0 \uc218\ud559 \uc131\uc801(Math)\uacfc \ud559\uc0dd \ud589\ubcf5\ub3c4(Happiness)\uc5d0 \ubbf8\uce58\ub294 \uc601\ud5a5&#8221;<\/strong>\uc744 \uc870\uc0ac\ud558\uace0\uc790 \ud569\ub2c8\ub2e4. \uadf8\ub7f0\ub370 \uc9c0\ub3c4\ub97c \ubcf4\ub2c8, \ud2b9\uc815 \uc2e0\ub3c4\uc2dc \uc9c0\uc5ed\uc5d0 \uc704\uce58\ud55c \ud559\uad50\ub4e4\uc774 \uc608\uc0b0\uacfc \ubb34\uad00\ud558\uac8c \uc804\ubc18\uc801\uc73c\ub85c \uc131\uc801\uacfc \ud589\ubcf5\ub3c4\uac00 \ubaa8\ub450 \ub192\uc740 &#8216;\uacf5\uac04\uc801 \uad70\uc9d1 \ud604\uc0c1&#8217;\uc744 \ubcf4\uc774\uace0 \uc788\uc5c8\uc2b5\ub2c8\ub2e4. \ub2e8\uc21c\ud788 \uc608\uc0b0\ub9cc \ubcfc \uac83\uc774 \uc544\ub2c8\ub77c, \uc9c0\ub9ac\uc801 \uadfc\uc811\uc131\uc5d0 \ub530\ub978 \ud6c4\uad11\ud6a8\uacfc(\uacf5\uac04 \uc0c1\uad00\uc131)\ub97c \ud1b5\uc81c\ud558\uace0 \uc9c4\uc9dc \uc608\uc0b0\uc758 \ud6a8\uacfc\ub97c \uc54c\uace0 \uc2f6\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 R\uc744 \ud65c\uc6a9\ud55c \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131<\/h3>\n\n\n\n<p>\uc774 \ubd84\uc11d\uc744 \uad6c\ud604\ud558\uae30 \uc704\ud55c R \ucf54\ub4dc\ub97c \uc791\uc131\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud544\uc694\ud55c \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nlibrary(MASS)\nlibrary(ggplot2)\n\n# 1. \uacf5\uac04 \uc88c\ud45c \uc0dd\uc131 (K\uc2dc \ub0b4 100\uac1c \ucd08\ub4f1\ud559\uad50)\nset.seed(2026)\nn_schools &lt;- 100\ncoords &lt;- cbind(Easting = runif(n_schools, 0, 10), Northing = runif(n_schools, 0, 10))\n\n# 2. \uacf5\uac04 \uac70\ub9ac \ud589\ub82c \ubc0f \uacf5\ubd84\uc0b0 \uad6c\uc870 \uc0dd\uc131\ndist_matrix &lt;- as.matrix(dist(coords))\nphi &lt;- 0.5 # \uacf5\uac04 \uac10\uc1e0 \ud30c\ub77c\ubbf8\ud130\nsigma_sq &lt;- 2.0 # \uacf5\uac04 \ubd84\uc0b0\nspatial_cov &lt;- sigma_sq * exp(-phi * dist_matrix)\n\n# 3. \uacf5\uac04 \uc784\uc758 \ud6a8\uacfc (Spatial random effects) \uc0dd\uc131\nu_math &lt;- mvrnorm(1, mu = rep(0, n_schools), Sigma = spatial_cov)\nu_happy &lt;- 0.6 * u_math + mvrnorm(1, mu = rep(0, n_schools), Sigma = spatial_cov * 0.5)\n\n# 4. \uc124\uba85 \ubcc0\uc218(\uad50\uc721 \uc608\uc0b0) \ubc0f \ucd5c\uc885 \uc885\uc18d \ubcc0\uc218 \uc0dd\uc131\nbudget &lt;- rnorm(n_schools, mean = 50, sd = 10)\nmath_score &lt;- 30 + 0.5 * budget + u_math + rnorm(n_schools, 0, 1) # \ubc31\uc0c9 \uc7a1\uc74c(nugget) \ucd94\uac00\nhappiness &lt;- 10 + 0.2 * budget + u_happy + rnorm(n_schools, 0, 0.5)\n\n# \ub370\uc774\ud130 \ud504\ub808\uc784 \uad6c\ucd95\nschool_data &lt;- data.frame(\n  School_ID = 1:n_schools,\n  Easting = coords&#91;,1],\n  Northing = coords&#91;,2],\n  Budget = budget,\n  Math = math_score,\n  Happiness = happiness\n)\n\n# \ub370\uc774\ud130 \ud655\uc778\nhead(school_data)\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. jamovi \ubc0f R\uc744 \ud65c\uc6a9\ud55c \ubd84\uc11d \ubc29\ubc95<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 jamovi\uc5d0\uc11c\uc758 \ud0d0\uc0c9\uc801 \ubd84\uc11d<\/h3>\n\n\n\n<p>jamovi\ub294 \uc9c1\uad00\uc801\uc778 UI\ub97c \uc81c\uacf5\ud558\uc5ec \uae30\ucd08 \ud1b5\uacc4\ub97c \ud655\uc778\ud558\uae30 \ub9e4\uc6b0 \uc88b\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>\uc704\uc5d0\uc11c \uc0dd\uc131\ud55c <code>school_data.csv<\/code>\ub97c jamovi\uc5d0 \ubd88\ub7ec\uc635\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>Exploration -> Descriptives<\/strong> \ud0ed\uc744 \ud074\ub9ad\ud558\uc5ec <code>Math<\/code>, <code>Happiness<\/code>, <code>Budget<\/code>\uc758 \ud3c9\uade0\uacfc \uc0b0\ud3ec\ub3c4\ub97c \ud655\uc778\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\ubcc0\uc218 \uac04\uc758 \ub2e8\uc21c\ud55c \uad00\uacc4\ub294 <strong>Regression -> Correlation Matrix<\/strong>\ub97c \ud1b5\ud574 \ud655\uc778\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><em>\uc8fc\uc758:<\/em> jamovi\uc758 \uae30\ubcf8 \uae30\ub2a5\uc774\ub098 GAMLj \ub2e4\uce35\ubaa8\ud615 \ubaa8\ub4c8\uc740 &#8216;\uc9c0\ub9ac\uc801 \uc88c\ud45c \uae30\ubc18\uc758 \uc5f0\uc18d\uc801 \uacf5\uac04 \uc0c1\uad00\uad6c\uc870&#8217;\ub97c \uc644\ubcbd\ud788 \ubaa8\ub378\ub9c1\ud558\ub294 \ub370 \ud55c\uacc4\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 R\uc744 \ud65c\uc6a9\ud55c \ubcf8\uaca9\uc801\uc778 \ubca0\uc774\uc9c0\uc548 \uacf5\uac04 \ubaa8\ub378\ub9c1 (<code>spBayes<\/code> \ud328\ud0a4\uc9c0)<\/h3>\n\n\n\n<p id=\"p-rc_eec79db64ea504fa-31\">\ubcf8\ubb38\uc5d0\uc11c \uc81c\uc2dc\ub41c \ubc14\uc640 \uac19\uc774, \uc810-\ucc38\uc870 \uacf5\uac04 \ubaa8\ub378\ub9c1\uc740 MCMC \uae30\ubc95\uc744 \ud65c\uc6a9\ud55c \ubca0\uc774\uc9c0\uc548 \ubc29\uc2dd\uc73c\ub85c \ucd94\uc815\ud558\uba70 <code>spBayes<\/code> \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud558\uba74 \ud6a8\uacfc\uc801\uc785\ub2c8\ub2e4. jamovi\uc758 <strong>Rj Editor<\/strong> \ubaa8\ub4c8\uc744 \uc5f4\uc5b4 \ub2e4\uc74c \ucf54\ub4dc\ub97c \uc2e4\ud589\ud558\uba74 \ubd84\uc11d\uc774 \uac00\ub2a5\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># spBayes \ud328\ud0a4\uc9c0 \ub85c\ub4dc (\uc124\uce58 \ud544\uc694: install.packages(\"spBayes\"))\nlibrary(spBayes)\n\n# \uc885\uc18d \ubcc0\uc218 \ud589\ub82c \uad6c\uc131\nY &lt;- as.matrix(school_data&#91;, c(\"Math\", \"Happiness\")])\n\n# \ud544\uc694\ud55c \ud328\ud0a4\uc9c0\uac00 \ubd88\ub7ec\uc640\uc838 \uc788\ub2e4\uace0 \uac00\uc815\ud569\ub2c8\ub2e4. (MASS, spBayes)\n\n# 1. \ub2e4\ubcc0\ub7c9 \ubaa8\ud615\uc744 \uc704\ud55c \uc218\uc2dd(Formula) \uc791\uc131\nformulas &lt;- list(Math ~ Budget, Happiness ~ Budget)\n\n# 2. \ubaa8\ud615 \uc801\ud569 (\ud37c\uc990 \uc870\uac01 \uac1c\uc218 \uc644\ubcbd \uc218\uc815 \ubc84\uc804!)\nn_iters &lt;- 1000 \nfit_mv &lt;- spMvLM(formulas, \n                 data = school_data,  \n                 coords = as.matrix(school_data&#91;, c(\"Easting\", \"Northing\")]),\n                 \n                 # \uc218\uc815 \ud3ec\uc778\ud2b8 1: A\ub294 \uae38\uc774 3 (\ud558\uc0bc\uac01\ud589\ub82c), Psi\ub294 \uae38\uc774 2 (\ub300\uac01\ud589\ub82c)\ub85c \uc124\uc815\n                 starting = list(\"beta\" = rep(0, 4), \n                                 \"phi\" = rep(0.5, 2), \n                                 \"A\" = c(1, 0, 1), \n                                 \"Psi\" = c(1, 1)),\n                 \n                 # \uc218\uc815 \ud3ec\uc778\ud2b8 2: tuning \ud30c\ub77c\ubbf8\ud130\ub3c4 starting\uc758 \uae38\uc774\uc5d0 \ub9de\ucda4\n                 tuning = list(\"phi\" = rep(0.1, 2), \n                               \"A\" = c(0.1, 0.1, 0.1), \n                               \"Psi\" = c(0.1, 0.1)), \n                 \n                 # \uc218\uc815 \ud3ec\uc778\ud2b8 3: \uc5ed\uc704\uc0e4\ud2b8 \ubd84\ud3ec(K.IW)\uc758 \uc790\uc720\ub3c4\ub97c 2\ubcf4\ub2e4 \ud070 3\uc73c\ub85c \ub450\uc5b4 \uc218\ud559\uc801 \uc548\uc815\uc131 \ud655\ubcf4\n                 priors = list(\"beta.flat\", \n                               \"phi.Unif\" = list(rep(0.1, 2), rep(2, 2)), \n                               \"K.IW\" = list(3, diag(2)), \n                               \"Psi.ig\" = list(c(2, 2), c(0.1, 0.1))),\n                 \n                 cov.model = \"exponential\",\n                 n.samples = n_iters)\n\n# 3. \ubaa8\ub378 \uc801\ud569 \ud6c4 \uc0ac\ud6c4\ud45c\ubcf8(posterior samples) \ubcf5\uc6d0\n# \uacf5\uac04 \uc784\uc758\ud6a8\uacfc\ub97c \ud3ec\ud568\ud558\uc5ec \ucd5c\uc885\uc801\uc73c\ub85c \ubca0\ud0c0(\ud68c\uadc0\uacc4\uc218)\ub97c \ubcf5\uc6d0\ud574 \ub0c5\ub2c8\ub2e4.\nfit_mv &lt;- spRecover(fit_mv, start = 501, thin = 1) \n\n# 4. \uacb0\uacfc \uc694\uc57d \ud655\uc778\nsummary(fit_mv$p.beta.recover.samples)\n<\/code><\/pre>\n\n\n\n<p>\uc774 \uacb0\uacfc\ub97c \ud1b5\ud574 \uc6b0\ub9ac\ub294 <strong>&#8220;\uc8fc\ubcc0 \ud559\uad50\uc758 \uacf5\uac04\uc801 \uc601\ud5a5\uc744 \ud1b5\uc81c\ud55c \ud6c4\uc5d0\ub3c4, \uad50\uc721 \uc608\uc0b0\uc774 \uc218\ud559 \uc131\uc801\uacfc \ud589\ubcf5\ub3c4\uc5d0 \uc720\uc758\ubbf8\ud55c \uc815(+)\uc758 \ud6a8\uacfc\ub97c \uac00\uc9c0\ub294\uc9c0&#8221;<\/strong> \uc815\ud655\ud558\uac8c \ud3c9\uac00\ud560 \uc218 \uc788\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\">5. \uc694\uc57d \ubc0f \ucc38\uace0\ubb38\ud5cc<\/h2>\n\n\n\n<p>\ub2e4\uce35\ubaa8\ud615\uc5d0\uc11c \uacf5\uac04 \ubaa8\ub378\ub9c1\uc73c\ub85c\uc758 \ud655\uc7a5\uc740 \uad50\uc721 \uc5f0\uad6c\uc5d0 \uc0c8\ub85c\uc6b4 \uc2dc\uac01\uc744 \uc81c\uacf5\ud569\ub2c8\ub2e4. \ud559\uc0dd\uc774\ub098 \ud559\uad50\ub97c \ub3c5\ub9bd\ub41c \uac1c\uccb4\ub85c \ubcf4\ub294 \uac83\uc744 \ub118\uc5b4, <strong>&#8220;\uc6b0\ub9ac\ub294 \uc9c0\ub9ac\uc801\uc73c\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4&#8221;<\/strong>\ub294 \uc0ac\uc2e4\uc744 \ub370\uc774\ud130\ub85c \uc99d\uba85\ud574 \ub0bc \uc218 \uc788\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p><strong>\ucc38\uace0\ubb38\ud5cc<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Banerjee, S., Carlin, B. P., &amp; Gelfand, A. E. (2004). <em>Hierarchical modeling and analysis for spatial data<\/em>. Chapman and Hall\/CRC Press. <\/li>\n\n\n\n<li>Finley, A. O., &amp; Banerjee, S. (2012). Point-Referenced Spatial Modeling. In <em>The SAGE Handbook of Multilevel Modeling<\/em> (pp. 559-579).<\/li>\n\n\n\n<li>Finley, A. O., Sang, H., Banerjee, S., &amp; Gelfand, A. E. (2009). Improving the performance of predictive process modeling for large datasets. <em>Computational Statistics and Data Analysis, 53<\/em>(8), 2873-2884. <\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \uc810-\ucc38\uc870 \uacf5\uac04 \ubaa8\ub378\ub9c1(Point-Referenced Spatial Modeling)\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \u201c\ud559\uad50 \ud604\uc7a5\uc758 \ub370\uc774\ud130\u201d\ub97c \uc608\uc2dc\ub85c \ub4e4\uc5b4 \uc9c1\uad00\uc801\uc778 \uc124\uba85\uacfc \uc218\ub9ac\uc801 \uc5c4\ubc00\ud568\uc744 \ubaa8\ub450 \uac16\ucd98 \ud615\ud0dc\ub85c \uc7ac\uad6c\uc131\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \ubd84\uc11d \ub3c4\uad6c\ub85c\ub294 jamovi\uc758 \uc0ac\uc6a9\ubc95\uc744 \uc124\uba85\ud558\ub418, jamovi\uc758 \uae30\ubc18\uc774 \ub418\ub294 R \ucf54\ub4dc\ub97c \ud568\uaed8 \uc81c\uc2dc\ud558\uc5ec \ubaa8\uc758 \ub370\uc774\ud130 \uc0dd\uc131\ubd80\ud130 \ubd84\uc11d, \uc2dc\uac01\ud654\uae4c\uc9c0 \uc644\ubcbd\ud558\uac8c \uad6c\ud604\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. 1. \ucd08\ub4f1\ud559\uc0dd\ub3c4 \uc774\ud574\ud558\ub294 &#8216;\uacf5\uac04 \ubaa8\ub378\ub9c1&#8217; 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