{"id":586,"date":"2025-12-29T15:37:42","date_gmt":"2025-12-29T06:37:42","guid":{"rendered":"http:\/\/waurimal.kr\/?p=586"},"modified":"2025-12-29T20:43:43","modified_gmt":"2025-12-29T11:43:43","slug":"chap-15-%ec%9d%b4%eb%b6%84%ed%98%95dichotomous-%eb%b0%8f-%ec%84%9c%ec%97%b4%ed%98%95ordered-polytomous-%eb%ac%b8%ed%95%ad%ec%97%90-%eb%8c%80%ed%95%9c-%ed%99%95%ec%9d%b8%ec%a0%81-%ec%b8%a1","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=586","title":{"rendered":"Chap 15. \uc774\ubd84\ud615(Dichotomous) \ubc0f \uc11c\uc5f4\ud615(Ordered Polytomous) \ubb38\ud56d\uc5d0 \ub300\ud55c \ud655\uc778\uc801 \uce21\uc815 \ubaa8\ub378"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc2ed\ub2c8\uae4c, <br>\uc6b0\ub9ac\uac00 \uad50\uc721 \ud604\uc7a5\uc5d0\uc11c \ud754\ud788 \ub9c8\uc8fc\ud558\ub294 <strong>\ubc94\uc8fc\ud615 \ub370\uc774\ud130(Categorical Data)<\/strong>\ub97c \uc5b4\ub5bb\uac8c \uacfc\ud559\uc801\uc73c\ub85c \uce21\uc815\ud558\uace0 \ubd84\uc11d\ud560 \uac83\uc778\uc9c0\uc5d0 \ub300\ud574 \uc2ec\ub3c4 \uc788\uac8c \ub2e4\ub904\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc6b0\ub9ac\uac00 \ud754\ud788 \uc0ac\uc6a9\ud558\ub294 &#8216;\uae30\ucd08\ud559\ub825 \uc9c4\ub2e8\ud3c9\uac00(\uc815\ub2f5\/\uc624\ub2f5)&#8217;\ub098 &#8216;\ud559\uad50\uc0dd\ud65c \ub9cc\uc871\ub3c4(\ub9ac\ucee4\ud2b8 \ucc99\ub3c4)&#8217;\ub294 \uc77c\ubc18\uc801\uc778 \ud655\uc778\uc801 \uc694\uc778\ubd84\uc11d(CFA)\uc774 \uac00\uc815\ud558\ub294 &#8216;\uc5f0\uc18d\uc131&#8217;\uacfc &#8216;\uc815\uaddc\uc131&#8217;\uc744 \ucda9\uc871\ud558\uc9c0 \ubabb\ud558\ub294 \uacbd\uc6b0\uac00 \ub9ce\uc2b5\ub2c8\ub2e4. \uc774\ub97c \ubb34\uc2dc\ud558\uace0 \ubd84\uc11d\ud560 \uacbd\uc6b0, \uacb0\uacfc\uac00 \uc65c\uace1\ub420 \uc218 \uc788\uc8e0. \uc774 \uc7a5\uc5d0\uc11c\ub294 \uc774\ub7ec\ud55c \ud55c\uacc4\ub97c \uadf9\ubcf5\ud558\uae30 \uc704\ud55c \uc774\ubd84\ud615 \ubc0f \uc11c\uc5f4\ud615 \ubb38\ud56d\uc5d0 \ub300\ud55c \ud655\uc778\uc801 \uce21\uc815 \ubaa8\ub378\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. \uc804\ud1b5\uc801 \ud655\uc778\uc801 \uc694\uc778\ubd84\uc11d(CFA)\uc758 \ud55c\uacc4\uc640 \ub3c4\uc804<\/h2>\n\n\n\n<p>\uc804\ud1b5\uc801\uc778 CFA \ubaa8\ub378\uc740 \uc694\uc778 \uc9c0\ud45c\uac00 \uc5f0\uc18d\uc801\uc774\uba70 \uae30\uc800 \uc694\uc778\uacfc \uc120\ud615 \uad00\uacc4\ub97c \ub9fa\uace0 \uc788\ub2e4\uace0 \uac00\uc815\ud569\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \uad50\uc721 \ud604\uc7a5\uc758 \ub370\uc774\ud130\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ud2b9\uc131\uc744 \ubcf4\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc774\ubd84\ud615 \uc9c0\ud45c<\/strong>: \uc218\ud559 \ubb38\uc81c\uc758 \uc815\ub2f5(1)\uacfc \uc624\ub2f5(0)<\/li>\n\n\n\n<li><strong>\uc11c\uc5f4\ud615 \uc9c0\ud45c<\/strong>: &#8220;\uc804\ud600 \uadf8\ub807\uc9c0 \uc54a\ub2e4&#8221;\uc5d0\uc11c &#8220;\ub9e4\uc6b0 \uadf8\ub807\ub2e4&#8221;\uae4c\uc9c0\uc758 \ub9ac\ucee4\ud2b8\ud615 \uc124\ubb38<\/li>\n<\/ul>\n\n\n\n<p>\uc774\ub7ec\ud55c \ub370\uc774\ud130\ub97c \uc5f0\uc18d\ud615\uc73c\ub85c \uac04\uc8fc\ud558\uace0 \ucd5c\ub300\uc6b0\ub3c4\ubc95(ML)\uc744 \uc801\uc6a9\ud558\uba74, \ubb38\ud56d \uac04\uc758 \uc5f0\uad00\uc131\uc774 \uc800\ud3c9\uac00\ub418\uac70\ub098 \ubd80\uc801\uc808\ud55c \ud45c\uc900\uc624\ucc28\uac00 \uc0b0\ucd9c\ub420 \uc704\ud5d8\uc774 \uc788\uc2b5\ub2c8\ub2e4. \ud2b9\ud788 \uc751\ub2f5 \ubc94\uc8fc\uac00 5\uac1c \ubbf8\ub9cc\uc778 \uacbd\uc6b0 \uc774\ub7ec\ud55c \ubb38\uc81c\ub294 \ub354\uc6b1 \uc2ec\uac01\ud574\uc9d1\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. \uac00\uc0c1\uc758 \uc2dc\ub098\ub9ac\uc624: &#8220;\uae40 \uad50\uc0ac\uc758 \uc218\ud559 \ud559\uc2b5 \ud0dc\ub3c4 \ubc0f \uc131\ucde8\ub3c4 \uc5f0\uad6c&#8221;<\/h2>\n\n\n\n<p>\uc774\ub860\uc801 \uc774\ud574\ub97c \ub3d5\uae30 \uc704\ud574, \uace0\ub4f1\ud559\uad50 \uc218\ud559\uad50\uc0ac\uc778 &#8216;\uae40 \uad50\uc0ac&#8217;\uc758 \ub370\uc774\ud130\ub97c \uac00\uc815\ud574 \ubd05\uc2dc\ub2e4.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\uc2dc\ub098\ub9ac\uc624<\/strong>: \uae40 \uad50\uc0ac\ub294 \ud559\uc0dd\ub4e4\uc758 &#8216;\uc218\ud559\uc801 \uc790\uc2e0\uac10(\uc815\uc758\uc801 \uc601\uc5ed)&#8217;\uacfc &#8216;\uae30\ucd08 \ub300\uc218 \ub2a5\ub825(\uc778\uc9c0\uc801 \uc601\uc5ed)&#8217;\uc744 \uce21\uc815\ud558\uace0\uc790 \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uae30\ucd08 \ub300\uc218 \ub2a5\ub825 (MATH_SKILL)<\/strong>: 5\uac1c\uc758 \uc774\ubd84\ud56d \ubb38\ud56d (\uc815\ub2f5 1, \uc624\ub2f5 0).<\/li>\n\n\n\n<li><strong>\uc218\ud559\uc801 \uc790\uc2e0\uac10 (MATH_CONF)<\/strong>: 5\uac1c\uc758 \ub9ac\ucee4\ud2b8 4\uc810 \ucc99\ub3c4 \ubb38\ud56d (1=\uc804\ud600 \uadf8\ub807\uc9c0 \uc54a\ub2e4 ~ 4=\ub9e4\uc6b0 \uadf8\ub807\ub2e4).<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">3. \ubc94\uc8fc\ud615 \uc9c0\ud45c\ub97c \uc704\ud55c \ub450 \uac00\uc9c0 \ud2c0 (Frameworks)<\/h2>\n\n\n\n<p>\ubc94\uc8fc\ud615 \uc9c0\ud45c\ub97c \ubaa8\ub378\ub9c1\ud558\ub294 \ub370\ub294 \ub450 \uac00\uc9c0 \uc8fc\uc694 \uc811\uadfc \ubc29\uc2dd\uc774 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 \uc7a0\uc7ac \uc751\ub2f5 \uacf5\uc2dd\ud654 (Latent Response Formulation)<\/h3>\n\n\n\n<p>\uc774 \ubc29\uc2dd\uc740 \uad00\ucc30\ub41c \ubc94\uc8fc\ud615 \ubcc0\uc218 <math data-latex=\"Y\"><semantics><mi>Y<\/mi><annotation encoding=\"application\/x-tex\">Y<\/annotation><\/semantics><\/math> \uc774\uba74\uc5d0\ub294 \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub974\ub294 \uc5f0\uc18d\uc801\uc778 \uc7a0\uc7ac \ubcc0\uc218 <math data-latex=\"Y^*\"><semantics><msup><mi>Y<\/mi><mo>\u2217<\/mo><\/msup><annotation encoding=\"application\/x-tex\">Y^*<\/annotation><\/semantics><\/math>\uac00 \uc874\uc7ac\ud55c\ub2e4\uace0 \uac00\uc815\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"Y_{i}^{*} = \\nu_{i} + \\lambda_{i}f + \\epsilon_{i}\"><semantics><mrow><msubsup><mi>Y<\/mi><mi>i<\/mi><mo lspace=\"0em\" rspace=\"0em\">\u2217<\/mo><\/msubsup><mo>=<\/mo><msub><mi>\u03bd<\/mi><mi>i<\/mi><\/msub><mo>+<\/mo><msub><mi>\u03bb<\/mi><mi>i<\/mi><\/msub><mi>f<\/mi><mo>+<\/mo><msub><mi>\u03f5<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Y_{i}^{*} = \\nu_{i} + \\lambda_{i}f + \\epsilon_{i}<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<p>\uc5ec\uae30\uc11c<math data-latex=\"Y^*\"><semantics><msup><mi>Y<\/mi><mo>\u2217<\/mo><\/msup><annotation encoding=\"application\/x-tex\">Y^*<\/annotation><\/semantics><\/math>\uac00 \ud2b9\uc815 \uc784\uacc4\uce58(Threshold, <math data-latex=\"\\tau\"><semantics><mi>\u03c4<\/mi><annotation encoding=\"application\/x-tex\">\\tau<\/annotation><\/semantics><\/math>)\ub97c \ub118\uc744 \ub54c \uc751\ub2f5 \ubc94\uc8fc\uac00 \ubc14\ub010\ub2e4\uace0 \ubd05\ub2c8\ub2e4. \uc774 \ubc29\uc2dd\uc740 \uc8fc\ub85c <strong>\ubc94\uc8fc\ud615 CFA(CCFA)<\/strong>\uc5d0\uc11c \uc0ac\uc6a9\ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 \uc77c\ubc18\ud654 \uc120\ud615 \ud63c\ud569 \ubaa8\ub378 (GLMM)<\/h3>\n\n\n\n<p>\ubb38\ud56d \ubc18\uc751 \uc774\ub860(IRT)\uc5d0\uc11c \uc8fc\ub85c \uc0ac\uc6a9\ud558\ub294 \ubc29\uc2dd\uc73c\ub85c, \ube44\uc120\ud615 \uad00\uacc4\ub97c \uc9c1\uc811 \ubaa8\ub378\ub9c1\ud569\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc774\ubd84\ud615 \ub370\uc774\ud130\uc5d0\uc11c\ub294 \ub85c\uc9d3(Logit) \ud639\uc740 \ud504\ub85c\ube57(Probit) \ub9c1\ud06c \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc131\uacf5 \ud655\ub960\uc744 \uc608\uce21\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. \ucd94\uc815 \ubc29\ubc95: \uc81c\ud55c \uc815\ubcf4 vs. \uc804\uccb4 \uc815\ubcf4<\/h2>\n\n\n\n<p>\uc5b4\ub5a4 \ucd94\uc815\uce58\ub97c \uc0ac\uc6a9\ud560\uc9c0\ub294 \ubd84\uc11d\uc758 \uc815\ud655\ub3c4\uc640 \ubcf5\uc7a1\ub3c4\uc5d0 \ud070 \uc601\ud5a5\uc744 \ubbf8\uce69\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>\uad6c\ubd84<\/strong><\/td><td><strong>\uc81c\ud55c \uc815\ubcf4 \ucd94\uc815 (Limited-Information)<\/strong><\/td><td><strong>\uc804\uccb4 \uc815\ubcf4 \ucd94\uc815 (Full-Information)<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>\ub300\ud45c \ucd94\uc815\uce58<\/strong><\/td><td>WLSMV (Weighted Least Squares Mean and Variance adjusted)<\/td><td>MML (Marginal Maximum Likelihood) \/ FIML<\/td><\/tr><tr><td><strong>\uc785\ub825 \ub370\uc774\ud130<\/strong><\/td><td>\uc694\uc57d \ud1b5\uacc4\ub7c9 (Polychoric correlation matrix \ub4f1)<\/td><td>\uc6d0\uc2dc \uc751\ub2f5 \ub370\uc774\ud130<\/td><\/tr><tr><td><strong>\uc7a5\uc810<\/strong><\/td><td>\ud45c\ubcf8 \ud06c\uae30\uac00 \ud074 \ub54c \ube60\ub974\uace0 \uc801\ud569\ub3c4 \uc9c0\uc218(CFI, RMSEA) \uc81c\uacf5<\/td><td>\ub354 \uc815\ubc00\ud55c \ud30c\ub77c\ubbf8\ud130 \ucd94\uc815 \uac00\ub2a5, \uacb0\uce21\uce58 \ucc98\ub9ac(MAR)\uc5d0 \uac15\ud568<\/td><\/tr><tr><td><strong>\ub2e8\uc810<\/strong><\/td><td>\uacb0\uce21\uce58 \ucc98\ub9ac\uc5d0 \ucde8\uc57d(MCAR \uac00\uc815)<\/td><td>\uc7a0\uc7ac \uc694\uc778\uc774 \ub9ce\uc544\uc9c8\uc218\ub85d \uacc4\uc0b0 \ubcf5\uc7a1\ub3c4 \uae09\uc99d <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">5. \uc774\ubd84\ud615 \ubb38\ud56d \ubaa8\ub378 (Dichotomous Indicators)<\/h2>\n\n\n\n<p>\uc218\ud559 \ubb38\uc81c \uc815\ub2f5 \uc5ec\ubd80\ub97c \ubd84\uc11d\ud560 \ub54c \uc0ac\uc6a9\ub418\ub294 \ubaa8\ub378\ub4e4\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 1\ubaa8\uc218 \ubaa8\ub378 (1PL \/ Rasch)<\/h3>\n\n\n\n<p>\ubaa8\ub4e0 \ubb38\ud56d\uc758 \ubcc0\ubcc4\ub3c4(<math data-latex=\"a\"><semantics><mi>a<\/mi><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math>)\uac00 \ub3d9\uc77c\ud558\ub2e4\uace0 \uac00\uc815\ud558\uace0 \ub09c\uc774\ub3c4(<math data-latex=\"b\"><semantics><mi>b<\/mi><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>)\ub9cc \ucd94\uc815\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"P_{i}(Y_{i}=1|\\theta) = \\frac{1}{1+\\exp(-a(\\theta-b_{i}))}\"><semantics><mrow><msub><mi>P<\/mi><mi>i<\/mi><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Y<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><mi>|<\/mi><mi>\u03b8<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mrow><mi>exp<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mi>a<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo>\u2212<\/mo><msub><mi>b<\/mi><mi>i<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P_{i}(Y_{i}=1|\\theta) = \\frac{1}{1+\\exp(-a(\\theta-b_{i}))}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 2\ubaa8\uc218 \ubaa8\ub378 (2PL)<\/h3>\n\n\n\n<p>\ubb38\ud56d\ub9c8\ub2e4 \ubcc0\ubcc4\ub3c4(<math data-latex=\"a_i\"><semantics><msub><mi>a<\/mi><mi>i<\/mi><\/msub><annotation encoding=\"application\/x-tex\">a_i<\/annotation><\/semantics><\/math>)\uc640 \ub09c\uc774\ub3c4(<math data-latex=\"b_i\"><semantics><msub><mi>b<\/mi><mi>i<\/mi><\/msub><annotation encoding=\"application\/x-tex\">b_i<\/annotation><\/semantics><\/math>)\ub97c \ubaa8\ub450 \ub2e4\ub974\uac8c \ucd94\uc815\ud569\ub2c8\ub2e4. \uae40 \uad50\uc0ac\uc758 \ub370\uc774\ud130\uc5d0\uc11c \ud2b9\uc815 \uc218\ud559 \ubb38\uc81c\uac00 \uc6b0\ub4f1\uc0dd\uacfc \uc5f4\ub4f1\uc0dd\uc744 \ub354 \uc798 \uad6c\ubd84\ud55c\ub2e4\uba74 \uc774 \ubaa8\ub378\uc774 \uc801\ud569\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.3 3\ubaa8\uc218 \ubc0f 4\ubaa8\uc218 \ubaa8\ub378 (3PL, 4PL)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3PL<\/strong>: &#8216;\ucd94\uce21 \ud30c\ub77c\ubbf8\ud130(<math data-latex=\"c_i\"><semantics><msub><mi>c<\/mi><mi>i<\/mi><\/msub><annotation encoding=\"application\/x-tex\">c_i<\/annotation><\/semantics><\/math>)&#8217;\ub97c \ucd94\uac00\ud558\uc5ec, \ub2a5\ub825\uc774 \ub0ae\uc544\ub3c4 \ub9de\ucd9c \ud655\ub960\uc744 \uace0\ub824\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>4PL<\/strong>: &#8216;\uc2e4\uc218 \ud30c\ub77c\ubbf8\ud130(<math data-latex=\"d_i\"><semantics><msub><mi>d<\/mi><mi>i<\/mi><\/msub><annotation encoding=\"application\/x-tex\">d_i<\/annotation><\/semantics><\/math>)&#8217;\ub97c \ucd94\uac00\ud558\uc5ec, \ub2a5\ub825\uc774 \ub192\uc544\ub3c4 \ud2c0\ub9b4 \ud655\ub960(\uc0c1\ud55c \uc810\uadfc\uc120)\uc744 \ubaa8\ub378\ub9c1\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">6. \uc11c\uc5f4\ud615(\ub9ac\ucee4\ud2b8) \ubb38\ud56d \ubaa8\ub378 (Ordinal Indicators)<\/h2>\n\n\n\n<p>&#8216;\uc218\ud559 \uc790\uc2e0\uac10&#8217; \uc124\ubb38\uacfc \uac19\uc740 \ub370\uc774\ud130\uc5d0 \uc801\ud569\ud55c \ubaa8\ub378\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.1 \ub4f1\uae09 \ubc18\uc751 \ubaa8\ub378 (Graded Response Model, GRM)<\/h3>\n\n\n\n<p>\uc751\ub2f5 \ubc94\uc8fc\uac00 \uc21c\uc11c\ub300\ub85c \ub098\uc5f4\ub418\uc5b4 \uc788\uc744 \ub54c, &#8220;k \ubc94\uc8fc \uc774\uc0c1\uc5d0 \uc751\ub2f5\ud560 \ud655\ub960&#8221;\uc744 \ubaa8\ub378\ub9c1\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p><math data-latex=\"P_{i}(Y_{i} \\ge k|\\theta) = \\frac{1}{1+\\exp(-a_{i}(\\theta-b_{ij}))}\"><semantics><mrow><msub><mi>P<\/mi><mi>i<\/mi><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Y<\/mi><mi>i<\/mi><\/msub><mo>\u2265<\/mo><mi>k<\/mi><mi>|<\/mi><mi>\u03b8<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mrow><mi>exp<\/mi><mo>\u2061<\/mo><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><msub><mi>a<\/mi><mi>i<\/mi><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo>\u2212<\/mo><msub><mi>b<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P_{i}(Y_{i} \\ge k|\\theta) = \\frac{1}{1+\\exp(-a_{i}(\\theta-b_{ij}))}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\uc5ec\uae30\uc11c <math data-latex=\"b_{ij}\"><semantics><msub><mi>b<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">b_{ij}<\/annotation><\/semantics><\/math>\ub294 \ubc94\uc8fc \uac04\uc758 \uacbd\uacc4 \uc9c0\uc810\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.2 \uc77c\ubc18\ud654 \ubd80\ubd84 \uc810\uc218 \ubaa8\ub378 (Generalized Partial Credit Model, GPCM)<\/h3>\n\n\n\n<p>\uac01 \ubc94\uc8fc \uac04\uc758 \uc804\uc774(transition)\ub97c \uc77c\ub828\uc758 2PL \ubaa8\ub378\ucc98\ub7fc \ub2e4\ub8f9\ub2c8\ub2e4. \ubb38\ud56d\ub9c8\ub2e4 \ubd80\ubd84 \uc810\uc218\uc758 \ubd80\uc5ec \ubc29\uc2dd\uc774 \ub2e4\ub97c \ub54c \uc720\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">7. jamovi \ubc0f R\uc744 \ud65c\uc6a9\ud55c \uc2e4\ubb34 \uac00\uc774\ub4dc<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">jamovi\uc5d0\uc11c\uc758 \ubd84\uc11d (\uae30\ubcf8)<\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>IRT \ubaa8\ub4c8<\/strong> \uc124\uce58: &#8216;Library&#8217;\uc5d0\uc11c &#8216;snowIRT&#8217; \ubaa8\ub4c8\uc744 \uc124\uce58\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ubd84\uc11d \uc218\ud589<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\uc774\ubd84\ud615: &#8216;IRT&#8217; -&gt; &#8216;Dichotomous&#8217; -&gt; \ubb38\ud56d \uc120\ud0dd.<\/li>\n\n\n\n<li>\uc11c\uc5f4\ud615: &#8216;IRT&#8217; -&gt; &#8216;Polytomous&#8217; -&gt; &#8216;Rating Scale Model&#8217; \ub610\ub294 &#8216;Partial Credit Model&#8217; \uc120\ud0dd.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\uacb0\uacfc \ud655\uc778<\/strong>: \ub09c\uc774\ub3c4, \ubb38\ud56d \ud2b9\uc131 \uace1\uc120(ICC)\uc744 \ud655\uc778\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">R\uc744 \ud65c\uc6a9\ud55c \uc815\ubc00 \ubd84\uc11d (mirt \ud328\ud0a4\uc9c0 \ud65c\uc6a9)<\/h3>\n\n\n\n<p>jamovi\uc5d0\uc11c \uc81c\uacf5\ud558\uc9c0 \uc54a\ub294 \uc138\ubd80 \ubaa8\ub378(4PL \ub4f1)\uc774\ub098 \ubcf5\uc7a1\ud55c CCFA\ub294 R\uc758 <code>mirt<\/code> \ub610\ub294 <code>lavaan<\/code> \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># 1. \ud544\uc694\ud55c \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nif(!require(mirt)) install.packages(\"mirt\")\nlibrary(mirt)\n\n# 2. \uac00\uc0c1 \ub370\uc774\ud130 \uc0dd\uc131 (N=500)\nset.seed(123)\nN &lt;- 500\ntheta &lt;- rnorm(N) # \uc7a0\uc7ac \ub2a5\ub825 (\ud3c9\uade0 0, \ud45c\uc900\ud3b8\ucc28 1) &#91;cite: 154, 176]\n\n# \uae30\ucd08 \ub300\uc218 \ub2a5\ub825 (\uc774\ubd84\ud615: 2PL \ubaa8\ub378 \uae30\ubc18 \uc0dd\uc131)\n# a: \ubcc0\ubcc4\ub3c4, b: \ub09c\uc774\ub3c4\na_skill &lt;- c(1.5, 2.0, 1.2, 1.8, 2.5)\nb_skill &lt;- c(-1.0, -0.5, 0, 0.5, 1.0)\ndata_skill &lt;- matrix(NA, N, 5)\nfor(i in 1:5) {\n  prob &lt;- 1 \/ (1 + exp(-a_skill&#91;i] * (theta - b_skill&#91;i])))\n  data_skill&#91;,i] &lt;- rbinom(N, 1, prob)\n}\ncolnames(data_skill) &lt;- paste0(\"SKILL_\", 1:5)\n\n# \uc218\ud559\uc801 \uc790\uc2e0\uac10 (\uc11c\uc5f4\ud615: GRM \ubaa8\ub378 \uae30\ubc18 \uc0dd\uc131)\n# data_conf \uac1d\uccb4 \uc0dd\uc131\ndata_conf &lt;- simdata(a = rep(1.5, 5), d = matrix(c(2, 0, -2), 5, 3, byrow=TRUE), \n                     N = N, itemtype = 'graded', Theta = as.matrix(theta))\ncolnames(data_conf) &lt;- paste0(\"CONF_\", 1:5)\n\n# 3. \ubd84\uc11d \uc218\ud589 (2PL \ubc0f GRM)\n# \uc774\ubd84\ud615 \ubd84\uc11d\nfit_skill &lt;- mirt(as.data.frame(data_skill), 1, itemtype = '2PL')\ncoef(fit_skill, IRTpars = TRUE, simplify = TRUE)\n\n# \uc11c\uc5f4\ud615 \ubd84\uc11d (GRM)\nfit_conf &lt;- mirt(as.data.frame(data_conf), 1, itemtype = 'graded')\nplot(fit_conf, type = 'trace') # \uce74\ud14c\uace0\ub9ac \ubc18\uc751 \uace1\uc120 (CRC) \ud655\uc778<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"848\" height=\"542\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/fig15-1.png\" alt=\"\" class=\"wp-image-587\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/fig15-1.png 848w, http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/fig15-1-300x192.png 300w, http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/fig15-1-768x491.png 768w, http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/fig15-1-624x399.png 624w\" sizes=\"auto, (max-width: 848px) 100vw, 848px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-71ccc68a-2985-4572-b1d4-e6793560038e\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/chap15.csv\">chap15<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2025\/12\/chap15.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-71ccc68a-2985-4572-b1d4-e6793560038e\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">8. \uacb0\ub860 \ubc0f \uc81c\uc5b8<\/h2>\n\n\n\n<p>\ubc94\uc8fc\ud615 \uc9c0\ud45c\ub97c \ud65c\uc6a9\ud55c \uce21\uc815 \ubaa8\ub378\ub9c1\uc740 \ub2e8\uc21c\ud788 \ud1b5\uacc4 \uae30\ubc95\uc758 \uc120\ud0dd\uc744 \ub118\uc5b4, \uc6b0\ub9ac\uac00 \uce21\uc815\ud558\uace0\uc790 \ud558\ub294 \uad50\uc721\uc801 \uad6c\uc778(Construct)\uc758 \ubcf8\uc9c8\uc744 \uc5bc\ub9c8\ub098 \uc815\ud655\ud558\uac8c \ubc18\uc601\ud558\ub290\ub0d0\uc758 \ubb38\uc81c\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc5f0\uc18d\uc131 \uac00\uc815\uc774 \uae68\uc9c4\ub2e4\uba74<\/strong>: \uc9c0\uccb4 \uc5c6\uc774 \ubc94\uc8fc\ud615 CFA\ub098 IRT \ubaa8\ub378\uc744 \uace0\ub824\ud558\uc2ed\uc2dc\uc624.<\/li>\n\n\n\n<li><strong>\uc801\ud569\ub3c4 \ud655\uc778<\/strong>: WLSMV\ub97c \ud1b5\ud574 CFI, TLI, RMSEA \ub4f1 \uc775\uc219\ud55c \uc9c0\ud45c\ub97c \ud655\uc778\ud560 \uc218 \uc788\uc9c0\ub9cc, \ubc94\uc8fc\ud615 \ub370\uc774\ud130\uc5d0\uc11c\uc758 \ucef7\uc624\ud504 \uae30\uc900\uc740 \uc8fc\uc758\ud574\uc11c \ud574\uc11d\ud574\uc57c \ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\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>Asparouhov, T., &amp; Muth\u00e9n, B. (2020). <em>IRT in Mplus (Version 4)<\/em>. Mplus webnote. <a href=\"https:\/\/www.statmodel.com\/download\/mplusirt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.statmodel.com\/download\/mplusirt.pdf<\/a><\/li>\n\n\n\n<li>Brown, T. A. (2006). <em>Confirmatory factor analysis for applied research<\/em>. Guilford Press.<\/li>\n\n\n\n<li>de Ayala, R. J. (2009). <em>The theory and practice of item response theory<\/em>. Guilford Press.<\/li>\n\n\n\n<li>Embretson, S. E., &amp; Reise, S. P. (2000). <em>Item response theory for psychologists<\/em>. Erlbaum.<\/li>\n\n\n\n<li>Koziol, N. A. (2025). Confirmatory measurement models for dichotomous and ordered polytomous indicators. In <em>Handbook of Structural Equation Modeling<\/em> (Chapter 15).<\/li>\n\n\n\n<li>Muth\u00e9n, L. K., &amp; Muth\u00e9n, B. O. (1998-2020). <em>Mplus user&#8217;s guide (8th ed.)<\/em>. Authors.<\/li>\n\n\n\n<li>Skrondal, A., &amp; Rabe-Hesketh, S. (2004). <em>Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models<\/em>. CRC Press.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc2ed\ub2c8\uae4c, \uc6b0\ub9ac\uac00 \uad50\uc721 \ud604\uc7a5\uc5d0\uc11c \ud754\ud788 \ub9c8\uc8fc\ud558\ub294 \ubc94\uc8fc\ud615 \ub370\uc774\ud130(Categorical Data)\ub97c \uc5b4\ub5bb\uac8c \uacfc\ud559\uc801\uc73c\ub85c \uce21\uc815\ud558\uace0 \ubd84\uc11d\ud560 \uac83\uc778\uc9c0\uc5d0 \ub300\ud574 \uc2ec\ub3c4 \uc788\uac8c \ub2e4\ub904\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc6b0\ub9ac\uac00 \ud754\ud788 \uc0ac\uc6a9\ud558\ub294 &#8216;\uae30\ucd08\ud559\ub825 \uc9c4\ub2e8\ud3c9\uac00(\uc815\ub2f5\/\uc624\ub2f5)&#8217;\ub098 &#8216;\ud559\uad50\uc0dd\ud65c \ub9cc\uc871\ub3c4(\ub9ac\ucee4\ud2b8 \ucc99\ub3c4)&#8217;\ub294 \uc77c\ubc18\uc801\uc778 \ud655\uc778\uc801 \uc694\uc778\ubd84\uc11d(CFA)\uc774 \uac00\uc815\ud558\ub294 &#8216;\uc5f0\uc18d\uc131&#8217;\uacfc &#8216;\uc815\uaddc\uc131&#8217;\uc744 \ucda9\uc871\ud558\uc9c0 \ubabb\ud558\ub294 \uacbd\uc6b0\uac00 \ub9ce\uc2b5\ub2c8\ub2e4. \uc774\ub97c \ubb34\uc2dc\ud558\uace0 \ubd84\uc11d\ud560 \uacbd\uc6b0, \uacb0\uacfc\uac00 \uc65c\uace1\ub420 \uc218 \uc788\uc8e0. \uc774 \uc7a5\uc5d0\uc11c\ub294 \uc774\ub7ec\ud55c \ud55c\uacc4\ub97c \uadf9\ubcf5\ud558\uae30 \uc704\ud55c \uc774\ubd84\ud615 \ubc0f \uc11c\uc5f4\ud615 \ubb38\ud56d\uc5d0 \ub300\ud55c <a class=\"read-more\" href=\"http:\/\/waurimal.kr\/?p=586\">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":[300],"tags":[324,145,166,323,301,327,326,325],"class_list":["post-586","post","type-post","status-publish","format-standard","hentry","category-sem","tag-irt","tag-jamovi","tag-sem","tag-snowirt","tag-301","tag-327","tag-326","tag-325"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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