國立臺中教育大學教育測驗統計研究所理學碩士論文
指導教授:郭伯臣 博士
電腦化適性測驗系統之研發
-以 MIRT 為基礎
研究生:丁境蔚 撰
中
華
民
國
九
十
八
年
六
月
謝辭
很快的,大學加上研究所的時間就這樣過去了,從大學時代就開始接觸研究所這 裡的人事與物,所以對我而言感觸越特別深,首先感謝郭伯臣教授從大學時代的提攜, 讓我更早擁有認識不同學術研究領域的機會,我永遠的記得在校園中與您的對話,開 啟我對研究領域的好奇與渴望;也感謝黃孝雲教授遠從台北下來參與指導我的口試, 讓我在統計方面有更嚴謹的思考,接著感謝施淑娟教授除了在我論文細微的地方給予 精闢的建議之外,也感謝她平時的關愛。 接著感謝台中教育大學測統所的各位授業恩師,郭伯臣所長、許天維院長、楊志 堅教授、施慶麟教授、曾建銘教授、施淑娟教授與林原宏教授,平日在課業上的督導 以及平時生活中的關心,讓我不只學到研究領域專業的知識,還讓我融入所上這個大 家庭。 再來是感謝電腦測驗與計算智能實驗室提供我研究發展的環境與夥伴,感謝研究 室的慧珉學姐、政軒學長、典佑學長、暄博學長、彥鈞學長、智為學長、育隆學長、 鈞翔學長、文俊學長、筱倩學姐總會在我需要幫忙時,給予最好的回應,也會陪我們 打球運動,讓我處於一個充滿活力研究環境,也感謝超可愛阿隆常常會陪我東扯西扯, 也會私底下帶我們去吃東西;也感謝研究室的同一屆的銘豪、秀聿、佳穎、佳樺、任 潔、士勛、志勝及仁傑陪我一起修課、吃飯或運動,如果少了你們,我的研究生活一 定會失去不少色彩;也感謝辰育、怡玲及慶皇都會替我分擔事務,讓我有更多時間專 注在研究上;也感謝研究室的助理亞君、兔子、默、孟君、大黑、敏嫻及阿惠在我生 活中作伴,也讓我額外學到不少東西。 最後感謝我的最親愛而且獨一無二的家人,老爸與老媽供應我這些年來的所需, 雖然在求學的階段沒有很常的時間一起相處,但是總在我的背後默默的關懷,也感謝 大哥與大嫂繼承家業,讓爸媽能放心退於幕後,也能替我陪伴爸媽,讓我在研究室傷 腦筋之餘,不需要在擔心家務,也感謝眉在這段時間的陪伴,雖然常常讓我生氣,但 是沒有妳,我這些日子就空白了一大塊,要感謝的人還很多,無法依序描述,但是我 會記在心裡,感謝所有的人與我一起度過人生中最精華的階段。 境蔚 筆ύЎᄔा
Ϟӭӛࡋႝတϯ܄ෳᡍࣴزύǴεӭаኳᔕࣴزࣁЬǴόӕෳᡍᜪࠠ ΠޑԋਏǴၨϿ໒วӭӛࡋႝတϯ܄ෳᡍޑჴሞسǴ୯ϣҞѝԖ୯ҥѠৣ ጄεᏢ௲ػຑ᠘ᆶวࣴزύЈ໒ว࣬ᜢޑسǴՠԜسࢎᄬύۘ҂уΕ၂ᚒޑ ᚼӀᆅǴ܌аҁࣴزࣴวޑسନΑࡌ٬Ҕޣϟय़ගٮڙ၂ޣՉӭӛࡋႝ တϯ܄ෳᡍǴᗋଞჹ၂ᚒՉᚼӀᆅǶ ୷ܭॊࣴزᐒǴҁࣴزҞޑӵΠǺ ǵࡌ֖ᚼӀᆅޑӭӛࡋႝတϯ܄ෳᡍسǴᡣڙ၂ޣёՉࡼෳᆶᆅ ޣёࡕᆄᆅǶ Βǵаჴቻၗኳᔕӭӛࡋႝတϯ܄ෳᡍسޑࢬำǴаຑسϐԋਏǶ ҁࣴز่݀ࣁࡌӭӛࡋႝတϯ܄ෳᡍޑ٬Ҕޣϟय़Ǵᡣڙ၂ޣёаୖуෳ ᡍ٠၌ԋ݀ǴΨૈᡣᆅޣᏱԖࡕᆄᆅޑѳѠǹӧ၂ᚒϸᔈኳԄБय़Ǵӧҁس уΕӭӛࡋ၂ᚒϸᔈኳԄޑӭӛࡋᒿᐒ߯ኧӭࢶ୷ኳԄȐmultidimensional random coefficients multinomial logit modelȑǹӧᚼӀᆅБय़ǴуΕSHCޑጕ ᚼӀᆅݤᆶаૈΚϩթࣁ୷ᘵϐSHCޑጕᚼӀᆅݤǴ࣪ᚼӀୖኧϸ ᙟॏжޑਔ໔ᆶှ،ॏж܌٬ҔኬҁکჴሞნኬҁࢂցठޑୢᚒǶ ӧόӕૈΚीݤޑኳᔕࣴزύǴว٬ҔԜӭӛࡋኧᏢࣽᚒਔǴᡏԶق යఈࡕᡍीݤᓬܭനεཷ՟ीݤǴ܌аࡌ٬ҔԜᚒਔǴ٬Ҕයఈࡕᡍी ݤǶ ᜢᗖӷǺႝတ܄ෳᡍǵ၂ᚒϸᔈኳԄǵӭӛࡋǵᚼӀᆅAbstract
The present age in the multidimensional computerized adaptive (MCAT) testing research, most of researches which discuss the effect on the different parts of the tests are simulate. Less of researches are developed the MCAT system. The present age in the domestic research, National Taiwan Normal University Center for Educational Research and Evaluation is developed the only system which is related to MCAT, but the exposure control doesn’t combine item with this system. So this research developed the system which is provided not only user interface for MACT but also item.
Based on the reason, the purposes are as follows:
1. To develop MCAT system which includes the exposure control, let examinee can examine and management can manage thing about the test.
2. Using the real data to simulate the CAT procedure, let estimate the result about this system
This research established the user interface for MACT, let examinee can examine and surf the result, and management can manage. In the item response theory, it added the multidimensional random coefficients multinomial logit model to this system. In the exposure control, it added the SHC and the SHC is base on ability on line procedure with freeze to this system. In the whole simulation, it discovered that the expected a posteriori with the high relation is better than maximum likelihood estimation on the multidimensional mathematical item bank.
Keywords: computerized adaptive testing, item response theory, multinomial, exposure control
Ҟᒵ
ύЎᄔा ... I Abstract... II Ҟᒵ ...III ߄Ҟᒵ ...IV კҞᒵ ...V ಃക ᆣፕ ...1 ಃ ࣴزᐒ...1 ಃΒ ࣴزҞޑ...2 ಃΟ Ӝຒှញ...2 ಃѤ ࣴزጄൎᆶज़ڋ...4 ಃΒക Ў ...5 ಃ ၂ᚒϸᔈፕ...5 ಃΒ ႝတϯ܄ෳᡍ...9 ಃΟ ᚼӀᆅ...21 ಃѤ س໒วБݤ...29 ಃϖ ႝတᆛၡמೌ...34 ಃΟക ࣴزБݤ ...37 ಃ ࣴزࢬำ...37 ಃΒ سϩᆶी...38 ಃΟ ኳᔕ MCAT ჴᡍी...44 ಃѤ ຑࡰ...45 ಃϖ ࣴزπڀ...46 ಃѤക ࣴز่݀ᆶፕ ...49 ಃسࡌԋ݀...49 ಃΒ ჴቻၗኳᔕӭӛࡋႝတ܄ෳᡍԋਏ...55 ಃϖക ่ፕᆶࡌ ...58 ಃ ่ፕ...58 ୖԵЎ ...60 ύЎୖԵЎ...60 मЎୖԵЎ...63 ߕᒵǵӭӛࡋኧᏢࣽᚒᜤࡋୖኧ ...66 ߕᒵΒǵسჴբԋ݀ ...68߄Ҟᒵ
߄ 1 SHO ᆶ SHOF ޑᚼӀୖኧፓБԄКၨ ... 26 ߄ 2 سวБݤޑКၨ... 34 ߄ 3 Ӛӛࡋޑѳ֡ኧᆶᡂ౦ኧ... 47 ߄ 4 ٬Ҕ MLE ݤᚼӀᆅᆶૈΚीԋਏ߄ ... 57 ߄ 5 ٬Ҕ EAP ݤᚼӀᆅᆶૈΚीԋਏ߄ ... 57კҞᒵ
კ 1 ᚒ໔ӭӛࡋෳᡍኳԄ ...7 კ 2 ᚒϣӭӛࡋෳᡍኳԄ ...8 კ 3 CAT ࡼෳࢬำ...20 კ 4 ᘣѲԄ໒วݤำׇ ...31 კ 5 ᚉࠠԄسวݤำׇ ...32 კ 6 ख़ᙟуமԄسวݤำׇ ...33 კ 7 ӄфૈԄسวݤำׇ ...34 კ 8 ΟቫԄЬவࢎᄬᡄᒠკ ...35 კ 9 ࣴزࢬำ ...38 კ 10 سࢎᄬኳԄ ...39 კ 11 ܄ෳᡍࢬำी ...40 კ 12 MIRT ኳಔࢎᄬ ...41 კ 13 ဦᆅኳಔ ...42 კ 14 ᚒᆢៈኳಔ ...42 კ 15 ෳᡍࡼෳኳಔ ...43 კ 16 ܄ෳᡍኳಔ ...43 კ 17 ԋ݀၌ኳಔ ...44 კ 18 ኧᆶໆӛࡋᜤࡋୖኧϩѲკ ...47 კ 19 ൳ՖӛࡋᜤࡋୖኧϩѲკ ...48 კ 20 жኧӛࡋᜤࡋୖኧϩѲკ ...48 კ 21 ܄ෳᡍϟय़ ...50 კ 22 ᚒᆅϟय़-1...51 კ 23 ᚒᆅϟय़-2...51 კ 24 ၂ڔᆅϟय़ ...52 კ 25 Ꮲಞບᘐൔϟय़-1...53 კ 26 Ꮲಞບᘐൔϟय़-2...54 კ 27 Ꮲಞບᘐൔϟय़-3...54 კ 28 MLE Ӛӛࡋᡂკ...55 კ 29 EAP Ӛӛࡋᡂკ...56ಃക ᆣፕ
ҁࣴزҞޑࢂࡌаӭӛࡋ၂ᚒϸᔈፕ(multidimensional item response theory, MIRT)ࣁ୷ᘵޑႝတϯ܄ෳᡍ(computerized adaptive testing, CAT)سǴ٠уΕᚼ ӀᆅޑᐒڋǴаᆢៈෳᡍᚒޑӼӄ܄ᆶჴҔ܄ǶҁጇፕЎϩԋϖകǴಃക ᇥܴࣁՖाՉҁࣴزޑᐒᆶҞޑǶಃΒകଞჹ၂ᚒϸᔈፕǵCATǵᚼӀ ᆅݤǵس໒วБݤϷႝတᆛၡמೌ࣬ᜢЎՉǶಃΟകᇥܴࣴزБݤǵ ࢬำϷࡌس܌ሡޑഢǶಃѤകևسࡌ่݀ᆶኳᔕ MCAT ޑԋਏǶಃ ϖകගр่ፕᆶࡌǶ
ಃ ࣴزᐒ
ӧჴࡼᏢࣽෳᡍਔǴҞεϩᗋࢂ௦ҔરෳᡍǴෳᡍ่״ ࡕǴᗋሡाΓΚՉץ᎙ϩǴ܈ஒၗᒡΕႝတՉϩǴ೭ᅿБԄόਔ ໔ᆶΓΚǴ٠Ъคݤזೲளډ࠼ᢀޑෳᡍ่݀Ƕ җܭᆛၡวޑِೲᆶႝတຼᜐഢޑεϯǴႝတϐ໔ޑቹॣၗᒡϷև ёаၲזೲЪᛙۓǴ܌аӧᆛၡჴࡼෳᡍࢂڀᡏёՉޑǹΨӢࣁၸႝတ ՉෳᡍᏱԖזೲၗೀޑᓬᗺǴ٬ளෳᡍၸำǵीǵϩᆶ่݀Ծ၁ಒᒵǴ ӢԜႝတϯෳᡍޑวុࣴزύǶෳᡍፕЬाϩࣁђڂෳᡍፕ(classical test theory, CTT)ᆶ၂ᚒϸᔈፕ (item response theory, IRT)ǴԶ IRT ၮҔӧҞޑ୯ύ୷ҁᏢΚෳᡍǴӧෳᡍጓᇙ ၸำа IRT ࣁ୷ᘵǴૈҗϩ၂ᚒᕇளᑔᒧၸ၂ᚒୖኧޑᚒǴаዴߥᚒࠔ፦ ޑӳᚯǴӧෳᡍࡼෳၸำа IRT ࣁ୷ᘵޑ CATǴૈଞჹόӕڙ၂ޣගٮӝڙ၂ޣ ҁيޑ၂ᚒǴӧёהޑᇤৡΠǴᡣෳᡍޑਔ໔ε൯ᕭอǴќѦԵໆᚒޑӼӄ܄Ǵ Ψૈၸ၂ᚒᚼӀᆅǴၲډࡋᆅڋǴӢԜа IRT ࣁ୷ᘵޑ܄سΨഌុӧ ࣴวȐЦޱǴ2004ǹഋཥᙦǴ2004ǹӓཱིǴ2004ǹླྀ᙭ሸǴ2006ǹጰЎᓪǴ2008ǹ
ᑵᡉയǵ௴ࡏǵෞӀࡿǴ2006ȑǶ
IRT ޑ ଷ ύ х ֖ ൂ ӛ ࡋ (unidimensionality) ᆶ ڙ ၂ ޣ ૈ Κ ी ޑ ό ᡂ ܄
(invariance)Ǵ٬ࡼෳόӕ၂ᚒޑڙ၂ޣ܌ᕇளૈΚीॶёаܫӧ࣬ӕޑໆЁ Кၨ(Hambleton & Swaminathan, 1985; Wainer, Dorans, Flaugher, Green, Mislevy, Steinberg, & Thissen, 1990)ǴՠΨӢൂӛࡋज़ڋ CAT ޑᔈҔǴᡣ CAT ѝૈ߳ज़٬Ҕ ӧൂӛࡋૈΚޑෳᡍǶჹܭЈෳᡍǵӭϡຑໆǵᆕӝૈΚෳᡍӭӛࡋෳᡍǴ Ҟᗋคݤ٬Ҕ CAT ٰՉǹࣁΑှ،ൂӛࡋ IRT ޑज़ڋǴᏢޣॺഌុගр MIRTǴ ٠ ่ ӝ ჴ ሞ ნ ޑ Ե ໆ ࡕ Ǵ ᔈ Ҕ ډ ӭ ӛ ࡋ ႝ တ ϯ ܄ ෳ ᡍ (multidimensional computerized adaptive testing; MCAT)ޑำׇύȐࡼቼᡕǴ2008ǹഋ࢙ᐫǵЦЎύǴ 2000aǴ2000bǹഋϘǵЦЎύǴ2005ǹഋ࢙ᐫǴ2004Ǵ2006ǹᑯǴ2006ǹHattie, 1981; Hsieh, Shih, & Chen, 2008; Luecht, 1996; Mckinley & Reckase, 1983; Reckase & Mckinley, 1991; Segall, 1996; Shih & Wang, 2007; Sympson, 1978ȑǶ
Ϟ MCAT ࣴزύǴεӭаኳᔕࣴزࣁЬǴόӕෳᡍᜪࠠΠޑԋਏǴၨϿ ໒ว MCAT ޑسǴ୯ϣҞѝԖ୯ҥѠৣጄεᏢ௲ػຑ᠘ᆶวࣴزύЈޑӭ ӛࡋႝတϯ܄ෳᡍࣴز࠻วႝတϯӭϡඵች܄ෳᡍȐhttp://140.122.69.163/ȑǴ ՠԜسύۘ҂уΕᚼӀᆅǴԶҁࣴزԵቾ၂ᚒᚼӀᆅჹᚒӼӄ܄ޑቹ ៜǴ܌аҁࣴزޑسфૈନΑёගٮڙ၂ޣՉ MCATǴᗋૈଞჹ၂ᚒՉᚼӀ ᆅǶ
ಃΒ ࣴزҞޑ
୷ܭॊࣴزᐒǴҁࣴزҞޑӵΠǺ ǵࡌ֖ᚼӀᆅޑ MCAT سǴᡣڙ၂ޣёՉࡼෳᆶᆅޣёࡕᆄᆅǶ Βǵаჴቻၗኳᔕ MCAT سޑࢬำǴаຑسϐ٬ҔԋਏǶಃΟ Ӝຒှញ
ଞჹҁጇፕЎதـޑӜຒǴ၁ಒᇥܴӵΠǺ
൘ǵൂӛࡋ၂ᚒϸᔈኳԄ
ൂӛࡋ IRT ࣁ೯ᆀޑ IRTǴѝෳໆᅿૈΚǴԶኳԄЬाϩԋΟᅿኳԄǺ ൂୖኧჹኧኳԄ(one-parameter logistic model, 1PLM; Rasch, 1960)ǵΒୖኧჹኧኳԄ
(two-parameter logistic model, 2PLM; Birnbaum, 1968) ǵ Ο ୖ ኧ ჹ ኧ ኳ Ԅ
(three-parameter logistic model, 3PLM; Lord, 1974)Ǵӧҁࣴزύ܌Ҕޑ IRT ኳԄࢂ 3PLMǶ
ມǵӭӛࡋ၂ᚒϸᔈኳԄ
Ҟதـޑ MIRT ኳԄεӭࢂൂӛࡋ IRT ኳԄޑ़ғኳԄǶٯӵǺӭӛࡋΒୖ ኧኳԄ(multidimensional two parameters model, M2PL; Mckinley & Reckase, 1983; Reckase & Mckinley, 1991)ǵӭӛࡋΟୖኧኳԄ(multidimensional three parameters model, M3PL; Hattie, 1981; Sympson, 1978)ǴϷӭӛࡋᒿᐒ߯ኧӭࢶ୷ኳԄ (multidimensional random coefficients multinomial logit model, MRCML; Adams, Wilson & Wang, 1997)Ǵӧҁࣴزύ܌Ҕޑ MIRT ኳԄࢂ MRCMLǶ
ୖǵૻ৲ڄኧ
၂ᚒૻ৲ڄኧ(item information function; Birnbaum, 1968; Lord, 1980)ࢂࡰीᆉ ၂ᚒૻ৲ໆޑϦԄǴ၀၂ᚒගٮ၀ڙ၂ޣޑૻ৲ໆຫεǴ߾၀ڙ၂ޣ܌ᕇளૈΚ ीॶޑᆒྗࡋ൩ຫଯǶ
စǵᚼӀᆅ
ᚼӀᆅޑཷۺനӃҗSympsonکHetter(1985)ගрᚼӀᆅޑཷۺǴ ᚒ၂ᚒԖჹᔈޑᚼӀୖኧǴຫܰࡼෳޑ၂ᚒ൩ԖຫᝄदޑᚼӀୖኧǴ၂ᚒ ᒧڗਔǴ߾ճҔᚼӀୖኧՉղᘐ၂ᚒࢂցࡼෳǴᡣதࡼෳޑ၂ᚒफ़եࡼෳޑ ᐒǶҴǵႝတϯ܄ෳᡍ
ҁࣴزޑ CAT ࢂၸᆛၡǴ٠่ӝ MIRT ܌ՉޑෳᡍǶࡼෳᚒ၂ᚒǴ ڙ၂ޣ൩ளډঁཥޑૈΚीॶǴӆҗཥޑૈΚीॶᒧрΠᚒՉࡼෳǴ Տڙ၂ޣ܌ࡼෳޑ၂ᚒόֹӄ࣬ӕǴૈᒧрၨӝڙ၂ޣޑ၂ᚒǴၲډՉෳ ᡍޑҞޑǶಃѤ ࣴزጄൎᆶज़ڋ
ҁࣴزࢂࡌ MCAT سǴՠࢂҗܭਔ໔ǵΓΚᆶނΚޑज़ڋǴคݤεໆࡼෳǴ ܌а௦Ҕኳᔕࣴزٰຑسޑ٬ҔБݤǹԶس܌٬Ҕޑᚒࢂ୯ҥᆵύ௲ػε Ꮲ௲ػޑෳᡍीᆶ܄ᏢಞࣴزύЈ܌ጓڋǴൂӛࡋᚒх֖ 94 Ꮲԃࡋࠄހኧ Ꮲࣽಃ 9 нȐ303 ᚒȑک 95 Ꮲԃࡋࠄހ୯ᇟࣽಃ 11 нȐ94 ᚒȑǴԶӭӛࡋᚒѝ х֖ኧᏢࣽૈΚࡰಃ 9 нǴӅ 3 ঁӛࡋǵ238 ᚒǶಃΒക Ў
ҁࣴزҞޑࢂࡌMCATسǴӢԜଞჹس໒วၸำύ܌ሡޕՉЎǴЬ ाБӛϩࣁIRTǵCATǵᚼӀڋǵس໒วБݤǵႝတᆛၡמೌǶಃ ၂ᚒϸᔈፕ
൘ǵൂӛࡋ၂ᚒϸᔈፕ
ǵൂӛࡋ၂ᚒϸᔈኳԄ IRTࢂճҔኧᏢኳԄٰ߄Ңڙ၂ޣወӧૈΚᆶ၂ᚒϐ໔ޑวғᐒǴIRT ኳԄѝ ෳໆᅿૈΚǴԶኳԄЬाϩԋΟᅿኳԄǺ 1PLMǵ2PLM ᆶ 3PLMǴаΠϩձϟಏǶ Ȑȑ1PLM җ Rasch(1960)ගр 1PLMǴх֖ڙ၂ޣޑૈΚୖኧᆶ၂ᚒޑᜤࡋୖኧǴӵϦԄ Ȑ1ȑ܌ҢǺ )) ( exp( 1 1 ) ( i i b P T T Ȑ1ȑ ځύǴPi(T)ࢂ߄Ңڙ၂ޣӧಃ i ᚒޑเჹᐒǹTࢂ߄Ңڙ၂ޣޑჴૈΚǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋǶ ȐΒȑ2PLM җ Birnbaum(1968)ගр 2PLMǴЬाҗ 1PLM уΕ၂ᚒޑ᠘ձࡋୖኧǴӵϦԄ Ȑ2ȑ܌ҢǺ )) ( exp( 1 1 ) ( i i i b a P T T Ȑ2ȑ ځύǴPi(T)ࢂ߄Ңڙ၂ޣӧಃ i ᚒޑเჹᐒǹTࢂ߄Ңڙ၂ޣޑჴૈΚǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋǹaiࣁಃ i ᚒ၂ᚒޑ᠘ձࡋǶ ȐΟȑ3PLMҗ Lord(1974)ගр 3PLMǴЬाҗ 2PLM уΕ၂ᚒޑෳࡋୖኧǴӵϦԄȐ3ȑ ܌ҢǺ )) ( exp( 1 1 ) 1 ( ) ( i i i i i b a c c P T T Ȑ3ȑ ځύǴPi(T)ࢂ߄Ңڙ၂ޣӧಃ i ᚒޑเჹᐒǹTࢂ߄Ңڙ၂ޣޑჴૈΚǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋǹaiࣁಃ i ᚒ၂ᚒޑ᠘ձࡋǹc ࣁಃ i ᚒ၂ᚒޑෳࡋǶӧҁࣴزޑi ൂӛࡋ CAT ύࢂ௦Ҕ 3PLMǶ Βǵൂӛࡋૻ৲ڄኧ ၂ᚒૻ৲ڄኧ(Birnbaum, 1968; Lord, 1980)ӵϦԄȐ4ȑࢂࡰीᆉ၂ᚒૻ৲ໆޑ ϦԄǴ၀၂ᚒගٮ၀ڙ၂ޣޑૻ৲ໆຫεǴ߾၀ڙ၂ޣ܌ᕇளૈΚीॶޑᆒྗ ࡋ൩ຫଯǶ 2 2 ))] ( exp( 1 [ ))] ( exp( [ ) 1 ( ) ( i i i i i i i i b a b a c c a I T T T Ȑ4ȑ ځύǴIi(T)ࣁڙ၂ޣޑૈΚॶӧಃ i ᚒ၂ᚒޑ၂ᚒૻ৲ڄኧǶ
ෳᡍૻ৲ڄኧ(test information function)ۓကࣁঁձ၂ᚒૻ৲ໆޑуᕴǴӵϦԄȐ5ȑ܌
ҢǶऩటቚуෳᡍૻ৲ໆёԖΒᅿБݤǴࣁӧෳᡍߏࡋόᡂΠǴቚу၂ᚒૻ৲ໆǹ Βࣁӧ၂ᚒૻ৲ໆόᡂޑݩΠǴቚуෳᡍߏࡋǶ
¦
n i i j T I I 1 ) ( ) (T T Ȑ5ȑ ځύǴ n ࣁෳᡍޑߏࡋǹIT(Tj)ࣁ n ᚒIi(T)уᕴޑෳᡍૻ৲ڄኧǶມǵӭӛࡋ၂ᚒϸᔈፕ
ǵӭӛࡋ၂ᚒϸᔈኳԄ ൂӛ܄(unidimensionality)ࢂ၂ᚒϸᔈፕځύϐޑ୷ҁଷǴࢂࡰෳᡍύޑ ܌Ԗ၂ᚒෳໆঁ࣬ӕޑૈΚǶՠӭෳᡍნதх֖ӭϩෳᡍǴόൂપѝ ԖෳໆൂૈΚǴٯӵЈෳᡍǵӭϡຑໆǵᆕӝૈΚෳᡍǶࣁΑᗉխڙ၂ޣӢᚒҞၸӭԶౢғޑੲമຝǴ೭٤ෳᡍ܌х֖ޑϩෳᡍ೯த όԖၸӭ၂ᚒǴऩаൂӛࡋ IRT ঁձՉӚϩෳᡍޑϩǴ߾ϩෳᡍޑߞࡋ όଯǶԶჴሞᔈҔൂӛ܄ଷ٠όܰၲԋǴӢԜԖᏢޣගрӭӛࡋ၂ᚒϸᔈ ፕ(Reckase, 1985; van der Linden & Hambleton, 1996)Ǵа၂ှ،ෳᡍჴሞᔈҔޑ ୢᚒǶ
Ȑȑӭӛࡋෳᡍ
ӭӛࡋෳᡍёаϩࣁٿᅿ(Wang, Wilson, & Adams, 1997)Ƕᅿࢂᚒ໔ӭӛࡋෳ ᡍ(between-item multidimensional test)Ǵ೭ᅿෳᡍ္ޑঁ၂ᚒѝෳໆൂᅿૈ ΚǴջൂӛࡋ၂ᚒǴԶҽෳᡍх֖ӭঁൂӛࡋޑ၂ᚒǶ೭ᜪࠠޑෳᡍӵკ 1 ܌ҢǶ ᆕӝૈΚෳᡍឦܭᚒ໔ӭӛࡋෳᡍޑᅿǴᚒ၂ᚒෳໆൂᅿૈΚǴԶҽෳᡍ ߾х֖Α೭٤ෳໆ࣬՟ૈΚޑൂӛࡋ၂ᚒǶ
კ1 ᚒ໔ӭӛࡋෳᡍኳԄ
ќᅿࢂᚒϣӭӛࡋෳᡍ(within-item multidimensional test)Ǵ೭ᅿෳᡍ္ޑᚒ ၂ᚒෳໆёૈόѝᅿૈΚǴ܌аൂ၂ᚒϣ൩х֖ӭӛࡋǶ೭ᜪࠠޑෳᡍӵკ 2 ܌ҢǶ ૈΚ A ၂ᚒ 1 ၂ᚒ 2 ૈΚ B ၂ᚒ 3 ၂ᚒ 4 ૈΚ C ၂ᚒ 5 ၂ᚒ 6 ၂ᚒ 7
კ2 ᚒϣӭӛࡋෳᡍኳԄ ȐΒȑӭӛࡋ၂ᚒϸᔈኳԄ Ҟதـޑӭӛࡋ IRT ኳԄεӭࢂൂӛࡋ IRT ኳԄޑ़ғኳԄǶٯӵǺ M2PL ک M3PLǴᗋԖځдᏢޣගрޑ MRCMLMǴаΠϩձϟಏǶ 1. M2PL җ Mckinley ک Reckase(1983)ගр M2PLǴջࣁ 2PLM ޑ़ғኳԄǴӕਔԵቾڙ ၂ޣӭᅿૈΚ٠ஒ၂ᚒޑ᠘ձࡋۓကࣁӛໆǴӵϦԄȐ6ȑ܌ҢǺ )] ( exp[ 1 1 ) , , | 1 ( i i i i i i b b U P c aș ș a Ȑ6ȑ ځύǴUiࣁڙ၂ޣࡼෳಃ i ᚒޑϸᔈࠠᄊǴเჹࣁ 1Ǵเᒱࣁ 0ǹaiࣁಃ i ᚒ၂ᚒޑ ᠘ձࡋӛໆୖኧǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋୖኧǹșࣁڙ၂ޣޑૈΚӛໆǶ 2. M3PL җ Sympson(1978)ᆶ Hattie(1981)܌ගрޑኳԄ࣬ᜪ՟, ࢂҗ 3PLM ޑ़ғ ኳԄǴࣁ M3PLǴӕਔԵቾڙ၂ޣӭᅿૈΚ٠ஒ၂ᚒޑ᠘ձࡋۓကࣁӛໆǴΨᜪ՟ ܭ M2PLǴৡձӧܭࢂցԵቾෳୖኧǴӵϦԄȐ7ȑ܌ҢǺ )] ( exp[ 1 1 ) , , , | 1 ( 1 ș a ș a i i i i i i i i b c c c b U P c Ȑ7ȑ ځύǴUiࣁڙ၂ޣࡼෳಃiᚒϸᔈࠠᄊǹșࣁڙ၂ޣૈΚӛໆǹaiࣁಃ i ᚒ၂ᚒޑ᠘ ձࡋӛໆୖኧǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋୖኧǹciࣁ၂ᚒޑෳୖኧǶԶࣁΑ٬၂ᚒޑ ૈΚ D ၂ᚒ 1 ၂ᚒ 2 ၂ᚒ 3 ૈΚ E ၂ᚒ 4 ၂ᚒ 5
ᜤࡋԋࣁӛໆҔаᆶૈΚӛໆ࣬෧Ǵࡺஒᜤࡋୖኧbiᆶӛໆ1 ࣬४Ƕ 3. MRCMLM
җ AdamsǵWilson ᆶ Wang(1997)܌ගрٰޑ MRCMLM ࣁ Rasch ኳԄޑ़ғኳ ԄǴӵϦԄȐ8ȑ܌ҢǺ
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c c c c c c i 1 ) exp( ) exp( ) , , ; 1 ( K u iu iu ik ik ik ik ik | X f ȟ a ș b ȟ a ș b ș ȟ b a Ȑ8ȑ ځύǴ ' 2 , 1 , 22 21 12 11, , , , , , ) ( n n i X X X X X X X ǴXikࣁڙ၂ޣӧಃ i ᚒಃ k ᅿޑϸᔈᜪࠠǴ i = 1,…,nǴk = 1,…,Kǹ>
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' 2 1, , , ȟ [ [ [n Ǵ[iࣁಃ i ᚒࣁΒϡीϩΠǴीޑᜤࡋǴऩ ಃ i ᚒࣁ 0ɴ2 ޑҽ๏ϩǴ߾ीޑᜤࡋԖ[i1ၟ[i2Ǵٿঁᜤࡋǹऩ၂ڔࣁΒϡी ϩǴ߾ಃ i ᚒޑीᜤࡋࣁ[iǴ>
@
' 2 1, , , ȟ [ [ [n Ǵऩ၂ڔࣁΟϡीϩǴ߾ಃ i ᚒޑ ीᜤࡋϩձࣁ[i1ၟ[i2Ǵ>
@
' 2 1 22 21 12 11, , , , , ȟ [ [ [ [ [n [n ǹ>
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' 2 1, , , ș T T TD ǴTdࣁӧෳᡍ ύǴෳډޑಃ d ᅿૈΚǴd = 1,…,Dǹaikࣁӧಃ i ᚒᕇளಃ k ᅿளϩޑीંତǹbik ࣁӧಃ i ᚒᕇளಃ k ᅿளϩޑளϩંତǹૈଷPi(ș)ࢂڙ၂ޣӧಃ i ᚒࣁಃ k ᅿޑϸ ᔈᜪࠠޑวғޑᐒӵϦԄȐ8ȑǶ Οǵӭӛࡋૻ৲ڄኧ Segall(1996)ගрӭӛࡋૻ৲ڄኧંତǴࢂஒșжΕςࡼෳၸޑ၂ᚒ܌ᕇள ) șˆ , ș ( I j ǴӆуșжΕᚒύ҂ࡼෳޑ၂ᚒ܌ᕇளI(ș,uk)ӵϦԄ(9) ܌ҢǺ ) , ș ( I ) șˆ , ș ( I j uk Ȑ9ȑ ځύu ࣁಃ k ᚒբเϸᔈǶkಃΒ ႝတϯ܄ෳᡍ
રෳᡍǴόፕڙ၂ޣޑૈΚଯեሡाֹֹҽෳᡍǴததวғ ଯૈΚޑڙ၂ޣள၂ڔϼᙁൂǴ࣬ϸӦեૈΚޑΓளϼ֚ᜤǴԶڙ၂ޣௗڙό ӝҁيૈΚޑ၂ڔǴΨคݤᆒྗޑෳໆрڙ၂ޣޑૈΚǶCAT ё٩ᏵՏڙ၂ޣޑόӕբเϸᔈՉૈΚीǴ٠ЪԾᒧӝҞૈΚीޑ၂ᚒǴа෧Ͽࡼ ෳޑᚒኧǵբเਔ໔ᆶफ़եڙ၂ޣޑᏢಞขቾǶ
ҁࣴزޑ CAT ࢂа IRT ࣁ୷ᘵޑ܄ෳᡍǴ܌ах֖Αϖ୷ҁाનǺෳᡍ ᚒǵෳᡍଆᗺǵૈΚीǵᒧᚒౣᆶෳᡍಖЗచҹ(է҇ჱǴ1992)ǴԶ٩ྣ CAT ޑόӕᜪࠠΞёϩբൂӛࡋ CAT ᆶӭӛࡋ CAT ٿεᜪǴаΠϩձଞჹόӕ CAT ჴ ࡼၸำ܌ሡޑाનՉᇥܴǶ
൘ǵෳᡍᚒ
CATᚒޑӳᚯ೯தаᚒελᆶ၂ᚒୖኧٰຑǶऩ CAT ࡼෳߏࡋࣁર ෳᡍߏࡋޑъǴ߾ CAT ᚒελനӳࢂરෳᡍߏࡋޑ 6 Կ 8 ७ǴΨ൩ࢂ ᇥᚒελԿϿࣁ CAT ࡼෳߏࡋޑ 12 ७(Stocking, 1994)Ƕᚒߏࡋࣁ 3 ७аǴ ᆒዴࡋᆶբเਏωԖᡉৡ౦(Hung, 1988)Ƕ ჹൂӛࡋ CAT ޑ 3PLM ٰᇥǴঁӳޑᚒځ᠘ձࡋᔈεܭ 0.8Ǵᜤࡋᔈ၀ᆶ ڙ၂ޣϐ҆ဂޑૈΚϩթ࣬߈Ǵෳࡋ߾ᔈλܭ 0.25(Цᝊ❲Ǵ1995)ǶRee(1981)ම аനεૻ৲ݤࣁᒧᚒౣޑࣴزǴӧؒԖᚼӀᆅΠǴᚒߏࡋεܭ 200 ᚒਔǴ ჹૈΚीޑᆒྗࡋ٠όܴᡉቚуǶჹӭӛࡋ CAT ٰᇥǴWang, Chen ᆶ Cheng(2004)ޑࣴزᡉҢǴᚒӛࡋϐ໔ ࣁଯ࣬ᜢਔǴӭӛࡋ IRT ϩёаε൯ගଯӚӛࡋޑߞࡋǴҗচҁޑ 0.6(ൂӛࡋ IRT ϩ)ගܹԿ 0.8Ƕ
ມǵෳᡍଆᗺ
CATޑ୷ҁচ߾ࢂ٩ྣڙ၂ޣૈΚගٮޑ၂ᚒᡣڙ၂ޣՉࡼෳǴՠӧෳ ᡍޑ໒ۈǴڙ၂ޣޑૈΚଯե҂ૈளޕޑచҹΠǴӢԜѸ،ۓෳᡍޑଆۈᗺǴ аᒧಃঁ၂ᚒٮڙ၂ޣՉࡼෳǶதҔܭ،ۓଆۈ၂ᚒޑБݤǴаΠϩձϟಏ ȐЦᝊ❲Ǵ1995ǹഋӵǴ1998ǹᒲ҉Ǵ2006ǹChang & Ansley, 2003ȑӃଷڙ၂ޣࣁύૈΚǴӧᚒύࡷᒧӝύૈΚᜤࡋޑᚒҞբࣁࡼෳޑ ଆۈ၂ᚒǴऩՏڙ၂ޣ٬Ҕ࣬ӕޑᚒҞ໒ۈǴ߾ଆۈ၂ᚒޑߥஏ܄ሡाձԵ ໆǶ Βǵ٩ڙ၂ޣૈΚᒧᚒ җڙ၂ޣޑ୷ҁၗȐԃសǵᏢಞᡍ܈ځдෳᡍ่݀ȑᆉڙ၂ޣޑૈΚ߃ ۈॶǴӆճҔૈΚ߃ۈॶ،ۓෳᡍޑଆۈ၂ᚒǶ ΟǵԾҗᒧᚒ җڙ၂ޣӧௗڙෳᡍޑਔংǴԾՉղۓԾρޑำࡋǴа،ۓࡼෳޑଆۈᚒǴՠ ܰڙډڙ၂ޣЬᢀղᘐޑቹៜǶ Ѥǵᒿᐒᒧᚒ җႝတᒿᐒᒧᚒǴՠज़ۓ၂ᚒᒧڗጄൎόёຬၸᚒҁيǶLord(1977)ว όӕଆۈᗺჹܭෳᡍྗᇤ(standard error of measurement)٠ؒԖࡐεৡձǶ
ϖǵᒿᐒݤ
ᒿᐒݤޑ୷ҁচࢂᙖҗᒿᐒᒧڗࡼෳ၂ᚒǴаᗉխଯૻ৲ໆޑ၂ᚒၸࡋᒧ
ڗǴMcBride & Martin(1983)ว߄ᒿᐒݤǶᒿᐒݤࢂӧࡼෳය٬Ҕᒿᐒᒧڗౣٰ
ᗉխᚒҞޑၸࡋᚼӀǴځჴࡼБݤࣁǺ ჹঁڙ၂ޣǴ٩ૈΚ߃ۈॶவᚒύᒧр 5 ঁૻ৲ໆനεޑᚒҞǴவ೭ 5 ᚒύᒿᐒᒧڗрᚒࡼෳ٠ख़ཥीૈΚॶǹ٩ཥीޑૈΚॶவᚒύᒧр 4 ঁ ૻ৲ໆനεޑᚒҞǴӆவ೭ 4 ᚒύᒿᐒᒧڗрᚒࡼෳ٠ख़ཥीૈΚॶǶख़ፄ࣬ ӕኳԄǴᒧڗࡼෳޑ 4 ᚒǴಃ 5 ᚒϐࡕ൩٬Ҕനεૻ৲ݤٰᒧڗࡼෳᚒҞǶԜѦ ਥᏵ Chang ᆶ Ansley(2003)ޑࣴزࡰрᒿᐒݤӧόӕᚒύޑКၨǴ၂ᚒനεᚼӀ ࣣϟܭ 0.64~0.74Ǵᇻଯܭёௗڙ၂ᚒനεᚼӀǶ Ϥǵ߃ۈ໘ࢤ b ॶϩቫᒿᐒᒧᚒݤ ᒲ҉(2006)ගр߃ۈ໘ࢤ b ॶϩቫᒿᐒᒧᚒݤٰՉෳᡍ߃යᒧᚒǴځჴࡼ
ᡯӵΠǺ ᡯǺஒᚒ٩ b ॶελϩԋ k ቫǴk ࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ᡯΒǺࡼෳ k ᚒਔǴϩձԾ k ቫύӚԾᒿᐒᒧڗঁ၂ᚒǴՉࡼෳǶ ࣴزᡉҢǴԜБݤёԖਏफ़ե၂ᚒനεᚼӀǵԖਏගଯᚒޑ٬ҔǶ
ୖǵૈΚी
ǵൂӛࡋ CAT CATதـޑૈΚीБݤԖനεཷ՟ीݤǵයఈࡕᡍीݤᆶനεࡕᡍी ݤǴаΠϩձϟಏǺ Ȑȑനεཷ՟ीݤനεཷ՟ीݤ(maximum likelihood estimation, MLE)ࢂෳᡍӅԖ n ঁ၂ᚒǴ ၂ᚒ໔۶ԜᐱҥǴ߾ཷ՟ڄኧё߄ҢࣁϦԄȐ10ȑ܌ҢǺ
n i X i X i n P iQ i X X L L 1 1 1,..., | | u T T Ȑ10ȑځύǴu ࣁ܌ԖբเϸᔈޑӛໆǴL
X1,...,Xn |Tࣁཷ՟ڄኧ(likelihood function)ǹTࣁڙ၂ޣޑჴૈΚǹXiࡰڙ၂ޣӧಃ i ᚒޑբเϸᔈǴเჹࣁ 1Ǵเᒱࣁ 0ǹPi ࡰڙ၂ޣӧಃ i ᚒޑเჹᐒǹQiࡰڙ၂ޣӧಃ i ᚒޑเᒱᐒǶ ࣁΑуೲפډཷ՟ڄኧޑനεॶǴ೯தࢂӃჹཷ՟ڄኧڗჹኧǴӆаФႥ-ऊՕ හ(Newton-Raphson)ݤٰՉॏжǶ٬Ҕ MLE ૈΚीޑϦԄӵϦԄȐ11ȑ܌ҢǴ Զಃ j ԛޑૈΚीޑᡂໆࣁį(j)ӵϦԄȐ12ȑ܌ҢǺ ) ( ) 1 -( ) ( - j j j T į T Ȑ11ȑ
ș L L į w w u w w T T T ln u| ] | u ln [ 2 -1 2 (j) Ȑ12ȑ ȐΒȑයఈࡕᡍीݤBock ک Mislevy(1982)ගрයఈࡕᡍݤ(expected a posteriori, EAP)ࢂ൨פૈΚ
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q q q k q q q q q k q q k q q q EAP f L f L f 1 1 1 )] ( ) | ( [ ) ( ) | ( ) | ( T T T T T T T T U U U Ȑ13ȑ ځύ u ࣁ܌ԖբเϸᔈޑӛໆǴLu|Tqࣁཷ՟ڄኧ(likelihood function)ǹTq ࣁڙ၂ޣޑჴૈΚǹq ࢂीᆉૈΚޑයఈॶਔ܌Ϫപԋޑϩപᗺ(quadrature point)ǴӅԖkqᗺǴkqཇεǴीᆉޑཇᆒዴǶόၸ೭ᅿीБݤόሡा٬ҔФႥ -ऊՕහݤٰՉॏжǴԶЪᒿ܌ᒧڗޑϩപᗺኧཇӭǴ܌ሡޑीᆉໆၨᚳ εǴीᆉਔ໔ΨКၨΦǶ ȐΟȑനεཷ՟ीݤنМനεࡕᡍݤ(maximum a posteriori, MAP)ࢂаڙ၂ޣޑ٣ૈΚϩѲ f(T)բ
ࣁуॶǴԋ٣ࡕᐒஏࡋڄኧǴ٠פрૈ٬Ԝ٣ࡕᐒஏࡋڄኧനεϯޑำࡋ ॶǴᆀࣁ MAPǶ٣ࡕᐒஏࡋڄኧीᆉБԄӵϦԄȐ14ȑ܌ҢǺ ) ( ) ( ) | ( ) | ( U U U f f L f T T T Ȑ14ȑ ځύǴL(U|T)ࢂڙ၂ޣT ޑཷ՟ڄኧǴ f(U)ࢂڙ၂ޣޑᜐሞᐒǴࢂҗ ) ( ) | ( T f T L U வf~fᑈϩ܌ளǴࣁΑуೲפډ٣ࡕᐒஏࡋڄኧޑനεॶǴ೯ தΨࢂаФႥ-ऊՕහ(Newton-Raphson)ݤٰՉॏжǶ ȐѤȑӚᅿૈΚीБݤޑКၨ ᗨฅ MLE ԖόᒱޑीਏૈǴՠԖჴ୍ޑज़ڋǴڙ၂ޣբเϸᔈࣁӄჹ ܈ӄᒱਔǴMLE คݤीڙ၂ޣૈΚॶ(Wang & Vispoel, 1998)ǶԶ EAP ܈ MAP ё аीӄჹ܈ӄᒱޑբเϸᔈǴՠऩ٣ϩଛό҅ዴǴ߾ૈΚीୃৡஒࡐε (Baker & Kim, 2004)Ƕ
ࢫᅸᗪǵֆျǵֆ៓ǵഋमᇬ(1992)բၸӚᅿૈΚीБݤޑКၨǴMLE КၨؒԖᘜ܄ޑୃᇤ(bias)Ǵՠ֡Бਥᇤ(root mean square of error, RMSE)ၨεǹ
Βǵӭӛࡋ CAT ӭӛࡋ CAT தـޑૈΚीБݤԖനεཷ՟ीݤǵයఈࡕᡍीݤᆶനε ࡕᡍीݤǴᆶൂӛࡋ CAT ޑीݤᜪ՟ǴЬाҗीൂঁૈΚॶᡂԋӕਔी ӭঁૈΚॶǴаΠϩձϟಏǺ Ȑȑനεཷ՟ीݤ Segall(1996)ගрӭӛࡋޑ MLE ࢂෳᡍӅԖ n ঁӭӛࡋޑ၂ᚒǴ၂ᚒ໔۶Ԝ ᐱҥǴ߾ཷ՟ڄኧӵϦԄȐ15ȑ܌ҢǺ
Ȟ 1 2 1, ,..., | ) ( ) ( ) ( ) | ( i u i u i n P iQ i u u u L L u T T T T Ȑ15ȑ ځ ύ Ǵ L(u|T)ࣁ ཷ ՟ ڄ ኧ (likelihood function) ǹșࣁ ڙ ၂ ޣ ޑ ჴ ૈ Κ ӛ ໆ Ǵ>
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' 2 1, , , ș T T TD ǹuiࡰڙ၂ޣӧಃ i ᚒޑբเϸᔈǴเჹࣁ 1Ǵเᒱࣁ 0ǹPiࡰڙ၂ ޣӧಃ i ᚒޑเჹᐒǹQiࡰڙ၂ޣӧಃ i ᚒޑเᒱᐒǶ ࣁΑуೲפډཷ՟ڄኧޑനεॶǴ೯தࢂӃჹཷ՟ڄኧڗჹኧǴӆаФႥ-ऊՕ හ(Newton-Raphson)ݤٰՉॏжǶ٬Ҕ MLE ૈΚीޑϦԄӵϦԄȐ16ȑ܌ҢǴ ԶԛૈΚीޑᡂໆࣁ ( ) į j ӵϦԄȐ17ȑ܌Ң(Wang, 1994)Ǻ ) ( ) 1 -( ) ( į -ș ș j j j Ȑ16ȑ ș ș | u ln ] ș ș ș | u ln [ į -1 2 (j) w w u w w w L L Ȑ17ȑ » » » » » » » » » ¼ º « « « « « « « « « ¬ ª w w w w w w w w ) ș ( ln ) ș ( ln ) ș ( ln ) ș ( ln ș 2 1 u u u u L ș L ș L ș L D ) ( ln ) ( ln ș u u ș L ș ș f r r w w w w¦
n i i i P u (ș)) (ऩಃ i ᚒ၂ᚒѝෳໆಃ r ᅿૈΚӛࡋǴ߾ [ (ș) (ș) ] (ș) ) 1 ( i i r u i u i Q u P P i i w w T ऩಃ i ᚒ၂ᚒؒԖෳໆಃ r ૈΚӛࡋǴ߾ r u i u i iQ i P T w w[ (ș) (ș)(1 )] = 0 ) ( ln 2 ș u L ș șrw s w w
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u n i i i Q P(ș) (ș)) ( » » » » » » » » » » ¼ º « « « « « « « « « « ¬ ª w w w w w w w w w w w w w w w 2 D 2 2 2 2 2 2 1 2 2 1 2 2 ) ș ( ln ) ș ( ln ) ș ( ln ) ș ( ln ) ș ( ln ș ș ) ș ( ln ) ș ( J ș f ș ș f ș f ș ș f ș f f D D u u u u u u ऩಃ i ᚒ၂ᚒѝෳໆಃ r ᅿૈΚӛࡋǴ߾ [ (ș) (ș) ] [ (ș) (ș)] ) 1 ( i i r r u i u i Q P Q P i i u w w w T T ऩಃ i ᚒ၂ᚒؒԖෳໆಃ r ᅿૈΚӛࡋǴ߾ r r u i u i iQ i P T T w w w[ (ș) (ș)(1 )] = 0 ȐΒȑයఈࡕᡍीݤ ӭӛࡋޑ EAP ࢂஒൂӛࡋޑ EAP ૈΚॶԵቾૈΚӛໆǴӵϦԄȐ18ȑ܌ҢǺ¦
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q q q k q q q q q k q q k q q q EAP f L f L f 1 1 1 )] ș ( ) ș | ( [ ) ș ( ) ș | ( ) | ș ( ș ș U U U T Ȑ18ȑ ځύ q ࢂीᆉૈΚޑයఈॶਔ܌Ϫപԋޑϩപᗺ(quadrature point)Ǵq ཇӭǴी ᆉޑཇᆒዴǹf(șq)ࢂӭᡂໆதᄊϩଛǴӵϦԄȐ19ȑ܌ҢǺ f f ) ) x f p p ( ) ( )], 2 1 exp[ ) 2 ( 1 ) , , ( ' 1 2 / 1 2 / 1 x ȝ x ȝ S T T Ȑ19ȑ ځύș [ș 1, ,șD] ' , ȝࣁșޑѳ֡ኧӛໆǴ [P1,,PD] ' ȝ Ǵ)ࣁșޑӅᡂኧંତǴऩᡂኧંତྗϯࡕǴջࣁ࣬ᜢંତǴ » » » ¼ º « « « ¬ ª ) 2 2 1 0 0 D V V ӧӭӛࡋύǴϩപᗺޑኧໆԋӛࡋኧޑࡰኧ७ቚуǴӛࡋኧቚуǴ߾ ૈΚीਔ໔൩ߏǴऩ෧ϿӚӛࡋޑϩപᗺǴΞफ़եૈΚीޑᆒྗࡋǶ ȐΟȑനεࡕᡍीݤ
Segall(1996)ගрӭӛࡋޑ MAPǴѬޑ٣ࡕᐒஏࡋڄኧᆶ EAP ࣬ӕǶࣁΑу
ೲפډ٣ࡕᐒஏࡋڄኧޑനεॶǴMAP Кྣ MLE ٩ФႥ-ऊՕහำׇٰՉǶ२ Ӄஒϩձჹ d ঁૈΚӛࡋՉୃ༾ϩǶMRCMLM ٣ࡕᐒࡋڄኧޑ໘ୃ༾ϩӛ ໆύޑϡનӵϦԄȐ20ȑᆶΒ໘ୃ༾ϩӛໆύޑϡનӵϦԄȐ21ȑȐഋ࢙ᐫǴ2001ǹ Wang, 1994ȑ )] ș ( ) ș [( ) ș ( ln ) ș ( ln ' 1 u u u u ) w w w w w w d d d ș L ș ș f )] ș ( ) ș [( )) ș ( ( u ') 1 u w w
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d V i i i ș P u Ȑ20ȑ ځύȝࣁșޑѳ֡ኧӛໆǴ)ࣁșޑӅᡂኧંତǶ ) ( ln 2 ș u L ș șrw s w w rs n i i i Q P u I¦
)) ș ( ) ș ( ( Ȑ21ȑ ځдำׇ߾Кྣനεཷ՟ीݤٰՉǶ ȐѤȑӚᅿૈΚीБݤޑКၨ ഋ࢙ᐫ(2006)Кၨ೭ΟᅿБݤӧӭӛࡋ CAT ύӚԖځᓬલᗺǴᗨฅவᡏߞࡋ ᆶෳໆᇤৡԶقǴMAP ࢂКၨӳޑǴՠࢂ㥲ᘜ܄ޑୃᇤΨࢂനᝄख़ޑǶEAP ޑी ᆒྗࡋᆶ MAP ৡόӭǴՠӛࡋኧၨଯਔǴૈΚी܌ሡޑਔ໔൩ϼΦǶMLE ࢂीᆒྗࡋၨৡޑБݤǶ܌аࡌૈΚӛࡋኧϿܭѤঁӛࡋёа٬Ҕ EAPǴа ෧Ͽ㥲ᘜ܄ୃᇤޑୢᚒǹՠࢂૈΚӛࡋၲډѤঁ܈ѤঁаਔǴനӳ٬Ҕ MAPٰՉǴόၸሡाݙཀ㥲ᘜ܄ୃᇤޑୢᚒǶ
စǵᒧᚒౣ
ǵൂӛࡋ CAT ᒧᚒБݤࢂႝတ܄ෳᡍύख़ाޑाનϐǴਥᏵόӕޑᒧᚒБݤᏤठόӕ ޑෳᡍਏǴӧԜϟಏதҔޑᒧᚒݤӵΠǺ Ȑȑനεૻ৲ݤ ҁࣴزύǴ၂ᚒޑᒧڗБݤനத٬Ҕനεૻ৲ݤǴځჴࡼᡯӵΠǺ ᡯǺଷڙ၂ޣҞૈΚीॶࣁTˆǴ٩ᏵTˆीᆉۘ҂ࡼෳ၂ᚒޑૻ৲ໆǴीᆉ ԄηୖԵϦԄȐ4ȑ܌ҢǺ ᡯΒǺᒧڗ၂ᚒૻ৲ໆനεޑ၂ᚒǴբΠࡼෳᚒҞǶ ȐΒȑനௗ߈ୃ౽ᜤࡋݤ ऩෳࡋcj z 0ਔǴᚒҞૻ৲നεॶόวғӧᜤࡋbjǴౢғୃ౽ԿmjǴന ௗ߈ୃ౽ᜤࡋݤࣁᒧᚒҞୃ౽ᜤࡋനௗ߈ڙ၂ޣૈΚीॶTˆޑᚒҞǴբࣁΠ ໘ࢤࡼෳޑᚒҞǶۓကୃ౽ᜤࡋmj(Birnbaum, 1968)ӵϦԄȐ22ȑ܌ҢǺ ¸ ¸ ¹ · ¨ ¨ © § 2 8 1 1 log 1 j j j j c a d b m Ȑ22ȑ ߾ᒧᚒਔᒧۘ҂ࡼෳЪᒧᚒڄኧFjനλޑᚒҞǴᒧᚒڄኧӵϦԄȐ23ȑ܌ҢǺ | ˆ | ) ˆ ( j j m F T T Ȑ23ȑ ȐΟȑ໔Ԅനεૻ৲ݤ ໔Ԅനεૻ৲ݤ٬Ҕ໔ૈΚॶޑᚒҞૻ৲ໆуᕴǴٰڗжӧࢌᗺૈΚॶޑᚒҞૻ৲ໆ(Veerkamp & Berger, 1997)Ƕ໔Ԅനεૻ৲ݤࢂᒧૻ৲ڄኧӧߞᒘ
໔ϣޑय़ᑈǴᒧനεޑૻ৲य़ᑈǴբࣁΠᚒࡼෳᚒҞǴࡺᒧᚒਔᒧڗۘ҂ࡼ ෳЪᒧᚒڄኧനεޣǴڄኧӵϦԄȐ24ȑ܌ҢǺ
³
u l d I Fj T j T T T T ˆ ˆ ( ) ) ( Ȑ24ȑ ځύǴ ) ) ˆ ( 96 . 1 ˆ , ) ˆ ( 96 . 1 ˆ ( ) ˆ , ˆ ( T T T T T T T T u l I I ǹ>
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) ( ) ( ) ( ) ˆ ( 2 T T T T j j j j Q P P I c Ƕ ȐѤȑԵቾ b ୖኧޑ a ϩቫݤChang, Qian & Ying(2001)ගрԵቾ b ୖኧޑ a ϩቫݤǴ׆ఈஒ a ϩቫݤӚϩቫ ύޑ b ॶϩթߥठ܄ǴٰѺઇ aǵb ϐ໔ޑ࣬ᜢ܄ǶځჴࡼᡯӵΠȐଷ L ࣁ ෳᡍߏࡋǹa ࣁ၂ᚒ᠘ձࡋǹb ࣁ၂ᚒᜤࡋȑǺ ᡯǺஒᚒ٩ྣ b ॶҗλԿεϩԋ T ঁ༧Ǵಃ 1 ঁ༧х֖നλޑ b ॶǴಃ Tঁ༧х֖നεޑ b ॶǶ ᡯΒǺӧಃ t ༧Ȑt =1,2,3,…,TȑǴஒᚒ٩ྣ a ॶҗλԿεϩԋ K ቫǴቫх ֖ၰ၂ᚒǴಃ 1 ቫх֖നλޑ a ॶǴಃ K ቫх֖നεޑ a ॶǶ ᡯΟǺ٩ׇஒঁ༧ޑಃ k ቫȐk=1,2,3,…,KȑӝٳԋቫǴӢԜᚒᡂԋڀ Ԗ K ቫޑ่ᄬǶ ᡯѤǺࡌҥӳ၂ᚒޑ่ᄬࡕǴڙ၂ޣ٩ׇவಃ 1 ቫ໒ۈࡼෳǴቫᒧڗ L/K ঁ ၂ᚒࡼෳǴޔࡼෳډಃ K ቫǴޔډڙ၂ޣࡼෳ L ᚒǶ ᖴ϶၃ǵቅ෩οǵդԽȐ2006ȑࣴزࡰрӧڰۓෳᡍߏࡋΠǴૈΚ֡Бਥৡ җλԶε௨ׇϩձࣁԵቾ b ୖኧޑ a ϩቫݤǵനௗ߈ୃ౽ᜤࡋݤǵᎃ߈ݤǵ໔Ԅ നεૻ৲ݤǹԵቾ b ୖኧޑ a ϩቫݤၨ໔Ԅനεૻ৲ݤԖၨեޑനεᚼӀǹӧ ࣬ӕૈΚीᆒྗࡋΠǴԵቾ b ୖኧޑ a ϩቫݤၨ໔Ԅനεૻ৲ݤԖၨեޑᚒҞ ख़ፄǶ Ȑϖȑa-ᎃ߈ݤ ᒲ҉ǵቅৎඁǵդԽȐ2005ȑගрׯᎃ߈ݤޑ a-ᎃ߈ݤǴځಃᡯࣁ ൂᗺԄനεૻ৲ݤǴಃΒᡯׯҗڋ a ॶǴ٬ԐයૈΚॶ҂ྗዴਔᒧҔ a ॶၨե ၂ᚒǴԶ a-ᎃ߈ݤޑჴࡼᡯӵΠǺ
ᡯǺஒᚒ٩ b ॶϩΟቫǴෳᡍයΟᚒ௦ڗᒿᐒᒧᚒǴ٬ڙ၂ޣӧෳᡍය ࡼෳᜤܰࡋ࣬ৡၨε၂ᚒǶ ᡯΒǺी߃ۈϯૈΚॶीॶTˆ ᡯΟǺਥᏵTˆᒧᚒύȐෳᡍߏࡋ-ςෳᡍᚒኧȑঁૻ৲ڄኧၨεޣޑ၂ᚒ ᡯѤǺӆவȐෳᡍߏࡋ-ςෳᡍᚒኧȑঁ၂ᚒύǴᒧځύᚒҞ a ॶനλෳᡍ ᡯϖǺख़ཥीૈΚॶࣁTˆǴӣډᡯΟǴޔډෳᡍᚒኧ่״Ƕ ਥᏵᒲ҉ǵቅৎඁǵդԽȐ2005ȑޑࣴزวǴ٬Ҕ a-ᎃ߈ݤǴᚒຫ εਔǴӧ၂ᚒᚼӀޑ֡Ϭࡋૈຫௗ߈ᎃ߈ݤǴЪૈΚीᇤৡၨեܭᎃ߈ݤǶ Βǵӭӛࡋ CAT Segall(1996)ஒཷ՟ڄኧڗჹኧޑΒ໘ୃ༾ϩၸϦԄȐ25ȑǴаഓૻ৲ڄኧڗ жǶ ) ș ( ǿ )] ș ( [ ( ) + ( j Ȑ25ȑ ځύǿ(ș)ࢂഓૻ৲ંତǴંତύಃrӈǵಃsՉޑϡનё߄ҢӵϦԄȐ26ȑ܌ҢǺ
¦
w w u w w » ¼ º « ¬ ª w w w ( n i i m i m s m i r m i s r m rs Q P ș P ș P ș ș L I ) ș ( ) ș ( ) ș ( ) ș ( ln ) ș ( ) ( ) ( ) ( ) ( 2 ) ( Ȑ26ȑ Ԅ߄Ңڙ၂ޣӧࡼෳֹmঁ၂ᚒࡕǴૈΚीॶࣁș(m)ޑഓૻ৲ંତǶԶಕуޑ ಃiᚒૻ৲ໆ߄ҢࣁIm(ș(m),ui)Ǵ߾ۓကӵϦԄȐ27ȑ܌ҢǺ ) ș ( ) ș ( ) ș ( ) ș ( ) , ș ( ) ( ) ( ) ( ) ( ) ( m i m i s m i r m i i m rs Q P ș P ș P u I w w u w w Ȑ27ȑ ӧӭӛࡋޑ CAT ύǴ٠ߚ٩ᏵӚൂӛࡋޑനεॶٰᒧᚒǴԶࢂᡣഓૻ৲ં ତޑՉӈԄॶനεϯޑ၂ᚒǴӵϦԄȐ28ȑ܌ҢǺ ) , ( ) (ș(m) , ș(m) ui , Ȑ28ȑ ځύ,(ș(m))߄Ңࡼෳֹmᚒϐࡕޑૻ৲ંତǴ,(ș(m),ui)ࢂ߄ҢᚒϣഭᎩ၂ᚒӧૈΚीӛໆș(m)ޑૻ৲ંତǶ Զ٬Ҕ MAP ਔǴځᒧᚒౣߡঅ҅ӵϦԄȐ29ȑ܌ҢǺ 1 ) ( ) ( ) ( , ) ( , ) , șm șm ui Ȑ29ȑ КၨϦԄȐ28ȑᆶȐ29ȑǴёаวѝৡӧૈΚӃᡍϩଛӅᡂ౦ኧંତޑϸંତ -1 ) Ƕ
ҴǵෳᡍಖЗచҹ
ෳᡍಖЗచҹޑЬाϩࣁȨനεෳᡍߏࡋȩᆶȨૈΚीޑനλᡂໆȩٿᅿ ȐഋӵǴ1998ǹഋཥᙦǴ1999ȑǴȨനεෳᡍߏࡋȩࢂࡰෳᡍޑᚒኧၲډႣޑ ߏࡋਔǴջଶЗෳᡍǹȨૈΚीޑനλᡂໆȩࢂࡰෳᡍޑૈΚीޑᡂໆ λܭႣॶǴջଶЗෳᡍǶ ٩Ᏽаഋॊޑाનӝԋ CAT ࡼෳࢬำǴӵკ 3 ܌ҢǺ კ3 CAT ࡼෳࢬำ ۓෳᡍଆᗺ ᒧᚒౣ ෳᡍ่״ ૈΚी όԋҥ ԋҥ ᒧෳᡍፕ ಖЗ చҹಃΟ ᚼӀᆅ
ӧԜλஒϟಏᚼӀᆅϐ࣬ᜢࣴزǴԶᚼӀᆅ܌Ҕᐒݤޑ୷ҁচ ࢂճҔ၂ᚒᚼӀୖኧٰᆅ၂ᚒࡼෳޑᐒǴаၲډ၂ᚒᚼӀڋӧႣጄ ൎǴаΠӃᇥܴ୷ҁޑϦԄӵϦԄȐ30ȑ܌ҢǺ ) | ( ) ( ) (A P S P A S P u Ȑ30ȑ ځύǴP(S)ࣁ၂ᚒᒧڗޑᐒǹP(A)ࣁ၂ᚒࡼෳޑᐒǹP(A|S)ࣁ၂ᚒӧᒧ ڗΠЪࡼෳޑᐒǴջࣁᚼӀୖኧEPǹrࣁёௗڙ၂ᚒനεᚼӀǶ ऩP(S)!rǴ߾з ) (S P r EP d ǴᙖԜٰᓸեଯᚼӀ၂ᚒޑрᐒǹऩP(S)drǴ ߾зEP 1ǴᙖԜᡣեᚼӀ၂ᚒޑрόڙज़ڋǶ ᆅ၂ᚒᚼӀޑБݤԖࡐӭǴёϩԋߚጕᚼӀᆅᆶጕᚼӀᆅǴ ߚጕᚼӀᆅനԐҗ Sympson ک Hetter(1985)ගрǴᙁᆀ SH ݤǴࢂჴ୍த٬ ҔޑБݤǴԖӭᏢޣஒځբۯ՜Ǵаၲډ׳ֹ๓ޑᆅǴٯӵǺASHCȐഋܹ০Ǵ2007ȑǵSHC(Chang, Ansley, & Twu, 2002)ǴԜᜪБݤᗨૈԖਏᆅ၂ᚒᚼӀǴ
ՠӧჴሞࡼෳϐѸӃॏжኳᔕᚼӀୖኧǴኳᔕᚼӀୖኧޑნکჴሞࡼෳ ნԖ܌όӕਔǴ၀Бݤޑᆅԋਏ൩όӵႣයǶ
ќᅿᚼӀᆅБݤࣁጕᚼӀᆅޑБԄǴٯӵǺSHOȐԙ܃։Ǵ2005ȑǵ
SHOF(Chen & LiaoǴ2005)ǵSHCOFȐᑯǴ2006ȑǵASHCOFȐጰᑑ݊Ǵ2008ȑǴ аΠϩࣁߚጕᚼӀᆅݤᆶጕᚼӀᆅݤٿᜪϟಏǶ
൘ǵߚጕᚼӀᆅݤ
ǵSHݤ Sympsonᆶ Hetter(1985)ගр SH ݤǴځᡯӵΠǺȐଷLࣁෳᡍߏࡋǹEPࣁ ᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀǶȑ ᡯǺۓ၂ᚒޑEP߃ۈॶࣁ 1ǶᡯΒǺଷڙ၂ޣҞࡼෳډಃ jᚒǴ٩Ᏽڙ၂ޣҞૈΚीॶǴճҔᒧᚒ ౣᒧڗΠᚒ၂ᚒiǶӆவU(0,1)ύᒧڗঁኧxǴऩx dEPiǴ߾ࡼෳԜ ၂ᚒǹऩx !EPiǴ߾όӆࡼෳԜ၂ᚒǶख़ᙟॊբݤޔډࡼෳֹᚒǶ ᡯΟǺਥᏵڙ၂ޣࡼෳಃ jᚒޑ่݀ीڙ၂ޣૈΚॶǴख़ᙟᡯΒޔډࡼෳֹL ᚒǶ ᡯѤǺख़ᙟᡯΒᆶᡯΟǴޔډ܌Ԗڙ၂ޣࡼෳֹǴਥᏵP(S)ٰፓ ၂ᚒޑEPǶ ऩP(S)!rǴ߾ ) (S P r EP ǹऩP(S)drǴ߾EP 1Ƕ ᡯϖǺפрLᚒEPനεޑ၂ᚒǴஒP(A|S)ॶࣁ 1ǶȐԜᡯࢂӢࣁᚒϼλǴ ஒԖᒧόډࡼෳ၂ᚒޑёૈ܄ȑ ᡯϤǺஒཥౢғޑEPǴख़ᙟᡯΒԿᡯϖǴޔډEPᛙۓЪP(A)λܭrǶ ॏжౢғޑᚼӀୖኧ൩ёၮҔӧჴሞޑ CATǶSH ݤᗨฅёаԖਏڋᚼӀǴ ՠࢂ SH ݤࡼෳϐӃॏжౢғᚼӀୖኧǴ࣬ӭޑਔ໔Ƕऩటࡼෳޑ҆ ᡏᆶॏжౢғᚼӀୖኧޑ҆ဂᡏόӕǴࣴزวჹᚼӀޑᆅஒόӵႣයȐԙ܃ ։Ǵ2005ȑǶCAT ᒧᚒਔǴ௦Ҕനεૻ৲ݤǴӢԜԋଯ᠘ձࡋᚒҞၸᒧ
ڗǴԶե᠘ձࡋᚒҞόܰᒧڗǴᚒޑ٬Ҕၨόଯ(Chang & Ying, 1999)ǶԶЪ
SHݤӧཱུᆄૈΚ໔Πޑ၂ᚒᚼӀ൳ၲ 100%(Chang & Ansley, 2003)Ƕ
ΒǵSHCݤ
Chang, Ansley & Twu(2002)ගр SHC ᚼӀᆅݤǴᆶ SH ᚼӀᆅݤ࣬ ՟ǴሡӃॏжᚼӀୖኧࡕӆՉࡼෳǴԶ SHC ݤׯؼޑҽࢂଞჹόӕޑૈΚ໔
ՉᚼӀୖኧޑॏжǶځᡯӵΠǺȐଷNࣁᚒߏࡋǹMࣁૈΚ໔ϩപኧǹEP
ࣁᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀȑ
ᡯǺஒڙ၂ޣૈΚϩթጄൎϪപԋMঁ໔Ƕ
ݤॏжౢғӚ໔܌ჹᔈޑEPॶǶനࡕԋঁM uNޑᚼӀୖኧં ତǶ
ஒԜM uNޑᚼӀୖኧંତၮҔӧჴሞޑCATǶᒧ၂ᚒਔǴڙ၂ޣૈΚ
ीॶTˆပӧ໔mȐm 1,2,3,,MȑǴ൩٬Ҕ໔mޑPKٰᆅ၂ᚒޑᚼӀǶ
SHCݤόፕڙ၂ޣޑ҆ဂϩթࣁՖǴࣣૈஒঁૈΚ໔ޑ၂ᚒᚼӀؼӳ ޑᆅǴฅԶځനεޑલᗺࢂૈΚीཞၸεȐChang, Ansley & Twu, 2002ǹ ᑯǴ2006ȑǶ ΟǵASHCᚼӀᆅݤ ഋܹ০Ȑ2007ȑගр ASHC ݤǴࣁΑׯ SHC ݤౢғૈΚीޑཞၸεޑ ୢᚒǴаගଯૈΚॶीᆒྗࡋǶASHC ᆶ SHC ݤ࣬՟ǴӃӧόӕૈΚ໔Ӄॏ жᚼӀୖኧࡕӆՉࡼෳǴԶ ASHC ݤׯؼޑҽࢂଞჹόӕޑૈΚ໔๏ϒόӕ ޑᚼӀᆅǴаගϲૈΚॶीǴଞჹڙ၂ޣΓኧၨӭޑૈΚ໔Ǵ๏ϒၨᝄ ޑᚼӀᆅǴӧ ASHC ݤύǴΞёа٩ྣ߃ۈۓࢂց٬Ҕ b ॶϩቫᒿᐒᒧᚒݤǴ ϩԋ ASHC1 ᆶ ASHC2ǹڙ၂ޣΓኧၨϿޑૈΚ໔Ǵ๏ϒၨቨޑᚼӀᆅǶ ځ ᡯ ӵ Π ǺȐ ଷ N ࣁ ᚒ ߏ ࡋ ǹLࣁ ෳ ᡍ ߏ ࡋ ǹM ࣁ ૈ Κ ໔ ϩ പ ኧ ǹ ) EP_spline( T ࣁࢌ၂ᚒ܌ԖᚼӀୖኧճҔϣකݤ܌ԋޑᚼӀୖኧԔጕǹrࣁёௗڙ ၂ᚒനεᚼӀȑ ȐȑASHC1 ᡯǺӃஒڙ၂ޣૈΚϩթጄൎϪപԋMঁ໔Ǵ٩Ᏽঁ໔ޑڙ၂ޣΓኧϩ ѲፓrॶǶڙ၂ޣΓኧКٯၨଯޑ໔ԖၨλޑrॶǴڙ၂ޣΓኧКٯၨ եޑ໔ԖၨεޑrॶǶ ᡯΒǺଞჹMঁૈΚ໔ǴӚ๏ۓSӜ֡ϩթڙ၂ޣǴ٩Ӛ໔rॶǴϩձ٬ Ҕ SH ݤǴॏжౢғӚ໔܌ჹᔈޑᚼӀୖኧǴനࡕԋঁM uNޑ ᚼӀୖኧંତǶ
ᡯΟǺଷڙ၂ޣૈΚीॶࣁTǴਥᏵനεૻ৲ݤפډΠၰࡼෳޑ၂ᚒ ) ... , , (n 123 N n ǴڗрᚼӀୖኧંତޑಃnՉǴճҔϣৡݤפрჹᔈTޑᚼ ӀୖኧEP_spline( ) T ȐऩEP_spline( ) T εܭ 1Ǵ߾зEP_spline( ) T ࣁ 1ȑǶջ ёճҔԜEP_spline( ) T ٰᆅ၂ᚒޑᚼӀǶख़ᙟᡯΟǴޔډڙ၂ޣࡼ ෳֹ܌Ԗ၂ᚒǶ ӧԜБݤύǴ၂ᚒύ܌ԖᚼӀୖኧࣣճҔϣකݤԋᚼӀୖኧԔጕǴૈΚ ीॶTόፕပӧՖೀࣣԖόӕޑᚼӀୖኧEP_spline( ) T ٰᆅ၂ᚒࡼෳᐒǶ ȐΒȑASHC2Ǻ ԜБݤޑEPંତᆶаૈΚϩթࣁ୷ᘵϐ SHC ᚼӀᆅݤ࣬ӕǴБݤޑόӕ ӧڙ၂ޣࡼෳޑkᚒǴ௦Ҕ b ॶϩቫᒿᐒᒧᚒݤٰᒧᚒǶځᡯӵΠǺ ᡯǺճҔ ASHC1 ᚼӀᆅݤޑ٣Ӄॏж่݀ǴڗளM uNޑEPંତǶ ᡯΒǺஒᚒ٩ b ॶελϩԋkቫǴ kࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ᡯΟǺڙ၂ޣࡼෳkᚒਔǴϩձԾkቫύӚᒿᐒᒧڗ၂ᚒǴՉࡼෳǶ ᡯѤǺ㲱Π(L k)ᚒۘ҂ࡼෳ၂ᚒǴଷڙ၂ޣૈΚीॶࣁTǴਥᏵനεૻ৲ ݤפډΠၰࡼෳޑ၂ᚒn(n 1,2,3...N)ǴڗрᚼӀୖኧંତޑಃnՉǴճ ҔϣකݤפрჹᔈTޑᚼӀୖኧEP_spline( ) T ȐऩEP_spline( ) T εܭ 1Ǵ߾ зEP_spline( ) T ࣁ 1ȑǶջёճҔԜEP_spline( ) T ٰᆅ၂ᚒޑᚼӀǶख़ ᙟᡯΟǴޔډڙ၂ޣࡼෳֹ܌ԖLၰ၂ᚒǶ
ASHC1ݤᆶ ASHC2 ݤӧૈΚीᆒྗࡋ֡ᓬܭ SHC ݤǹASHC2 ӧᚼӀ
ᆅǴӧ၂ᚒᚼӀѳ֡ॶǵ҂٬Ҕ၂ᚒኧࡰǴᡏਏૈന٫ǹӧڙ၂ޣࣁ தᄊϩթਔǴASHC2 ݤޑ߄όᇽܭ SHC ݤȐഋܹ০Ǵ2007ȑǶ
ॶǴቚуჴሞᔈҔޑ֚ᜤǴЪคݤᗉխࡼෳॏжኳᔕᚼӀୖኧޑၸำǴѿࡼ ෳნᆶচӃॏжᚼӀୖኧਔޑნόӕਔǴᚼӀୖኧߡคݤԖਏᆅ၂ᚒᚼӀ ǴԜѦӧୃᄊޑნΠǴASHC ޑനεᚼӀԖୃଯޑຝǶ
ມǵጕᚼӀᆅݤ
ǵSHOݤ ԙ܃։Ȑ2005ȑගр SH_online(SHO)ݤǴᚼӀୖኧаጕᕇளڗж SH ݤ٣ ӃॏжౢғǴҔٰᆅΠՏԵғޑ၂ᚒࡼෳᐒǴаၲډᚼӀᆅǶᚼӀୖኧ ॏжᆶࡼෳӕՉǴځᡯӵΠǺȐଷ L ࣁෳᡍߏࡋǹEPࣁᚼӀୖኧǹ r ࣁё ௗڙ၂ᚒനεᚼӀǶȑ ᡯǺۓ၂ᚒޑEP߃ۈॶࣁ 1Ƕ ᡯΒǺଷڙ၂ޣҞࡼෳډಃ jᚒǴ٩Ᏽڙ၂ޣҞૈΚीॶǴճҔനεૻ ৲ݤᒧڗΠၰࡼෳ၂ᚒiǶவU(0,1)ύᒧڗኧxǴऩx d EPiǴ߾ࡼෳ Ԝ၂ᚒǹऩx !EPiǴ߾όӆࡼෳԜ၂ᚒǶख़ᙟॊբݤޔډֹԋᚒࡼෳǶ ᡯΟǺਥᏵڙ၂ޣࡼෳֹ jᚒޑ่݀ीڙ၂ޣૈΚॶǴख़ᙟᡯΒޔډࡼෳֹL ᚒǶ ᡯѤǺਥᏵय़ڙ၂ޣޑᒧᚒǴीᆉрP(S)ٰፓ၂ᚒޑEPǶ ऩP(S)!rǴ߾ ) (S P r EP ǹऩP(S)drǴ߾EP=1Ƕ ᡯϖǺפрLᚒEPനεޑ၂ᚒǴஒEPॶࣁ 1ǶȐԜᡯࢂӢࣁᚒϼλǴஒ Ԗᒧόډࡼෳ၂ᚒޑёૈ܄ȑ ᡯϤǺஒཥౢғޑEPǴख़ᙟᡯΒԿᡯϖǴޔ܌Ԗڙ၂ޣࡼෳֹǶ SHOёᗉխ SH ݤ٣ӃॏжᚼӀୖኧǹӧࡼෳნ౦ΠǴ٩ฅૈԖਏᚼ ӀޑᆅȐԙ܃։Ǵ2005ȑǶSHO ݤޑჴࡼၸำሡ٩ᒘՏڙ၂ޣޑᒧᚒ่݀ ٰፓᚼӀୖኧǴऩԖဂڙ၂ޣӕਔௗڙෳᡍǴ߾চԖޑᄽᆉݤஒόҔǶΒǵSHOFᚼӀᆅݤ
ࣁΑׯ๓ SHO ӧࡼෳ߃යޑᚼӀᆅԋਏǴChen & Liao(2005)ࡌஒ Freeze ำׇ(Revuelta & Ponsoda,1998)уΕ SHO ύǴаගଯᚼӀᆅޑਏૈǴ၀Бݤᆀࣁ The SHO procedure with Freeze(SHOF)ǶFreeze ࢂঁᝄޑᚼӀᆅำׇǴѝा၂
ᚒޑᚼӀεܭrmaxǴFreeze ߡଶЗࡼෳ၀၂ᚒǴޔډځᚼӀλܭ܈ܭrmaxǴ
ωࡠൺ၀၂ᚒޑࡼෳǶ SHOFޑჴࡼࢬำک SHO ࣬՟ǴځനЬाৡ౦ӧܭᚼӀୖኧޑፓБԄǴӵ߄ 1Ǻ ߄ 1SHO ᆶ SHOF ޑᚼӀୖኧፓБԄКၨ SHO SHOF ऩP(S)>r Ǵ߾EP= ) (S P r ऩP(S) drǴ߾P(A|S)= 1Ƕ ऩP(A)>rǴ߾EP = 0ȐFreezeȑ ऩP(A)dr ЪP(S)>rǴ߾EP= ) (S P r ऩP(A)dr ЪP(S) drǴ߾EP = 1 ၸ Freeze ޑᝄᆅǴSHOF ׯ๓ጕᆅݤӧࡼෳ߃යᚼӀᆅόᛙۓޑ ǴЪڀԖၨեޑෳᡍख़᠄Ϸၨଯޑᚒ٬ҔǴ٠ᆢؼӳޑૈΚीྗዴ ܄Ȑֆދ࣓Ǵ2006ȑǶSHOF ᗨฅᡏᚼӀᆅԋਏόᒱǴՠऩଞჹӚঁૈΚНྗٰ ࣮ǴځԋਏёૈόᅰགྷǶ ΟǵSHCOFݤ ࣁΑჹӚૈΚϩѲ໔׳ӳޑᚼӀᆅǴᑯȐ2006ȑගрΑ The Conditional SH online Procedure with Freeze Control(SHCOF)ǴSHCOF ᆶ SHC ࣬՟Ǵ ЬाޑόӕӧܭᚼӀୖኧޑፓБԄǴځᡯӵΠǺଷ N ࣁᚒߏࡋǹM ࣁૈΚ
໔ϩപኧǹP(A|S)ࣁᚼӀୖኧǹr ࣁёௗڙ၂ᚒനεᚼӀǶ
ኧંତ PE ޑᚼӀୖኧॶ k Ⴃॶࣁ 1Ƕ ᡯΒǺа SHC ޑჴࡼБԄჹಃ j ঁڙෳޣࡼෳǶ ᡯΟǺଞჹಃ j ঁڙෳޣࡼෳ่݀Ǵख़ཥीᆉ၂ᚒӚૈΚ໔ޑP(A)ϷP(S)Ǵ ٠аΠय़ᄽᆉݤፓᚼӀୖኧ kǶऩP(A)!rǴ߾EP= 0ǹऩP(A)drЪ r S P( )! Ǵ߾ ) (S P r EP ǹऩP
A drЪP
S drǴ߾EP=1Ƕ ᡯѤǺаፓၸޑᚼӀୖኧંତEPǴख़ᙟᡯΒԿᡯϖǴޔډ܌Ԗڙ၂ޣࡼ ෳֹǶ SHCOF ݤ࣪ౣΑ SHC ॏжᚼӀୖኧޑਔၸำǴଞჹӚૈΚ໔ޑᚼӀբ Ԗਏޑᆅǹӧᚒಔ၂ᚒϷӭӛࡋ၂ᚒΠǴᑯ(2006)ว SHCOF ޑૈΚॶी ၨ SHC Ԗၨ٫ޑԋਏǴՠӧᚼӀᆅόӵ SHCǶ ѤǵASHCOFᚼӀᆅݤ
ጰᑑ݊Ȑ2008ȑගр ASHC online with freeze(ASHCOF)ᙖԜׯ๓ ASHC ݤǴӢ ࣁ ASHC ݤϩࣁٿ ASHC1 ᆶ ASHC2Ǵ܌а ASHCOF Ψϩࣁ ASHCOF1 ᆶ
ASHCOF2ǴځᡯϩॊӵΠǺȐଷNࣁᚒߏࡋǹM ࣁૈΚ໔ϩപኧǹEPࣁ ᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀǶEP_spline( ) T ࣁࢌ၂ᚒޑMঁᚼӀୖኧճҔ ϣකݤ܌ԋޑᚼӀୖኧԔጕǶȑ ȐȑASHCOF1 ᡯǺஒڙ၂ޣૈΚϩթጄൎϩപԋMঁ໔Ǵ٩Ᏽঁ໔ޑڙ၂ޣКٯፓ rॶǴႣڙ၂ޣૈΚϩଛ໒ۈࣁѳ֡ϩଛǵr=1ϷঁEPॶ֡ࣁ 1Ƕ ᡯΒǺଷڙ၂ޣ jૈΚीॶࣁTǴਥᏵനεૻ৲ݤפډΠၰࡼෳޑ၂ᚒ ) ... , , (n 123 N n ǴڗрEPંତޑಃnՉǴճҔϣৡݤפрჹᔈTޑᚼӀୖኧ ) EP_spline( T ȐऩEP_spline( ) T εܭ 1Ǵ߾зEP_spline( ) T ࣁ 1ȑǶ٩ࡼෳၸ
ำύཥीޑૈΚॶTख़ᙟ٬ҔEP_spline( ) T ᆅӚૈΚ໔ޑᚼӀǴޔ ډڙ၂ޣjࡼෳֹ܌Ԗ၂ᚒǶ ᡯΟǺ٩ᡯΒǴՉ j 1ঁڙ၂ޣࡼෳǴ႖cঁڙ၂ޣǴ߾ख़ཥीᆉঁ ໔ޑڙ၂ޣΓኧКٯፓrॶǶڙ၂ޣКٯၨଯޑ໔ԖၨλޑrॶǴڙ၂ ޣКٯၨեޑ໔ԖၨεޑrॶǶࡼෳֹcঁΓ߾٩ᏵόӕૈΚ׳ཥࡕ ޑrॶǴፓӚૈΚ໔ޑ၂ᚒᚼӀୖኧંତޑঁEPॶǶ ऩ P(A)!rǴ߾зEP=0ǹऩ P(A)drЪP(S)!rǴ߾з ) (S P r EP ǹऩ r A P( )d ЪP(S)drǴ߾зEP=1Ƕ ᡯѤǺख़ᙟᡯΒǴޔډ܌Ԗڙ၂ޣڙෳ่״Ƕ ȐΒȑASHCOF2 ԜБݤ ASHCOF1 ᜪ՟Ǵόӕܭڙ၂ޣࡼෳޑkᚒǴ௦Ҕ b ॶϩቫᒿᐒᒧᚒ ݤٰᒧᚒǴځᡯӵΠǺ ᡯǺஒڙ၂ޣૈΚϩթጄൎϩപԋMঁ໔Ǵ٩Ᏽঁ໔ޑڙ၂ޣКٯፓ rॶǴႣڙ၂ޣૈΚϩଛ໒ۈࣁѳ֡ϩଛǵr=1ϷঁEPॶ֡ࣁ 1Ƕ ᡯΒǺஒᚒ٩ b ॶελϩԋ k ቫǴk ࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ᡯΟǺڙ၂ޣjࡼෳ k ᚒਔǴϩձԾ k ቫύӚᒿᐒᒧڗ၂ᚒǴՉࡼෳǶ㲱 Π(L k)ᚒۘ҂ࡼෳ၂ᚒǴଷڙ၂ޣ jૈΚीॶࣁTǴਥᏵനεૻ৲ݤ פډΠၰࡼෳޑ၂ᚒn(n 1,2,3...N)ǴڗрEPંତޑಃnՉǴճҔϣৡݤ פрჹᔈTޑᚼӀୖኧEP_spline( ) T ȐऩEP_spline( ) T εܭ 1Ǵ߾з ) EP_spline( T ࣁ 1ȑǶ٩ࡼෳၸำύཥीޑૈΚॶTख़ᙟ٬ҔEP_spline( ) T ᆅӚૈΚ໔ޑᚼӀǴޔډڙ၂ޣ jࡼෳֹ܌Ԗ၂ᚒǶ ᡯѤǺ٩ᡯΟǴՉ j 1ঁڙ၂ޣࡼෳǴ႖cঁڙ၂ޣǴ߾ख़ཥीᆉঁ
໔ޑڙ၂ޣΓኧКٯፓrॶǶڙ၂ޣКٯၨଯޑ໔ԖၨλޑrॶǴڙ၂ ޣКٯၨեޑ໔ԖၨεޑrॶǶࡼෳֹcঁΓ߾٩ᏵόӕૈΚ׳ཥࡕ ޑrॶǴፓӚૈΚ໔ޑ၂ᚒᚼӀୖኧંତޑঁEPॶǶ ऩ P(A)!rǴ߾зEP=0ǹऩ P(A)drЪP(S)!rǴ߾з ) (S P r EP ǹऩ r A P( )d ЪP(S)drǴ߾зEP=1ǶᡯϖǺख़ᙟᡯΟǴޔډ܌Ԗڙ၂ޣ ڙෳ่״Ƕ ጰᑑ݊Ȑ2008ȑගр ASHCOF ૈᗉխॏжኳᔕᚼӀୖኧޑ֚ᘋǴᡣࡼෳԋਏό ڙࡼෳნ౦܌ቹៜǴࣴزวǴASHCOF ૈԖਏׯ๓ ASHC ᚼӀᆅǴӧૈ ΚॶෳᆢؼӳޑਏૈǴ٠ЪӧᚼӀᆅၨቨϷᚒၨεޑݩΠᓬܭ SHOFݤᆶ SHCOF ݤǶ
ಃѤ س໒วБݤ
ၗૻسޑࡌࢂሡाεໆޑΓΚǵਔ໔ᆶނΚǴԶЪሡाس ϩᆶीΓωǴӢࣁӧسޑࡌၸำύǴϩᆶीޑբӵ݀ؒԖዴჴ ӳǴёૈᏤठঁسޑѨ௳Ǵ܌аѸӸӧঁБݤǴբࣁسวޑ٩ᏵȐ ϡǴ1998ȑǶวၗૻسҗ໒ۈډֹԋޑᡯᆶၸำǴᆀբࣁسวғڮຼය(system development life cycle, SDLC)ǴҗܭঁسԖځόӕޑ܄ǴӢԜ ᜢܭسวғڮຼයޑჄϩᆶೕჄǴ٠ؒԖڰۓޑྗኳԄǶۭΠ൩ᘣѲԄǵᚉ ࠠԄǵख़ᙟуமԄϷӄфૈԄسวݤϩձӵΠǶ
൘ǵᘣѲԄسวݤ
Royce(1970)ගрǴԜวݤаسቫԛࣁଆᗺǴҗϩǵीǵำԄኗቪǵ ෳ၂Ϸᆢៈ໘ࢤՉ೬ᡏวำׇǴӵკ 4 ܌ҢǴᘣѲԄسวݤࣁനђԴԶ ЪԿϞϝࣁ٬ҔനቶݱޑБݤǴځӚ໘ࢤޑπբख़ᗺӵΠ܌ॊȐϡǴ1998ǹε ໋Ǵ2001ȑǺǵ߃ϩ ՉᇆπբϷۓကسҺ୍ޑҞǴפр܌ԖёՉБਢࡕǴՉࣴزᆶǴ פрന٫БਢǴ٠ԋҁਏϩǶ Βǵሡϩ ଞჹ߃ϩޑሡ׳ుΕޑࣴزǴԶقǴሡϩޑख़ᗺӧܭᕕှس ሡाϙሶǻ೯தѸዴᇡسޑфૈሡǵၗሡǵ٬Ҕޣϟय़ሡǵ܄ૈሡ ǵ೬ฯᡏሡǵӼӄϷڋሡϷسଛሡǶ Οǵ೬ᡏी ЬाޑҞޑӧܭሡϩ໘ࢤ܌ዴᇡޑӚᅿфૈሡǴᔕрҽှ،೭ ঁୢᚒޑБਢǶঁسҗӭኳಔ܌ಔԋǴኳಔҁيගٮΑࢌਸфૈǴᙖҗ ኳಔϐ໔ޑᜢᖄڋǴֹٰԋ٬ҔޣሡޑфૈǶ ѤǵำԄኗቪ ЬाπբࣁᒧӝޑำԄᇟقǴճҔ܌ᒧڗޑำԄᇟقஒ٬Ҕޣሡᙯඤԋ ҅ޑำԄዸǶ ϖǵෳ၂ ෳ၂πբЬाଞჹำԄኗቪޑำԄዸǴՉೱՍޑᡍϷჴޑπբǴዴᇡ ࢂց಄ӝسޑሡǶ Ϥǵᆢៈ ᆢៈࢂس҅ԄၮբࡕǴёૈҗܭᒱᇤǵфૈঅׯǵ೬ฯᡏޑ׳ཥǴԶჹܭ চԖޑำԄϷЎҹՉঅׯǶѬёૈՉ׳҅܄ᆢៈǵᔈ܄ᆢៈǵֹ๓܄ᆢៈϷ Ⴃٛ܄ᆢៈǶ
კ4 ᘣѲԄ໒วݤำׇ
ມǵᚉࠠԄسวݤ
Boar(1984)२ӃගрᚉࠠԄسวݤǴӵკ 5 ܌ҢǴԜᅿБݤࡪྣ٬Ҕޣޑ߃ ሡǴᏃೲֹԋঁᚉࠠسٮ٬Ҕޣ٬ҔǴϐࡕӆόᘐӦਥᏵ٬Ҕޣޑཀـ ՉسޑঅׯԿ٬ҔޣᅈཀࣁЗϐ೬ᡏس໒วБݤǶҗܭӧཥسวਔǴ٬Ҕ ޣ೯தѝૈගрϩޑሡǴ܌аऩ௦Ҕᚉࠠݤ߾ёаࡐזٰᕕှ٬ҔޣޑሡǴ ٠ૈᒿਔᆶسวޣޑྎ೯ǴԜᅿБݤҭёаҔٰᒣձ٬Ҕޣޑᄊфૈ ሡǴ܈ޣஒπբᚉࠠຑঅ҅ԋനಖޑ೬ᡏౢࠔǶᚉࠠسวݤၸำёϩࣁሡ ϩǵזೲᇙբǵࡌᚉࠠǵຑঅ҅Ϸֹԋس໘ࢤǴӚ໘ࢤޑπբख़ᗺӵ Π܌ॊȐε໋Ǵ2001ȑǺ ǵሡϩ ໒วޣᆶ٬Ҕޣሡଆፕ٠ۓက೬ᡏޑҞϷ܌ԖޑфૈሡǴӕਔӈрѸ ుΕۓကޑӦБǶ Βǵזೲᇙբ ߃ϩ ೬ᡏी ำԄኗቪ ෳ၂ ᆢៈ ሡϩख़ӧ٬Ҕޣё࣮ډޑϟय़ǴӵᒡΕᒡрϐฝय़Ϸൔ߄Ǵ໒วޣ٬ҔԖ ޑำԄኳހ܈ᔈҔ࣬ᜢπڀǴӵൔ߄ϷԄౢғᏔٰၲԋזೲीޑҞޑǶ Οǵࡌᚉࠠ ֹԋёՉޑ೬ᡏᚉࠠౢࠔǶ Ѥǵຑس܈ֹԋس ၸ٬ҔޣޑჴሞᏹբᆶሡຑǴගрሡޑፓǶ ၸॊޑำׇຼԶൺۈޑՉǴޔډᅈى٬ҔޣϐሡǴωᝩុՉࡕុϩ Ǵी…໘ࢤǴӢԜ໒วޣӧԜ໘ࢤջૈкϩΑှٗ٤фૈࢂѸीǶ კ5 ᚉࠠԄسวݤำׇ
ୖǵख़ᙟуமԄسวݤ
ख़ᙟуமԄسวݤΞᆀሀቚԄسวݤǴѬࢂ௦ҔᡯቚໆޑБԄٰ วǴᚐѦޑηسфૈࢂӧԛቚуޑၸำύуΕԿ೬ᡏسǴ٠ख़ཥՉ ीǵᇙբϷᚉࠠঅ҅ޑπբǴӵԜख़ᙟቚໆޔډ܌ԖηسфૈуΕسࣁЗǴ ӵკ 6 ܌ҢǶ זೲᇙբ ࡌᚉࠠ ሡϩ অ҅ ຑس όঅ҅ ֹԋسკ6 ख़ᙟуமԄسวݤำׇ ځπբᡯԖΟǺ1.ࡌೀڋమൂǵ2.ቚໆᡯǵ3.ղᘐೀڋమൂࢂ ց่״ǶਥᏵϡ(1998)ޑှញǺ२ӃѸሡࡌೀڋమൂǴѬёۓကঁسѸ ڀഢޑ܌ԖᔈҔسфૈǴΨёаᕕှډຯᚆֹԋޑسᗋԖӭᇻǴЪҗቚໆ ᡯύԾೀڋమൂ׀ᆄڗϩπբǴזೲࡌᚉࠠǴҗ٬Ҕޣޑຑ่݀ᕇ ளঅ҅ޑཀـǴѬх֖ीǵᇙբϷϩǴځύीҽёԾᒧीБݤǴᇙբБ य़߾ሡхࡴำԄޑኗቪϷෳ၂Ǵϩ߾ࢂҗ٬Ҕޣ٬ҔࡕǴගٮཀـ٠ၸຑ ޑำׇǴஒ܌ሡޑঅ҅Ǵܫೀమൂޑ׀ᆄǶനࡕղᘐೀڋమൂࢂց่״Ǵ ऩࢂ߾ঁسֹԋǴऩࣁց߾ख़ᙟՉቚໆᡯǶၸԜᅿၸำख़ᙟόᘐӦჴՉ ϐࡕǴૈֹ๓Ӧஒ܌ሡޑфૈߕуӧسύǶ
စǵӄфૈԄسวݤ
ԭ੫(2003)ගрӄфૈԄس໒วБԄࢂࡰঁၗૻسޑ໒วѸҗȨسϩȩ(system analysis)ǵȨسीȩ(system design)ǵȨسࡌȩ(system
development)ǵȨسჴࡼȩ(system implementation)ǵȨسຑ᠘ȩ(system evaluation)
ϖঁำׇǴঁسޑ໒วωᆉֹֹԋǶඤѡ၉ᇥǴ໒วسѸӃΑှس ޑҞޑϷሡǴௗीسޑϣᆶࢬำǴฅࡕ໒ۈኗቪำԄǴനࡕҬ๏٬Ҕޣ ٬ҔᆶຑǴҗ٬ҔޣՉຑ᠘πբϐࡕǴ൩ֹԋֹ๓ޑၗૻسǴӄфૈԄ س໒วำׇӵკ 7 ܌ҢǶ ी 0 ᇙբ 0 ϩ 0
Ǿ
ቚໆᡯ ी 1 ᇙբ 1 ϩ 1 ी 2 ᇙբ 2 ϩ 2 ी n ᇙբ n ϩ n ቚໆᡯკ7 ӄфૈԄسวݤำׇ வаѤᅿسวБݤύǴрӚᅿسวБݤޑ܌ਔ໔ǵᓬᗺᆶ લᗺǴӵΠ߄ 2Ǻ ߄ 2 سวБݤޑКၨ سวБݤ ਔ໔ ᓬᗺ લᗺ ᘣѲԄ ၨߏ ൻׇᅌǴܰඓඝঁس ࢎᄬǶ ऩԖᒱᇤǴёૈा࣬ ӭޑਔୢٰঅ҅Ƕ ᚉࠠԄ ၨอ זೲӦᇙрᚉࠠǴӆ٩٬ ҔޣሡǴόᘐӦঅ҅Ǵᗉ խε൯ᒱᇤޑঅׯǶ ሡाόᘐෳ၂Ǵ܌ ޑෳ၂ΓΚ࣬ჹቚуǶ ख़ᙟуமԄ ၨอ ёаᕕှຯᚆسֹԋᗋԖ ӭᇻǶ ሡाόᘐෳ၂Ǵ܌ ޑෳ၂ΓΚ࣬ჹቚуǶ ӄфૈԄ ၨอ ᙁዅޑीࢬำ ؒԖঅ҅ޑำׇ வ߄ 2 ޑКၨύǴёаޕၰѤᅿسวБݤӚԖځᓬલᗺǶԶҁࣴزज़ܭਔ ໔ޑୢᚒǴคݤ௦ҔᘣѲԄޑسวݤǴЪӧΓΚϷ׆ఈسӧֹԋࡕૈ಄ӝ٬ ҔޣሡޑԵໆΠǴҁࣴزޑس໒วБݤǴஒ٩ᚉࠠԄسวݤٰวа MIRT ࣁ୷ᘵޑ CAT سǶ
ಃϖ ႝတᆛၡמೌ
ࡌسନΑሡाፕЍϐѦǴᗋሡाᙖҗႝတᆛၡБय़ޑמѯஒཷۺჴᡏ ϯǶҁسޑࡌҥၸำࢂ୷ܭӼӄ܄ǵჴҔ܄ϷᔮਏᔈޑԵໆǴ܌аჹܭբ سޑᒧǴࢂаၨӼӄǵᛙۓޑ Linux سࣁѳѠǴځᎩ࣬ᜢ໒วπڀΨаխǵ سϩ سी سࡌ سჴࡼ سຑ᠘ᛙۓࣁᓬӃԵໆǶԜѦҁسࢂࡌӧᆛሞᆛၡᕉნύǴӢԜ௦ҔᆛၡΟቫԄЬவ ࢎᄬၗמೌǴаΠϩձᇥܴ࣬ᜢπڀǺ
൘ǵΟቫԄЬவࢎᄬၗמೌ
೭ঁࢎᄬЬाӧҔЊᆄک՛ܺᏔᆄϐ໔уύϟቫǴԋࣁΟቫԄޑЬவࢎᄬ (Client/Server)Ƕӧ೭ᅿࢎᄬΠǴҔЊᆄ٬Ҕྗޑ೯ૻڐۓ(ٯӵǺTCP/IP)ᆶύϟቫ ྎ೯ǹύϟቫ٬Ҕྗޑၗ೯ૻڐۓ܈ၗύϟ೬ᡏᆶࡕᆄޑၗྎ೯Ƕ ΟቫԄЬவࢎᄬᡄᒠቫޑ่ᄬӵკ 8 ܌ҢǴӚቫޑҺ୍Ԗх֖٬Ҕޣϟय़ޑၗև ቫ (Presentation Tier) ǵ ᏹ բ ၗ ೀ ޑ ᡄ ᒠ ቫ Ǵ Ξ ᆀ ᡄ ᒠ ቫ (Functionality/Business Tier)аϷٮᔈၗޑӸڗ୍ܺޑၗ୍ܺቫ(Data Tier)Ȑර ৰǴ2000ȑǶҗკ 8 ளޕǴᡄᒠೀቫၸ PHP(Hypertext Preprocessor)ೀၗǴ٠ճҔ่ ᄬϯ၌ᇟق(Structure Query Language, SQL)ٰᆅၗǶSQL ࣁߚำׇ܄ᇟق (non-procedural)ǴѬҁيόૈᐱҥӸӧǴሡा٩ྣঁำׇೀӭޑբٰӸ ڗၗȐරৰǴ2000ȑǶ კ8 ΟቫԄЬவࢎᄬᡄᒠკ
ມǵ໒วπڀ
PHP(Hypertext Preprocessor)ࢂᅿቶݱ٬ҔǵӭҔޑ໒ܫচۈዸဌҁᇟق (Script Language)ǴΜϩӝܭᆛ।ޑ໒วǴ٠ё൪Ε HTML ᆛ।ύǶନԜϐѦᗋё ᘤំᏔ Apache/PHP ၗȐMySQLȑ ၗևቫ ᡄᒠೀቫ ၗӸڗቫаᔈҔӧ໒วำԄǴࢂ࣬ڀԖ໒วቸ܄ޑᇟقǶPHP Ьा٬Ҕܭ՛ܺᏔ(Server) ᆄޑᄊᆛ।ޑ໒วǴфૈᆶ ASP(Active Serve Page)ǵJSP(Java Server Pages)ǵCold
Fusion࣬՟ǶќѦ PHP ޑᇟݤᜪ՟ܭ C/C++ե໘ᇟقǴ܌аၗૻΓ܈ࢂዕ
ځдำԄᇟقޣࣣ࣬ܰЋǶ܌аӧჴբၠѳѠسਔࢂߚதӳҔޑπڀǴ ٠ЪЍජӭᅿၗǶځд࣬ᜢၗૻፎୖྣ۔Бᆛઠ(http://www.php.net/)Ƕ
ୖǵၗس
MySQL ࢂڀԖזೲǵӭՉᆣ(multithread)ǵӭ٬ҔޣЪфૈமεޑᜢᖄ
Ԅၗᆅس(relational database management system, RDBMS)ǴаЬவԄࢎᄬޑ БԄٰჴǴ٠Ъၸঁ՛ܺᏔᆄޑ MySQL ᆶӭόӕҔЊᆄޑڄԄޑಔ ԋǶуՉ୷ҁ SQL ࡰзޑਏߚதِೲǴᆶ༾೬ SQL(MS-SQL)ϷҘମЎ(Oracle) ҔၗٰКၨࢂడόᇽՅǴ׳ख़ाޑᗺࢂ MySQL ҔӧߚҔࢂխ Ǵ٠ЪЍජύЎεϖዸ(Big5)ǴќѦଞჹӭόӕޑѳѠΨԖჹᔈޑЍජǴӧӼ းۓय़Ψࢂ࣬ܰǶӢԜҁࣴزޑࡕᆄၗ،ۓ௦Ҕ MySQLǶځд࣬ᜢၗ ૻፎୖྣ۔Бᆛઠ(http://www.mysql.com/)Ƕ
စǵᆛၡ՛ܺᏔ
Apache ࢂԾҗ೬ᡏǴΨࢂଯਏૈޑᆛઠ՛ܺᏔ(Web Server)ǴҞ
ቶݱၮҔӧӚᅿբѳѠय़ǴᛙۓЪၨϿޑၗྍǴӧᆛሞᆛၡޑ՛ܺᏔѳѠ य़ࢂε൯ሦӃځдቷǶԶЪ Apache ᆛၡ՛ܺᏔҁيගٮΑ࣬ӭኬϯޑኳಔǴ سीޣёаவύࡷᒧӝޑϩ๏ϒӼး٬ҔǴᘉк܄࣬மεǴԶЪڀԖЍ ජ PHP ޑኳಔǶځд࣬ᜢၗૻፎୖྣ۔Бᆛઠ(http://www.apache.org /)Ƕ
ҴǵӝԄᆛၡ՛ܺᏔ
XAMPPࢂӝԄᆛၡ՛ܺᏔǴх֖ ApacheǵMySQLǵPHP ᆶ PerlǴҞխ
ගٮѤᅿހҁ(LinuxǵWindowsǵMac OS X Ϸ Solaris)ǶૈᡣᆛၡسࢎઠޣБߡֹ ԋ୷ҁޑࢎઠۓǶ
ಃΟക ࣴزБݤ
ҁࣴزЬाҞޑࢂࡌаMIRTࣁ୷ᘵޑCATسǴ٠уΕᚼӀᆅޑᐒڋǴ аᆢៈෳᡍᚒޑӼӄ܄ᆶჴҔ܄Ƕ ਥᏵҁࣴزޑҞޑՉࣴزीǴҁകЬाϩࣁΟঁϩٰᇥܴঁࣴزࢎ ᄬǶϩձࢂࣴزࢬำǵسϩᆶीǵኳᔕMCATჴᡍीᆶࣴزπڀǶಃ ࣴزࢬำ
ࣴزࢬำӵკ9܌ҢǴ२ӃՉسࡌᆶෳᡍ࣬ᜢፕޑЎǴ،ۓࣴز ЬᚒࡕǴБय़ӃଞჹࣴزޑسሡՉϩᆶीǴௗ໒ว٬ҔޣኳಔǴฅ ࡕኗቪMCATਡЈำԄǴќБय़җჴቻၗჹኧᏢࣽᚒՉӭӛࡋኳԄޑୖኧ ϩǴӆҗीֹԋޑ၂ᚒୖኧᆶڙ၂ޣբเϸᔈٰኳᔕMCAT٠ϩ่݀Ǵӆஒ ኳᔕϩ่݀ӣ㎸๏سǴӆவՉسෳ၂ၸำ܌วޑୢᚒՉঅ҅Ǵനࡕኗ ቪࣴز่݀ᆶࡌǶკ9 ࣴزࢬำ
ಃΒ سϩᆶी
൘ǵسࢎᄬϩ
ҁࣴزࡌޑMCATس௦ҔЬவԄࢎᄬǴӵკ10܌ҢǶسёϩࣁҔЊᆄ ȐClient SideȑϷ՛ܺᏔᆄȐServer SideȑǺҔЊᆄࣁ٬Ҕޣᏹբϟय़ҽǴ٬Ҕޣ ၸᆛ।ᘤំᏔҗHTMLᇻᆄฦΕسǹ՛ܺᏔᆄޑբس௦ҔCentOS 5ȐLinux ހҁȑǴࡕᆄၗ՛ܺᏔ௦ҔMySQLǴҔٰՉำׇᆶӸܫҁسޑ٬Ҕޣၗǵ ԋᕮǵᚒǴᆛ।՛ܺᏔ೬ᡏࣁApacheǴᆛ।՛ܺᏔᆄޑำԄᇟقࣁPHPǴᙖҗ PHPٰวӚኳಔфૈำԄ٠ᆶၗՉೱ่ǴќѦ٩ྣჴሞޑሡǴӧPHP Ў سሡϩी ٬Ҕޣϟय़໒ว ኳᔕ! ႝတϯ܄ෳᡍ! ኗቪ MCAT ਡЈำԄ ෳᡍ߃ۈۓ ᒧᚒౣ ૈΚीݤ ᚼӀᆅ سෳ၂ᆶঅ҅ ϩ่݀! ኧᏢࣽᚒ! ୖኧϩ! ่݀ᆶࡌ!
ޑำԄύΨ่ӝHTMLǵJavaScript ځдᆛ।ำԄᇟقǴӅӕֹԋӚኳಔޑфૈ ሡǶ კ10 سࢎᄬኳԄ
ມǵ܄ෳᡍࢬำी
ҁࣴز܌ೕჄ܄ෳᡍࢬำӵკ11܌ҢǴՏڙ၂ޣୖуෳᡍࡕǴӃۓ Ӛӛࡋޑ߃ۈૈΚॶᆶ၂ᚒǴڙ၂ޣֹ߃ۈۓޑ၂ᚒࡕǴӧૈΚीБय़ё ᒧMLEᆶEAPٿᅿૈΚीޑБݤǴ٩ྣۓޑૈΚीݤՉૈΚीǴӧᒧ ᚒౣБय़ёᒧനεૻ৲ݤǴ٠٩ྣीޑૈΚॶᆶۓᒧᚒౣǴவᚒύࡷ ᒧ၂ᚒǴᚒࡷᒧޑ၂ᚒၸᚼӀᆅǴа،ۓࡷᒧ၂ᚒࢂցёаࡼෳǴ ऩόૈࡼෳǴ߾Ԝ၂ᚒჹӕՏڙ၂ޣόૈӆᒧڗǴӧᒧᚒౣБय़ёᒧ SHCOǵSHCOFǵASHCOϷASHCOFǴऩςၲډനεෳᡍߏࡋ܈ૈΚीനλᡂ ໆਔǴ߾่״ෳᡍౢғᏢಞບᘐൔǴց߾ᝩុࡼෳᆶૈΚीޔډ಄ӝෳᡍύ ЗచҹǶ Request HTML Document ࠼Њᆄ Internet HTML Document ՛ܺᏔᆄ CentOS 5 HTML JavaScript ᘤំᏔ! ٬Ҕޣ PHP ၗ ȐMySQLȑ ᆛၡ ՛ܺᏔ ȐApacheȑკ11 ܄ෳᡍࢬำी
ୖǵسኳಔी
ҁࣴز܌ीޑسኳಔᆶ٬ҔޣϷၗޑᜢ߯ӵკ12܌ҢǴନΑගٮ܄ ෳᡍኳಔϐѦǴᗋԖځдфૈޑኳಔǶჹڙ၂ޣԶقǴёаၸ܄ෳᡍኳಔǴ٩ Ᏽόӕޑ၂ᚒϸᔈኳԄǵᒧᚒౣǵૈΚीݤǵᚼӀᆅᆶෳᡍύЗۓՉ ԋҥ ۓӚӛࡋ ߃ۈૈΚᆶ၂ᚒ ᒧᚒౣ Ȑനεૻ৲ݤȑ ౢғᏢಞບᘐൔ ૈΚी ȐMLE ᆶ EAPȑ όԋҥ ಖЗచҹ Ȑനεෳᡍߏࡋ܈ ૈΚीനλᡂໆȑ ڙ၂ޣ ᚒ ᚼӀᆅ ȐSHCOǵSHCOFǵ ASHCOϷ ASHCOFȑ ԋҥ όԋҥ܄ෳᡍǴΨёаၸԋ݀၌ኳಔǴ၌ԛෳᡍᐕำǹჹᆅޣԶقǴёа ၸဦᆅኳಔǴཥቚ܈մନڙ၂ޣဦᆶஏዸǴΨёаၸᚒᆢៈኳಔǴՉ ᚒޑཥቚ܈অׯǴΨёаၸෳᡍࡼෳኳಔǴۓӚڙ၂ޣ܌ឦભޑෳᡍᜪࠠǴ х֖ᒧόӕޑᚒᆶۓόӕޑ܄ෳᡍБԄǴᗋёаၸԋ݀၌ኳಔǴ၌ ܌Ԗڙ၂ޣޑ܌ԖෳᡍᐕำǶ კ12 MIRT ኳಔࢎᄬ ӚኳಔޑಒᇥܴӵΠǺ ǵဦᆅኳಔ ӵკ 13 ܌ҢǴڙ၂ޣѝૈჹԾρޑဦၗՉঅׯǹᆅޣёаଞჹࢌՏ٬ Ҕޣཥቚ܈অׯဦၗǴΨёаԛ༊Ε܈༊рӭဦၗǴΨёаץԛঅׯ ۓၗǴᗋёа၌ၗύ܌Ԗ٬ҔޣޑဦǶ ᚒᆢៈኳಔ ဦᆅኳಔ ܄ෳᡍኳಔ ᆅޣ ڙ၂ޣ ဦၗ ၂ᚒၗ ෳᡍԋ݀ ෳᡍࡼෳኳಔ ෳᡍၗ ᒧᚒၗ ԋ݀၌ኳಔ ٬Ҕޣ سኳಔ ၗ
კ13 ဦᆅኳಔ Βǵᚒᆢៈኳಔ ӵკ 14 ܌ҢǴᚒޑᆢៈޣёаཥቚ܈ጓঅᚒӜᆀϷᚒ࣬ᜢၗǴΨёа ଞჹᚒޑ၂ᚒՉཥቚǵጓঅ܈մନǴᗋёа༊Ε܈༊р၂ᚒୖኧȐ᠘ձࡋୖኧǵ ᜤࡋୖኧǵෳࡋୖኧȑǶ კ14 ᚒᆢៈኳಔ Οǵෳᡍࡼෳኳಔ ӵკ 15 ܌ҢǴӧҁسύԵໆၗޑॄᆶჴሞޑၮҔǴஒෳᡍࡰࢴа ભࣁൂՏǴ܌аෳᡍޑᆅޣёаᒧటࡼෳޑભǴӆᒧགྷाࡼෳޑᚒǴ നࡕӆᒧࡼෳᅿᜪȐ၂ᚒϸᔈኳԄǵᒧᚒౣǵૈΚीݤǵᚼӀᆅᆶനε ෳᡍߏࡋȑǴ൩ёаࡰࢴෳᡍ๏ભࡼෳǴ࣬ჹΨёаڗෳᡍǶ ᚒᆢៈኳಔ ᚒ! ཥቚǵጓঅ ၂ᚒཥቚ! ጓঅ܈մନ ၂ᚒୖኧ! ༊Εǵ༊р ဦᆅኳಔ ဦ! ༊Εǵ༊р ဦ! ץԛঅׯ ဦ၌ ൂဦ! ཥቚǵঅׯ
კ15 ෳᡍࡼෳኳಔ Ѥǵ܄ෳᡍኳಔ ӵკ 16 ܌ҢǴڙ၂ޣ໒ۈෳᡍࡕǴҗόӕޑ၂ᚒϸᔈኳԄᆶૈΚीݤी ૈΚǴӆҗኩਔीૈΚᆶᒧᚒౣᒧ܄ᚒҞǴӧၸᚼӀᆅǴ،ۓࢂց ෳᡍԜᚒǴޔډၲԋෳᡍಖЗచҹֹԋ܄ෳᡍǶ җЎޑКၨᆶჴሞज़ڋԵໆΠǴҁسӧ၂ᚒϸᔈኳԄ໒วΑൂӛࡋ ၂ᚒϸᔈኳԄᆶӭӛࡋ၂ᚒϸᔈኳԄǹӧᒧᚒౣ໒วΑനεૻ৲ݤǹӧૈΚी ݤ໒วΑ MLE ᆶ EAPǹӧᚼӀᆅ໒วΑ SHCOǵSHCOFǵASHCO ᆶ ASHCOFǶ
კ16 ܄ෳᡍኳಔ ϖǵԋ݀၌ኳಔ ӵკ 17 ܌ҢǴڙ၂ޣёа࣮ډҁيޑ୷ҁၗǵൂϡᏢಞइᒵϷෳᡍບᘐൔ ǹᆅޣёаଞჹ܌Ԗڙ၂ޣޑෳᡍ่݀Ƕ ܄ෳᡍኳಔ ၂ᚒ ϸᔈኳԄ ૈΚ ीݤ ᒧᚒౣ ᚼӀ ᆅ ෳᡍࡼෳኳಔ ࡼෳભ! ޑᆅ ࡼෳᚒ! ޑᆅ ࡼෳᅿᜪ! ޑᆅ
კ17 ԋ݀၌ኳಔ
ಃΟ ኳᔕMCATჴᡍी
ҁࣴزޑჴቻၗࢂҗ୯ҥᆵύ௲ػεᏢ௲ػޑෳᡍीᆶ܄ᏢಞࣴزύЈ ගٮǴෳᡍ၂ᚒਥᏵ୯λϖԃભኧᏢࣽૈΚࡰࣴวǴ٠ஒځϩࣁኧᆶໆǵ൳Ֆǵ жኧΟঁӛࡋǶෳᡍᚒӅх֖ 238 ᚒǴࡼෳኬҁ 775 ΓǴԶჴᡍीϩࣁٿঁ ҽǴঁࢂૈΚीޑຑǴќঁࢂᚼӀᆅޑຑǴаΠϩձᇥܴǺ൘ǵૈΚी
ӧኳᔕ MCAT ၸำύǴԾᡂࣁૈΚीݤ(MLE, EAP)ǴᒿෳᡍߏࡋቚуǴ ຑӚӛࡋޑ֡Бਥৡ(root mean squared error, RMSE)ޑΠफ़Ƕ