電腦化適性測驗系統之研發-以MIRT為基礎

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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

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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

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ύЎᄔा

౜Ϟӭӛࡋႝတϯ፾܄ෳᡍࣴزύǴεӭаኳᔕࣴزࣁЬǴ௖૸όӕෳᡍᜪࠠ ΠޑԋਏǴၨϿ໒วӭӛࡋႝတϯ፾܄ෳᡍޑჴሞس಍Ǵ୯ϣҞ߻ѝԖ୯ҥѠ᡼ৣ ጄεᏢ௲ػຑ᠘ᆶว৖ࣴزύЈ໒ว࣬ᜢޑس಍ǴՠԜس಍ࢎᄬύۘ҂уΕ၂ᚒޑ ᚼӀ౗௓ᆅǴ܌аҁࣴزࣴวޑس಍ନΑࡌ࿼٬Ҕޣϟय़ගٮڙ၂ޣ຾Չӭӛࡋႝ တϯ፾܄ෳᡍǴᗋଞჹ၂ᚒ຾ՉᚼӀ౗௓ᆅǶ ୷ܭ΢ॊࣴز୏ᐒǴҁࣴزҞޑӵΠǺ ΋ǵࡌ࿼֖ᚼӀ౗௓ᆅޑӭӛࡋႝတϯ፾܄ෳᡍس಍Ǵᡣڙ၂ޣё຾Չࡼෳᆶᆅ౛ ޣёࡕᆄᆅ౛Ƕ Βǵаჴቻၗ਑ኳᔕӭӛࡋႝတϯ፾܄ෳᡍس಍ޑࢬำǴаຑ՗س಍ϐԋਏǶ ҁࣴز่݀ࣁࡌ࿼ӭӛࡋႝတϯ፾܄ෳᡍޑ٬Ҕޣϟय़Ǵᡣڙ၂ޣёаୖуෳ ᡍ٠ࢗ၌ԋ݀ǴΨૈᡣᆅ౛ޣᏱԖࡕᆄᆅ౛ޑѳѠǹӧ၂ᚒϸᔈኳԄБय़Ǵӧҁس ಍уΕӭӛࡋ၂ᚒϸᔈኳԄޑӭӛࡋᒿᐒ߯ኧӭ໨ࢶ୷ኳԄȐmultidimensional random coefficients multinomial logit modelȑǹӧᚼӀ౗௓ᆅБय़ǴуΕSHCޑጕ΢ ᚼӀ౗௓ᆅݤᆶаૈΚϩթࣁ୷ᘵϐSHCޑጕ΢ᚼӀ౗௓ᆅݤǴ࿯࣪ᚼӀ౗ୖኧϸ ᙟॏжޑਔ໔ᆶှ،ॏж܌٬Ҕኬҁکჴሞ௃ნኬҁࢂց΋ठޑୢᚒǶ ӧόӕૈΚ՗ीݤޑኳᔕࣴزύǴว౜٬ҔԜӭӛࡋኧᏢࣽᚒ৤ਔǴ᏾ᡏԶق යఈࡕᡍ՗ीݤᓬܭനεཷ՟՗ीݤǴ܌аࡌ᝼٬ҔԜᚒ৤ਔǴ٬Ҕයఈࡕᡍ՗ी ݤǶ ᜢᗖӷǺႝတ፾܄ෳᡍǵ၂ᚒϸᔈኳԄǵӭӛࡋǵᚼӀ౗௓ᆅ

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Abstract

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

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Ҟᒵ

ύЎᄔा ... I Abstract... II Ҟᒵ ...III ߄Ҟᒵ ...IV კҞᒵ ...V ಃ΋ക ᆣፕ ...1 ಃ΋࿯ ࣴز୏ᐒ...1 ಃΒ࿯ ࣴزҞޑ...2 ಃΟ࿯ Ӝຒှញ...2 ಃѤ࿯ ࣴزጄൎᆶज़ڋ...4 ಃΒക Ў᝘௖૸ ...5 ಃ΋࿯ ၂ᚒϸᔈ౛ፕ...5 ಃΒ࿯ ႝတϯ፾܄ෳᡍ...9 ಃΟ࿯ ᚼӀ౗௓ᆅ...21 ಃѤ࿯ س಍໒วБݤ...29 ಃϖ࿯ ႝတᆛၡמೌ...34 ಃΟക ࣴزБݤ ...37 ಃ΋࿯ ࣴزࢬำ...37 ಃΒ࿯ س಍ϩ݋ᆶ೛ी...38 ಃΟ࿯ ኳᔕ MCAT ჴᡍ೛ी...44 ಃѤ࿯ ຑ՗ࡰ኱...45 ಃϖ࿯ ࣴزπڀ...46 ಃѤക ࣴز่݀ᆶ૸ፕ ...49 ಃ΋࿯س಍ࡌ࿼ԋ݀...49 ಃΒ࿯ ჴቻၗ਑ኳᔕӭӛࡋႝတ፾܄ෳᡍԋਏ...55 ಃϖക ่ፕᆶࡌ᝼ ...58 ಃ΋࿯ ่ፕ...58 ୖԵЎ᝘ ...60 ύЎୖԵЎ᝘...60 मЎୖԵЎ᝘...63 ߕᒵ΋ǵӭӛࡋኧᏢࣽᚒ৤ᜤࡋୖኧ ...66 ߕᒵΒǵس಍ჴբԋ݀ ...68

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߄Ҟᒵ

߄ 1 SHO ᆶ SHOF ޑᚼӀୖኧፓ᏾БԄКၨ ... 26 ߄ 2 س಍ว৖БݤޑКၨ... 34 ߄ 3 Ӛӛࡋޑѳ֡ኧᆶᡂ౦ኧ... 47 ߄ 4 ٬Ҕ MLE ݤᚼӀ౗௓ᆅᆶૈΚ՗ीԋਏ߄ ... 57 ߄ 5 ٬Ҕ EAP ݤᚼӀ౗௓ᆅᆶૈΚ՗ीԋਏ߄ ... 57

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კҞᒵ

კ 1 ᚒ໔ӭӛࡋෳᡍኳԄ ...7 კ 2 ᚒϣӭӛࡋෳᡍኳԄ ...8 კ 3 CAT ࡼෳࢬำ...20 კ 4 ᘣѲԄ໒วݤำׇ ...31 კ 5 ᚉࠠԄس಍ว৖ݤำׇ ...32 კ 6 ख़ᙟуமԄس಍ว৖ݤำׇ ...33 კ 7 ӄфૈԄس಍ว৖ݤำׇ ...34 კ 8 ΟቫԄЬவࢎᄬᡄᒠკ ...35 კ 9 ࣴزࢬำ ...38 კ 10 س಍ࢎᄬኳԄ ...39 კ 11 ፾܄ෳᡍࢬำ೛ी ...40 კ 12 MIRT ኳಔࢎᄬ ...41 კ 13 ஦ဦᆅ౛ኳಔ ...42 კ 14 ᚒ৤ᆢៈኳಔ ...42 კ 15 ෳᡍࡼෳኳಔ ...43 კ 16 ፾܄ෳᡍኳಔ ...43 კ 17 ԋ݀ࢗ၌ኳಔ ...44 კ 18 ኧᆶໆӛࡋᜤࡋୖኧϩѲკ ...47 კ 19 ൳ՖӛࡋᜤࡋୖኧϩѲკ ...48 კ 20 жኧӛࡋᜤࡋୖኧϩѲკ ...48 კ 21 ፾܄ෳᡍϟय़ ...50 კ 22 ᚒ৤ᆅ౛ϟय़-1...51 კ 23 ᚒ৤ᆅ౛ϟय़-2...51 კ 24 ၂ڔᆅ౛ϟय़ ...52 კ 25 Ꮲಞບᘐൔ֋ϟय़-1...53 კ 26 Ꮲಞບᘐൔ֋ϟय़-2...54 კ 27 Ꮲಞບᘐൔ֋ϟय़-3...54 კ 28 MLE Ӛӛࡋᡂ୏კ...55 კ 29 EAP Ӛӛࡋᡂ୏კ...56

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ಃ΋ക ᆣፕ

ҁࣴزҞޑࢂࡌ࿼аӭӛࡋ၂ᚒϸᔈ౛ፕ(multidimensional item response theory, MIRT)ࣁ୷ᘵޑႝတϯ፾܄ෳᡍ(computerized adaptive testing, CAT)س಍Ǵ٠уΕᚼ Ӏ౗௓ᆅޑᐒڋǴаᆢៈෳᡍᚒ৤ޑӼӄ܄ᆶჴҔ܄ǶҁጇፕЎϩԋϖകǴಃ΋ക ᇥܴࣁՖा຾Չҁࣴزޑ୏ᐒᆶҞޑǶಃΒകଞჹ၂ᚒϸᔈ౛ፕǵCATǵᚼӀ౗௓ ᆅݤǵس಍໒วБݤϷႝတᆛၡמೌ฻࣬ᜢЎ᝘຾Չ௖૸ǶಃΟകᇥܴࣴزБݤǵ ࢬำϷࡌ࿼س಍܌ሡޑ೛ഢ฻ǶಃѤകև౜س಍ࡌ࿼่݀ᆶኳᔕ MCAT ޑԋਏǶಃ ϖകගр่ፕᆶࡌ᝼Ƕ

ಃ΋࿯ ࣴز୏ᐒ

ӧჴࡼ΋૓ᏢࣽෳᡍਔǴҞ߻ε೽ϩᗋࢂ௦Ҕ໺಍ર฽ෳᡍǴ؂྽ෳᡍ่״ ࡕǴᗋሡाΓΚ຾Չץ᎙ϩ݋Ǵ܈ஒၗ਑ᒡΕႝတ຾Չϩ݋Ǵ೭ᅿБԄό໻઻຤ਔ ໔ᆶΓΚǴ٠Ъคݤזೲளډ࠼ᢀޑෳᡍ่݀Ƕ җܭᆛၡว৖ޑِೲᆶႝတຼᜐ೛ഢޑε౲ϯǴႝတϐ໔ޑቹॣၗ਑໺ᒡϷև ౜೿ёаၲזೲЪᛙۓǴ܌аӧᆛၡ΢ჴࡼෳᡍࢂڀᡏёՉޑǹΨӢࣁ೸ၸႝတ຾ ՉෳᡍᏱԖזೲၗ਑ೀ౛ޑᓬᗺǴ٬ளෳᡍၸำǵ಍ीǵϩ݋ᆶ่݀Ծ୏၁ಒ૶ᒵǴ ӢԜႝတϯෳᡍޑว৖࡭ុ೏ࣴزύǶ

ෳᡍ౛ፕЬाϩࣁђڂෳᡍ౛ፕ(classical test theory, CTT)ᆶ၂ᚒϸᔈ౛ፕ (item response theory, IRT)ǴԶ IRT ೏ၮҔӧҞ߻ޑ୯ύ୷ҁᏢΚෳᡍǴӧෳᡍጓᇙ ၸำа IRT ࣁ୷ᘵǴૈ࿶җϩ݋၂ᚒᕇளᑔᒧၸ၂ᚒୖኧޑᚒ৤Ǵаዴߥᚒ৤ࠔ፦ ޑӳᚯǴӧෳᡍࡼෳၸำа IRT ࣁ୷ᘵޑ CATǴૈଞჹόӕڙ၂ޣගٮ፾ӝڙ၂ޣ ҁيޑ၂ᚒǴӧё৒הޑᇤৡΠǴᡣෳᡍޑਔ໔ε൯ᕭอǴќѦԵໆᚒ৤ޑӼӄ܄Ǵ Ψૈ೸ၸ၂ᚒᚼӀ౗௓ᆅǴၲډ፾ࡋᆅڋǴӢԜа IRT ࣁ୷ᘵޑ፾܄س಍Ψഌុӧ ࣴวȐЦ໥ޱǴ2004ǹഋཥᙦǴ2004ǹ໳ӓཱིǴ2004ǹླྀ᙭ሸǴ2006ǹጰЎᓪǴ2008ǹ

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ᑵᡉയǵ໳௴ࡏǵෞӀࡿǴ2006ȑǶ

IRT ޑ ଷ ೛ ύ х ֖ ൂ ӛ ࡋ (unidimensionality) ᆶ ڙ ၂ ޣ ૈ Κ ՗ ी ޑ ό ᡂ ܄

(invariance)Ǵ٬ࡼෳόӕ၂ᚒޑڙ၂ޣ܌ᕇளૈΚ՗ीॶёа೏ܫӧ࣬ӕޑໆЁ΢ Кၨ(Hambleton & Swaminathan, 1985; Wainer, Dorans, Flaugher, Green, Mislevy, Steinberg, & Thissen, 1990)ǴՠΨӢൂӛࡋज़ڋ CAT ޑᔈҔǴᡣ CAT ѝૈ߳ज़٬Ҕ ӧൂӛࡋૈΚޑෳᡍ΢ǶჹܭЈ౛ෳᡍǵӭϡຑໆǵᆕӝૈΚෳᡍ฻ӭӛࡋෳᡍǴ Ҟ߻ᗋคݤ٬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 2000aǴ2000bǹഋϘ෕ǵЦЎύǴ2005ǹഋ࢙ᐫǴ2004Ǵ2006ǹ᝵໡ᑯǴ2006ǹHattie, 1981; Hsieh, Shih, & Chen, 2008; Luecht, 1996; Mckinley & Reckase, 1983; Reckase & Mckinley, 1991; Segall, 1996; Shih & Wang, 2007; Sympson, 1978ȑǶ

౜Ϟ MCAT ࣴزύǴεӭаኳᔕࣴزࣁЬǴ௖૸όӕෳᡍᜪࠠΠޑԋਏǴၨϿ ໒ว MCAT ޑس಍Ǵ୯ϣҞ߻ѝԖ୯ҥѠ᡼ৣጄεᏢ௲ػຑ᠘ᆶว৖ࣴزύЈޑӭ ӛࡋႝတϯ፾܄ෳᡍࣴز࠻ว৖ႝတϯӭϡඵች፾܄ෳᡍȐhttp://140.122.69.163/ȑǴ ՠԜس಍ύۘ҂уΕᚼӀ౗௓ᆅǴԶҁࣴزԵቾ၂ᚒᚼӀ౗௓ᆅჹᚒ৤Ӽӄ܄ޑቹ ៜǴ܌аҁࣴزޑس಍фૈନΑёගٮڙ၂ޣ຾Չ MCATǴᗋૈଞჹ၂ᚒ຾ՉᚼӀ ౗௓ᆅǶ

ಃΒ࿯ ࣴزҞޑ

୷ܭ΢ॊࣴز୏ᐒǴҁࣴزҞޑӵΠǺ ΋ǵࡌ࿼֖ᚼӀ౗௓ᆅޑ MCAT س಍Ǵᡣڙ၂ޣё຾Չࡼෳᆶᆅ౛ޣёࡕᆄᆅ౛Ƕ Βǵаჴቻၗ਑ኳᔕ MCAT س಍ޑࢬำǴаຑ՗س಍ϐ٬ҔԋਏǶ

ಃΟ࿯ Ӝຒှញ

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ଞჹҁጇፕЎதـޑӜຒǴ၁ಒᇥܴӵΠǺ

൘ǵൂӛࡋ၂ᚒϸᔈኳԄ

ൂӛࡋ IRT ࣁ΋૓೯ᆀޑ IRTǴѝෳໆ΋ᅿૈΚǴԶኳԄЬाϩԋΟᅿኳԄǺ ൂୖ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

Ҟ߻தـޑ 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)ǴϷӭӛࡋᒿᐒ߯ኧӭ໨ࢶ୷ኳԄ (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৲ໆޑϦԄǴ྽၀၂ᚒගٮ၀ڙ၂ޣޑૻ৲ໆຫεǴ߾၀ڙ၂ޣ܌ᕇளૈΚ ՗ीॶޑᆒྗࡋ൩ຫଯǶ

စǵᚼӀ౗௓ᆅ

ᚼӀ౗௓ᆅޑཷۺനӃҗSympsonکHetter(1985)ගрᚼӀ౗௓ᆅޑཷۺǴ؂΋ ᚒ၂ᚒ೿ԖჹᔈޑᚼӀୖኧǴຫ৒ܰ೏ࡼෳޑ၂ᚒ൩ԖຫᝄदޑᚼӀୖኧǴ྽၂ᚒ ೏ᒧڗਔǴ߾ճҔᚼӀୖኧ຾Չղᘐ၂ᚒࢂցࡼෳǴᡣத೏ࡼෳޑ၂ᚒफ़եࡼෳޑ ᐒ౗Ƕ

(11)

Ҵǵႝတϯ፾܄ෳᡍ

ҁࣴزޑ CAT ࢂ೸ၸᆛၡǴ٠่ӝ MIRT ܌຾ՉޑෳᡍǶ؂྽ࡼෳ΋ᚒ၂ᚒǴ ڙ၂ޣ൩཮ளډ΋ঁཥޑૈΚ՗ीॶǴӆҗཥޑૈΚ՗ीॶᒧрΠ΋ᚒ຾ՉࡼෳǴ ؂Տڙ၂ޣ܌ࡼෳޑ၂ᚒό཮ֹӄ࣬ӕǴૈᒧрၨ፾ӝڙ၂ޣޑ၂ᚒǴၲډ፾Չෳ ᡍޑҞޑǶ

ಃѤ࿯ ࣴزጄൎᆶज़ڋ

ҁࣴزࢂࡌ࿼ MCAT س಍Ǵՠࢂҗܭਔ໔ǵΓΚᆶނΚޑज़ڋǴคݤεໆࡼෳǴ ܌а௦Ҕኳᔕࣴزٰຑ՗س಍ޑ٬ҔБݤǹԶس಍܌٬Ҕޑᚒ৤ࢂ୯ҥᆵύ௲ػε Ꮲ௲ػޑෳᡍ಍ीᆶ፾܄ᏢಞࣴزύЈ܌ጓڋǴൂӛࡋᚒ৤х֖ 94 Ꮲԃࡋࠄ΋ހኧ Ꮲࣽಃ 9 нȐ303 ᚒȑک 95 Ꮲԃࡋࠄ΋ހ୯ᇟࣽಃ 11 нȐ94 ᚒȑǴԶӭӛࡋᚒ৤ѝ х֖ኧᏢࣽૈΚࡰ኱ಃ 9 нǴӅ 3 ঁӛࡋǵ238 ᚒǶ

(12)

ಃΒക Ў᝘௖૸

ҁࣴزҞޑࢂࡌ࿼MCATس಍ǴӢԜଞჹس಍໒วၸำύ܌ሡޕ᛽຾ՉЎ᝘௖૸ǴЬ ा௖૸БӛϩࣁIRTǵCATǵᚼӀ౗௓ڋǵس಍໒วБݤǵႝတᆛၡמೌǶ

ಃ΋࿯ ၂ᚒϸᔈ౛ፕ

൘ǵൂӛࡋ၂ᚒϸᔈ౛ፕ

΋ǵൂӛࡋ၂ᚒϸᔈኳԄ IRTࢂճҔኧᏢኳԄٰ߄Ңڙ၂ޣወӧૈΚᆶ၂ᚒϐ໔ޑวғᐒ౗ǴIRT ኳԄѝ ෳໆ΋ᅿૈΚǴԶኳԄЬाϩԋΟᅿኳԄǺ 1PLMǵ2PLM ᆶ 3PLMǴаΠϩձϟಏǶ Ȑ΋ȑ1PLM җ Rasch(1960)ගр 1PLMǴх֖ڙ၂ޣޑૈΚୖኧᆶ၂ᚒޑᜤࡋୖኧǴӵϦԄ Ȑ1ȑ܌ҢǺ )) ( exp( 1 1 ) ( i i b P    T T Ȑ1ȑ ځύǴPi(T)ࢂ߄Ңڙ၂ޣӧಃ i ᚒޑเჹᐒ౗ǹTࢂ߄Ңڙ၂ޣޑ੿ჴૈΚǹbiࣁಃ 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 ᚒޑเჹᐒ౗ǹTࢂ߄Ңڙ၂ޣޑ੿ჴૈΚǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋǹaiࣁಃ i ᚒ၂ᚒޑ᠘ձࡋǶ ȐΟȑ3PLM

(13)

җ Lord(1974)ගр 3PLMǴЬाҗ 2PLM уΕ၂ᚒޑ౒ෳࡋୖኧǴӵϦԄȐ3ȑ ܌ҢǺ )) ( exp( 1 1 ) 1 ( ) ( i i i i i b a c c P      T T Ȑ3ȑ ځύǴPi(T)ࢂ߄Ңڙ၂ޣӧಃ i ᚒޑเჹᐒ౗ǹTࢂ߄Ңڙ၂ޣޑ੿ჴૈΚǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋǹaiࣁಃ i ᚒ၂ᚒޑ᠘ձࡋǹc ࣁಃ i ᚒ၂ᚒޑ౒ෳࡋǶӧҁࣴزޑi ൂӛࡋ CAT ύࢂ௦Ҕ 3PLMǶ Βǵൂӛࡋૻ৲ڄኧ ၂ᚒૻ৲ڄኧ(Birnbaum, 1968; Lord, 1980)ӵϦԄȐ4ȑࢂࡰीᆉ၂ᚒૻ৲ໆޑ ϦԄǴ྽၀၂ᚒගٮ၀ڙ၂ޣޑૻ৲ໆຫεǴ߾၀ڙ၂ޣ܌ᕇளૈΚ՗ीॶޑᆒྗ 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৲ໆёԖΒᅿБݤǴ΋ࣁӧෳᡍߏࡋόᡂΠǴቚу؂΋၂ᚒૻ৲ໆǹ Βࣁӧ၂ᚒૻ৲ໆόᡂޑ௃ݩΠǴቚуෳᡍߏࡋǶ

¦

n i i j T I I 1 ) ( ) (T T Ȑ5ȑ ځύǴ n ࣁෳᡍޑߏࡋǹIT(Tj)ࣁ n ᚒIi(T)уᕴޑෳᡍૻ৲ڄኧǶ

ມǵӭӛࡋ၂ᚒϸᔈ౛ፕ

΋ǵӭӛࡋ၂ᚒϸᔈኳԄ ൂӛ܄(unidimensionality)ࢂ၂ᚒϸᔈ౛ፕځύϐ΋ޑ୷ҁଷ೛Ǵࢂࡰෳᡍύޑ ܌Ԗ၂ᚒ೿ෳໆ΋ঁ࣬ӕޑૈΚǶՠ೚ӭෳᡍ௃ნ࿶தх֖೚ӭϩෳᡍǴόൂપѝ Ԗෳໆൂ΋ૈΚǴٯӵЈ౛ෳᡍǵӭϡຑໆǵᆕӝૈΚෳᡍǶ

(14)

ࣁΑᗉխڙ၂ޣӢᚒҞၸӭԶౢғޑੲമ౜ຝǴ೭٤ෳᡍ܌х֖ޑϩෳᡍ೯த ೿ό཮Ԗၸӭ၂ᚒǴऩаൂӛࡋ IRT ঁձ຾ՉӚϩෳᡍޑϩ݋Ǵ߾ϩෳᡍޑߞࡋ೿ όଯǶԶჴሞᔈҔ΢ൂӛ܄ଷ೛٠ό৒ܰၲԋǴӢԜԖᏢޣගрӭӛࡋ၂ᚒϸᔈ౛ ፕ(Reckase, 1985; van der Linden & Hambleton, 1996)Ǵа჋၂ှ،ෳᡍჴሞᔈҔ΢ޑ ୢᚒǶ

Ȑ΋ȑӭӛࡋෳᡍ

ӭӛࡋෳᡍёаϩࣁٿᅿ(Wang, Wilson, & Adams, 1997)Ƕ΋ᅿࢂᚒ໔ӭӛࡋෳ ᡍ(between-item multidimensional test)Ǵ೭ᅿෳᡍ္ޑ؂΋ঁ၂ᚒѝෳໆൂ΋ᅿૈ ΚǴջൂӛࡋ၂ᚒǴԶ᏾ҽෳᡍх֖ӭঁൂӛࡋޑ၂ᚒǶ೭ᜪࠠޑෳᡍӵკ 1 ܌ҢǶ ᆕӝૈΚෳᡍឦܭᚒ໔ӭӛࡋෳᡍޑ΋ᅿǴ؂ᚒ၂ᚒෳໆൂ΋ᅿૈΚǴԶ᏾ҽෳᡍ ߾х֖Α೭٤ෳໆ࣬՟ૈΚޑൂӛࡋ၂ᚒǶ

1 ᚒ໔ӭӛࡋෳᡍኳԄ

ќ΋ᅿࢂᚒϣӭӛࡋෳᡍ(within-item multidimensional test)Ǵ೭ᅿෳᡍ္ޑ؂ᚒ ၂ᚒෳໆёૈόѝ΋ᅿૈΚǴ܌аൂ΋၂ᚒϣ൩х֖ӭӛࡋǶ೭ᜪࠠޑෳᡍӵკ 2 ܌ҢǶ ૈΚ A ၂ᚒ 1 ၂ᚒ 2 ૈΚ B ၂ᚒ 3 ၂ᚒ 4 ૈΚ C ၂ᚒ 5 ၂ᚒ 6 ၂ᚒ 7

(15)

2 ᚒϣӭӛࡋෳᡍኳԄ ȐΒȑӭӛࡋ၂ᚒϸᔈኳԄ Ҟ߻தـޑӭӛࡋ 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   ș a Ȑ6ȑ ځύǴUiࣁڙ၂ޣࡼෳಃ i ᚒޑϸᔈࠠᄊǴเჹࣁ 1Ǵเᒱࣁ 0ǹaiࣁಃ i ᚒ၂ᚒޑ ᠘ձࡋӛໆୖኧǹbiࣁಃ i ᚒ၂ᚒޑᜤࡋୖኧǹșࣁڙ၂ޣޑૈΚӛໆǶ 2. M3PL җ Sympson(1978)ᆶ Hattie(1981)܌ගрޑኳԄ࣬྽ᜪ՟, ೿ࢂҗ 3PLM ޑ़ғ ኳԄǴࣁ M3PLǴӕਔԵቾڙ၂ޣӭᅿૈΚ٠ஒ၂ᚒޑ᠘ձࡋۓကࣁӛໆǴΨᜪ՟ ܭ M2PLǴৡձӧܭࢂցԵቾ౒ෳୖኧǴӵϦԄȐ7ȑ܌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 ᚒ၂ᚒޑᜤࡋୖኧǹciࣁ၂ᚒޑ౒ෳୖኧǶԶࣁΑ٬၂ᚒޑ ૈΚ D ၂ᚒ 1 ၂ᚒ 2 ၂ᚒ 3 ૈΚ E ၂ᚒ 4 ၂ᚒ 5

(16)

ᜤࡋԋࣁӛໆҔаᆶૈΚӛໆ࣬෧Ǵࡺஒᜤࡋୖኧbiᆶӛໆ1 ࣬४Ƕ 3. MRCMLM

җ AdamsǵWilson ᆶ Wang(1997)܌ගрٰޑ MRCMLM ࣁ Rasch ኳԄޑ़ғኳ ԄǴӵϦԄȐ8ȑ܌ҢǺ

¦

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

>

@

' 2 1, , , ȟ [ [  [n Ǵ[iࣁಃ i ᚒࣁΒϡीϩΠǴ՗ीޑᜤࡋǴऩ ಃ i ᚒࣁ 0ɴ2 ޑ೽ҽ๏ϩǴ߾՗ीޑᜤࡋ཮Ԗ[i1ၟ[i2Ǵٿঁᜤࡋǹऩ၂ڔࣁΒϡी ϩǴ߾ಃ i ᚒޑ՗ीᜤࡋࣁ[iǴ

>

@

' 2 1, , , ȟ [ [  [n Ǵऩ၂ڔࣁΟϡीϩǴ߾ಃ i ᚒޑ՗ ीᜤࡋϩձࣁ[i1ၟ[i

>

@

' 2 1 22 21 12 11, , , , , ȟ [ [ [ [  [n [n ǹ

>

@

' 2 1, , , ș T T TD ǴTdࣁӧෳᡍ ύǴෳډޑಃ d ᅿૈΚǴd = 1,…,Dǹaikࣁӧಃ i ᚒᕇளಃ k ᅿளϩޑ೛ीંତǹbik ࣁӧಃ i ᚒᕇளಃ k ᅿளϩޑளϩંତǹૈଷ೛Pi(ș)ࢂڙ၂ޣӧಃ i ᚒࣁಃ k ᅿޑϸ ᔈᜪࠠޑวғޑᐒ౗ӵϦԄȐ8ȑǶ Οǵӭӛࡋૻ৲ڄኧ Segall(1996)ගрӭӛࡋૻ৲ڄኧંତǴࢂஒșжΕςࡼෳၸޑ၂ᚒ܌ᕇள ) șˆ , ș ( I j Ǵӆу΢șжΕᚒ৤ύ҂ࡼෳޑ၂ᚒ܌ᕇளI(ș,uk)ӵϦԄ(9) ܌ҢǺ ) , ș ( I ) șˆ , ș ( I j  uk Ȑ9ȑ ځύu ࣁಃ k ᚒբเϸᔈǶk

ಃΒ࿯ ႝတϯ፾܄ෳᡍ

໺಍ર฽ෳᡍǴόፕڙ၂ޣޑૈΚଯե೿ሡाֹ᏾଺ֹ΋ҽෳᡍǴதத཮วғ ଯૈΚޑڙ၂ޣ᝺ள၂ڔϼᙁൂǴ࣬ϸӦեૈΚޑΓ᝺ளϼ֚ᜤǴԶڙ၂ޣௗڙό ፾ӝҁيૈΚޑ၂ڔǴΨคݤᆒྗޑෳໆрڙ၂ޣޑૈΚǶCAT ё٩Ᏽ؂Տڙ၂ޣ

(17)

ޑόӕբเϸᔈ຾ՉૈΚ՗ीǴ٠ЪԾ୏ᒧ᏷፾ӝҞ߻ૈΚ՗ीޑ၂ᚒǴа෧Ͽࡼ ෳޑᚒኧǵբเਔ໔ᆶफ़եڙ၂ޣޑᏢಞขቾǶ

ҁࣴزޑ CAT ࢂа IRT ࣁ୷ᘵޑ፾܄ෳᡍǴ܌ах֖Αϖ໨୷ҁाનǺෳᡍ ᚒ৤ǵෳᡍଆᗺǵૈΚ՗ीǵᒧᚒ฼ౣᆶෳᡍಖЗచҹ(է҇ჱǴ1992)ǴԶ٩ྣ CAT ޑόӕᜪࠠΞёϩբൂӛࡋ CAT ᆶӭӛࡋ CAT ٿεᜪǴаΠϩձଞჹόӕ CAT ჴ ࡼၸำ܌ሡޑाન຾ՉᇥܴǶ

൘ǵෳᡍᚒ৤

CATᚒ৤ޑӳᚯ೯தаᚒ৤ελᆶ၂ᚒୖኧٰຑ՗Ƕऩ CAT ࡼෳߏࡋࣁ໺಍ર ฽ෳᡍߏࡋޑ΋ъǴ߾ CAT ᚒ৤ελനӳࢂ໺಍ર฽ෳᡍߏࡋޑ 6 Կ 8 ७ǴΨ൩ࢂ ᇥᚒ৤ελԿϿࣁ CAT ࡼෳߏࡋޑ 12 ७(Stocking, 1994)Ƕ྽ᚒ৤ߏࡋࣁ 3 ७а΢Ǵ ᆒዴࡋᆶբเਏ౗ωԖᡉ๱ৡ౦(Hung, 1988)Ƕ ჹൂӛࡋ CAT ޑ 3PLM ٰᇥǴ΋ঁӳޑᚒ৤ځ᠘ձࡋᔈεܭ 0.8Ǵᜤࡋᔈ၀ᆶ ڙ၂ޣϐ҆ဂޑૈΚϩթ࣬߈Ǵ౒ෳࡋ߾ᔈλܭ 0.25(Цᝊ❲Ǵ1995)ǶRee(1981)ම аനεૻ৲ݤࣁᒧᚒ฼ౣޑࣴزǴӧؒԖᚼӀ౗௓ᆅΠǴᚒ৤ߏࡋεܭ 200 ᚒਔǴ ჹૈΚ՗ीޑᆒྗࡋ٠ό཮ܴᡉቚуǶ

ჹӭӛࡋ CAT ٰᇥǴWang, Chen ᆶ Cheng(2004)ޑࣴزᡉҢǴ྽ᚒ৤ӛࡋϐ໔ ࣁଯ࣬ᜢਔǴӭӛࡋ IRT ϩ݋ёаε൯ගଯӚӛࡋޑߞࡋǴҗচҁޑ 0.6(ൂӛࡋ IRT ϩ݋)ගܹԿ 0.8Ƕ

ມǵෳᡍଆᗺ

CATޑ୷ҁচ߾ࢂ٩ྣڙ၂ޣૈΚගٮ፾྽ޑ၂ᚒᡣڙ၂ޣ຾ՉࡼෳǴՠӧෳ ᡍޑ΋໒ۈǴڙ၂ޣޑૈΚଯե҂ૈளޕޑచҹΠǴӢԜѸ໪،ۓෳᡍޑଆۈᗺǴ аᒧ᏷ಃ΋ঁ၂ᚒٮڙ၂ޣ຾ՉࡼෳǶதҔܭ،ۓଆۈ၂ᚒޑБݤǴаΠϩձϟಏ ȐЦᝊ❲Ǵ1995ǹഋ᜽ӵǴ1998ǹᒲ҉଄Ǵ2006ǹChang & Ansley, 2003ȑ

(18)

Ӄଷ೛ڙ၂ޣࣁύ฻ૈΚǴӧᚒ৤ύࡷᒧ፾ӝύ฻ૈΚᜤࡋޑᚒҞբࣁࡼෳޑ ଆۈ၂ᚒǴऩ؂Տڙ၂ޣ೿٬Ҕ࣬ӕޑᚒҞ໒ۈǴ߾ଆۈ၂ᚒޑߥஏ܄ሡा੝ձԵ ໆǶ Βǵ٩ڙ၂ޣૈΚᒧᚒ җڙ၂ޣޑ୷ҁၗ਑ȐԃសǵᏢಞ࿶ᡍ܈ځдෳᡍ่݀ȑ՗ᆉڙ၂ޣޑૈΚ߃ ۈॶǴӆճҔૈΚ߃ۈॶ،ۓෳᡍޑଆۈ၂ᚒǶ ΟǵԾҗᒧᚒ җڙ၂ޣӧௗڙෳᡍޑਔংǴԾՉղۓԾρޑำࡋǴа،ۓࡼෳޑଆۈᚒǴՠ ৒ܰڙډڙ၂ޣЬᢀղᘐޑቹៜǶ Ѥǵᒿᐒᒧᚒ җႝတᒿᐒᒧᚒǴՠ΋૓ज़ۓ၂ᚒᒧڗጄൎόёຬၸᚒ৤ҁيǶLord(1977)ว౜ όӕଆۈᗺჹܭෳᡍ኱ྗᇤ(standard error of measurement)٠ؒԖࡐεৡձǶ

ϖǵᒿᐒݤ

ᒿᐒݤޑ୷ҁচ౛ࢂᙖҗᒿᐒᒧڗࡼෳ၂ᚒǴаᗉխଯૻ৲ໆޑ၂ᚒ೏ၸࡋᒧ

ڗǴMcBride & Martin(1983)ว߄ᒿᐒݤǶᒿᐒݤࢂӧࡼෳ߻ය٬Ҕᒿᐒᒧڗ฼ౣٰ

ᗉխᚒҞޑၸࡋᚼӀǴځჴࡼБݤࣁǺ ჹ؂΋ঁڙ၂ޣǴ٩ૈΚ߃ۈॶவᚒ৤ύᒧр 5 ঁૻ৲ໆനεޑᚒҞǴவ೭ 5 ᚒύᒿᐒᒧڗр΋ᚒࡼෳ٠ख़ཥ՗ीૈΚॶǹ٩ཥ՗ीޑૈΚॶவᚒ৤ύᒧр 4 ঁ ૻ৲ໆനεޑᚒҞǴӆவ೭ 4 ᚒύᒿᐒᒧڗр΋ᚒࡼෳ٠ख़ཥ՗ीૈΚॶǶख़ፄ࣬ ӕኳԄǴᒧڗࡼෳޑ߻ 4 ᚒǴಃ 5 ᚒϐࡕ൩٬Ҕനεૻ৲ݤٰᒧڗࡼෳᚒҞǶԜѦ ਥᏵ Chang ᆶ Ansley(2003)ޑࣴزࡰрᒿᐒݤӧόӕᚒ৤ύޑКၨǴ၂ᚒനεᚼӀ ౗ࣣϟܭ 0.64~0.74Ǵᇻଯܭёௗڙ၂ᚒനεᚼӀ౗Ƕ Ϥǵ߃ۈ໘ࢤ b ॶϩቫᒿᐒᒧᚒݤ ᒲ҉଄(2006)ගр߃ۈ໘ࢤ b ॶϩቫᒿᐒᒧᚒݤٰ຾Չෳᡍ߃යᒧᚒǴځჴࡼ؁

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ᡯӵΠǺ ؁ᡯ΋Ǻஒᚒ৤٩ b ॶελϩԋ k ቫǴk ࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ؁ᡯΒǺࡼෳ߻ k ᚒਔǴϩձԾ k ቫύӚԾᒿᐒᒧڗ΋ঁ၂ᚒǴ຾ՉࡼෳǶ ࣴزᡉҢǴԜБݤёԖਏफ़ե၂ᚒനεᚼӀ౗ǵԖਏගଯᚒ৤ޑ٬Ҕ౗Ƕ

ୖǵૈΚ՗ी

΋ǵൂӛࡋ CAT CATதـޑૈΚ՗ीБݤԖനεཷ՟՗ीݤǵයఈࡕᡍ՗ीݤᆶനεࡕᡍ՗ी ݤǴаΠϩձϟಏǺ Ȑ΋ȑനεཷ՟՗ीݤ

നεཷ՟՗ीݤ(maximum likelihood estimation, MLE)ࢂ೛ෳᡍӅԖ 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 Ȑ10ȑ

ځύǴu ࣁ܌ԖբเϸᔈޑӛໆǴL

X1,...,Xn |T

ࣁཷ՟ڄኧ(likelihood function)ǹ

Tࣁڙ၂ޣޑ੿ჴૈΚǹXiࡰڙ၂ޣӧಃ i ᚒޑբเϸᔈǴเჹࣁ 1Ǵเᒱࣁ 0ǹPi ࡰڙ၂ޣӧಃ i ᚒޑเჹᐒ౗ǹQiࡰڙ၂ޣӧಃ i ᚒޑเᒱᐒ౗Ƕ ࣁΑуೲפډཷ՟ڄኧޑനεॶǴ೯தࢂӃჹཷ՟ڄኧڗჹኧǴӆаФႥ-ऊՕ හ(Newton-Raphson)ݤٰ຾ՉॏжǶ٬Ҕ MLE ૈΚ՗ीޑϦԄӵϦԄȐ11ȑ܌ҢǴ Զಃ j ԛޑૈΚ՗ीޑᡂ୏ໆࣁį(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 ȐΒȑයఈࡕᡍ՗ीݤ

Bock 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܌ԖբเϸᔈޑӛໆǴL

u|Tq

ࣁཷ՟ڄኧ(likelihood function)ǹTq ࣁڙ၂ޣޑ੿ჴૈΚǹq ࢂीᆉૈΚޑයఈॶਔ܌Ϫപԋޑϩപᗺ(quadrature point)ǴӅԖkqᗺǴkqཇεǴीᆉޑཇᆒዴǶόၸ೭ᅿ՗ीБݤόሡा٬ҔФႥ -ऊՕහݤٰ຾ՉॏжǴԶЪᒿ๱܌ᒧڗޑϩപᗺኧཇӭǴ܌ሡޑीᆉໆၨᚳ εǴीᆉਔ໔ΨКၨΦǶ ȐΟȑനεཷ՟՗ीݤ

نМനεࡕᡍݤ(maximum a posteriori, MAP)ࢂаڙ၂ޣޑ٣߻ૈΚϩѲ f(T)բ

ࣁу៾ॶǴ׎ԋ٣ࡕᐒ౗ஏࡋڄኧǴ٠פрૈ٬Ԝ٣ࡕᐒ౗ஏࡋڄኧനεϯޑำࡋ ॶǴᆀࣁ MAPǶ٣ࡕᐒ౗ஏࡋڄኧीᆉБԄӵϦԄȐ14ȑ܌ҢǺ ) ( ) ( ) | ( ) | ( U U U f f L f T T T Ȑ14ȑ ځύǴL(U|T)ࢂڙ၂ޣT ޑཷ՟ڄኧǴ f(U)ࢂڙ၂ޣޑᜐሞᐒ౗Ǵࢂҗ ) ( ) | ( T f T L U வf~fᑈϩ܌ளǴࣁΑуೲפډ٣ࡕᐒ౗ஏࡋڄኧޑനεॶǴ೯ தΨࢂаФႥ-ऊՕහ(Newton-Raphson)ݤٰ຾ՉॏжǶ ȐѤȑӚᅿૈΚ՗ीБݤޑКၨ ᗨฅ MLE Ԗόᒱޑ՗ीਏૈǴՠԖჴ୍΢ޑज़ڋǴ྽ڙ၂ޣբเϸᔈࣁӄჹ ܈ӄᒱਔǴMLE คݤ՗ीڙ၂ޣૈΚॶ(Wang & Vispoel, 1998)ǶԶ EAP ܈ MAP ё а՗ीӄჹ܈ӄᒱޑբเϸᔈǴՠऩ٣߻ϩଛό҅ዴǴ߾ૈΚ՗ीୃৡஒ཮ࡐε (Baker & Kim, 2004)Ƕ

ࢫᅸᗪǵֆျ੻ǵֆ៓໢ǵഋमᇬ(1992)բၸӚᅿૈΚ՗ीБݤޑКၨǴMLE КၨؒԖ଑ᘜ܄ޑୃᇤ(bias)Ǵՠ֡Бਥᇤ(root mean square of error, RMSE)ၨεǹ

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Βǵӭӛࡋ CAT ӭӛࡋ CAT தـޑૈΚ՗ीБݤԖനεཷ՟՗ीݤǵයఈࡕᡍ՗ीݤᆶനε ࡕᡍ՗ीݤǴᆶൂӛࡋ CAT ޑ՗ीݤᜪ՟ǴЬाҗ՗ीൂ΋ঁૈΚॶᡂԋӕਔ՗ी ӭঁૈΚॶǴаΠϩձϟಏǺ Ȑ΋ȑനεཷ՟՗ीݤ Segall(1996)ගрӭӛࡋޑ MLE ࢂ೛ෳᡍӅԖ 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

>

@

' 2 1, , , ș T T TD ǹuiࡰڙ၂ޣӧಃ i ᚒޑբเϸᔈǴเჹࣁ 1Ǵเᒱࣁ 0ǹPiࡰڙ၂ ޣӧಃ i ᚒޑเჹᐒ౗ǹQiࡰڙ၂ޣӧಃ i ᚒޑเᒱᐒ౗Ƕ ࣁΑуೲפډཷ՟ڄኧޑനεॶǴ೯தࢂӃჹཷ՟ڄኧڗჹኧǴӆаФႥ-ऊՕ හ(Newton-Raphson)ݤٰ຾ՉॏжǶ٬Ҕ MLE ૈΚ՗ीޑϦԄӵϦԄȐ16ȑ܌ҢǴ Զ؂ԛૈΚ՗ीޑᡂ୏ໆࣁ ( ) 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)) (

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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

¦

 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 ȐΒȑයఈࡕᡍ՗ीݤ ӭӛࡋޑ EAP ࢂஒൂӛࡋޑ EAP ૈΚॶԵቾૈΚӛໆǴӵϦԄȐ18ȑ܌ҢǺ

¦

¦

¦

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 ᆉޑཇᆒዴǹfq)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)ࣁșޑӅᡂኧંତǴ

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ऩᡂኧંତ኱ྗϯࡕǴջࣁ࣬ᜢંତǴ » » » ¼ º « « « ¬ ª ) 2 2 1 0 0 D V V      ӧӭӛࡋύǴϩപᗺޑኧໆ཮ԋӛࡋኧޑࡰኧ७ቚуǴ྽ӛࡋኧቚуǴ߾ ૈΚ՗ीਔ໔൩཮܎ߏǴऩ෧ϿӚӛࡋޑϩപᗺǴΞ཮फ़եૈΚ՗ीޑᆒྗࡋǶ ȐΟȑനεࡕᡍ՗ीݤ

Segall(1996)ගрӭӛࡋޑ MAPǴѬޑ٣ࡕᐒ౗ஏࡋڄኧᆶ EAP ࣬ӕǶࣁΑу

ೲפډ٣ࡕᐒ౗ஏࡋڄኧޑനεॶǴMAP Кྣ MLE ٩ФႥ-ऊՕහำׇٰ຾ՉǶ२ Ӄஒϩձჹ d ঁૈΚӛࡋ຾Չୃ༾ϩǶMRCMLM ٣ࡕᐒ౗ࡋڄኧޑ΋໘ୃ༾ϩӛ 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    

¦

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՟՗ीݤٰ຾ՉǶ ȐѤȑӚᅿૈΚ՗ीБݤޑКၨ ഋ࢙ᐫ(2006)Кၨ೭ΟᅿБݤӧӭӛࡋ CAT ύӚԖځᓬલᗺǴᗨฅவ᏾ᡏߞࡋ ᆶෳໆᇤৡԶقǴMAP ࢂКၨӳޑǴՠࢂ㥲ᘜ܄ޑୃᇤΨࢂനᝄख़ޑǶEAP ޑ՗ी ᆒྗࡋᆶ MAP ৡόӭǴՠ྽ӛࡋኧၨଯਔǴૈΚ՗ी܌ሡޑਔ໔൩཮ϼΦǶMLE ࢂ՗ीᆒྗࡋၨৡޑБݤǶ܌аࡌ᝼྽ૈΚӛࡋኧϿܭѤঁӛࡋёа٬Ҕ EAPǴа ෧Ͽ㥲ᘜ܄ୃᇤޑୢᚒǹՠࢂ྽ૈΚӛࡋၲډѤঁ܈Ѥঁа΢ਔǴനӳ٬Ҕ MAP

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ٰ຾ՉǴόၸሡाݙཀ㥲ᘜ܄ୃᇤޑୢᚒǶ

စǵᒧᚒ฼ౣ

΋ǵൂӛࡋ CAT ᒧᚒБݤࢂႝတ፾܄ෳᡍύख़ाޑाનϐ΃ǴਥᏵόӕޑᒧᚒБݤ཮Ꮴठόӕ ޑෳᡍਏ౗ǴӧԜϟಏதҔޑᒧᚒݤӵΠǺ Ȑ΋ȑനεૻ৲ݤ ҁࣴزύǴ၂ᚒޑᒧڗБݤനத٬Ҕനεૻ৲ݤǴځჴࡼ؁ᡯӵΠǺ ؁ᡯ΋Ǻଷ೛ڙ၂ޣҞ߻ૈΚ՗ीॶࣁTˆǴ٩ᏵTˆीᆉۘ҂ࡼෳ၂ᚒޑૻ৲ໆǴीᆉ ԄηୖԵϦԄȐ4ȑ܌ҢǺ ؁ᡯΒǺᒧڗ၂ᚒૻ৲ໆനεޑ၂ᚒǴ྽բΠ΋ࡼෳᚒҞǶ ȐΒȑനௗ߈ୃ౽ᜤࡋݤ ऩ౒ෳࡋcj z 0ਔǴᚒҞૻ৲നεॶό཮วғӧᜤࡋbjǴ཮ౢғୃ౽ԿmjǴന ௗ߈ୃ౽ᜤࡋݤࣁᒧ᏷ᚒҞୃ౽ᜤࡋനௗ߈ڙ၂ޣૈΚ՗ीॶTˆޑᚒҞǴբࣁΠ΋ ໘ࢤࡼෳޑᚒҞǶۓကୃ౽ᜤࡋmj(Birnbaum, 1968)ӵϦԄȐ22ȑ܌ҢǺ ¸ ¸ ¹ · ¨ ¨ © §   ˜  2 8 1 1 log 1 j j j j c a d b m Ȑ22ȑ ߾ᒧᚒਔᒧ᏷ۘ҂ࡼෳЪᒧᚒڄኧFjനλޑᚒҞǴᒧᚒڄኧӵϦԄȐ23ȑ܌ҢǺ | ˆ | ) ˆ ( j j m F T T  Ȑ23ȑ ȐΟȑ୔໔Ԅനεૻ৲ݤ ୔໔Ԅനεૻ৲ݤ٬Ҕ୔໔ૈΚॶޑᚒҞૻ৲ໆуᕴǴٰڗжӧࢌ΋ᗺૈΚॶ

ޑᚒҞૻ৲ໆ(Veerkamp & Berger, 1997)Ƕ୔໔Ԅനεૻ৲ݤࢂᒧ᏷ૻ৲ڄኧӧߞᒘ

୔໔ϣޑय़ᑈǴᒧ᏷നεޑૻ৲य़ᑈǴբࣁΠ΋ᚒࡼෳᚒҞǴࡺᒧᚒਔᒧڗۘ҂ࡼ ෳЪᒧᚒڄኧനεޣǴڄኧӵϦԄȐ24ȑ܌ҢǺ

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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 ϩቫݤ

Chang, Qian & Ying(2001)ගрԵቾ b ୖኧޑ a ϩቫݤǴ׆ఈஒ a ϩቫݤӚϩቫ ύޑ b ॶϩթߥ࡭΋ठ܄ǴٰѺઇ aǵb ϐ໔ޑ࣬ᜢ܄Ƕځჴࡼ؁ᡯӵΠȐଷ೛ L ࣁ ෳᡍߏࡋǹa ࣁ၂ᚒ᠘ձࡋǹb ࣁ၂ᚒᜤࡋȑǺ ؁ᡯ΋Ǻஒᚒ৤٩ྣ b ॶҗλԿεϩԋ T ঁ୔༧Ǵಃ 1 ঁ୔༧х֖നλޑ b ॶǴಃ Tঁ୔༧х֖നεޑ b ॶǶ ؁ᡯΒǺӧಃ t ୔༧Ȑt =1,2,3,…,TȑǴஒᚒ৤٩ྣ a ॶҗλԿεϩԋ K ቫǴ؂΋ቫх ֖΋ၰ၂ᚒǴಃ 1 ቫх֖നλޑ a ॶǴಃ K ቫх֖നεޑ a ॶǶ ؁ᡯΟǺ٩ׇஒ؂ঁ୔༧ޑಃ k ቫȐk=1,2,3,…,Kȑӝٳԋ΋ቫǴӢԜᚒ৤ᡂԋ΋ڀ Ԗ K ቫޑ่ᄬǶ ؁ᡯѤǺࡌҥӳ၂ᚒޑ่ᄬࡕǴڙ၂ޣ٩ׇவಃ 1 ቫ໒ۈࡼෳǴ؂΋ቫᒧڗ L/K ঁ ၂ᚒࡼෳǴ΋ޔࡼෳډಃ K ቫǴޔډڙ၂ޣࡼෳ L ᚒǶ ᖴ϶၃ǵቅ෩οǵ೾դԽȐ2006ȑࣴزࡰрӧڰۓෳᡍߏࡋΠǴૈΚ֡Бਥৡ җλԶε௨ׇϩձࣁԵቾ b ୖኧޑ a ϩቫݤǵനௗ߈ୃ౽ᜤࡋݤǵᎃ߈ݤǵ୔໔Ԅ നεૻ৲ݤǹԵቾ b ୖኧޑ a ϩቫݤၨ୔໔Ԅനεૻ৲ݤԖၨեޑനεᚼӀ౗ǹӧ ࣬ӕૈΚ՗ीᆒྗࡋΠǴԵቾ b ୖኧޑ a ϩቫݤၨ୔໔Ԅനεૻ৲ݤԖၨեޑᚒҞ ख़ፄ౗Ƕ Ȑϖȑa-ᎃ߈ݤ ᒲ҉଄ǵቅৎඁǵ೾դԽȐ2005ȑගрׯ຾ᎃ߈ݤޑ a-ᎃ߈ݤǴځಃ΋؁ᡯࣁ ൂᗺԄനεૻ৲ݤǴಃΒ؁ᡯׯҗ௓ڋ a ॶǴ٬ԐයૈΚॶ҂ྗዴਔᒧҔ a ॶၨե ၂ᚒǴԶ a-ᎃ߈ݤޑჴࡼ؁ᡯӵΠǺ

(26)

؁ᡯ΋Ǻஒᚒ৤٩ b ॶϩΟቫǴෳᡍ߻යΟᚒ௦ڗᒿᐒᒧᚒǴ٬ڙ၂ޣӧෳᡍ߻ය ࡼෳᜤܰࡋ࣬ৡၨε၂ᚒǶ ؁ᡯΒǺ՗ी߃ۈϯૈΚॶ՗ीॶTˆ ؁ᡯΟǺਥᏵTˆᒧ᏷ᚒ৤ύȐෳᡍߏࡋ-ςෳᡍᚒኧȑঁૻ৲ڄኧၨεޣޑ၂ᚒ ؁ᡯѤǺӆவȐෳᡍߏࡋ-ςෳᡍᚒኧȑঁ၂ᚒύǴᒧځύᚒҞ a ॶനλෳᡍ ؁ᡯϖǺख़ཥ՗ीૈΚॶࣁTˆǴӣډ؁ᡯΟǴޔډෳᡍᚒኧ่״Ƕ ਥᏵᒲ҉଄ǵቅৎඁǵ೾դԽȐ2005ȑޑࣴزว౜Ǵ٬Ҕ a-ᎃ߈ݤǴ྽ᚒ৤ຫ εਔǴӧ၂ᚒᚼӀ౗ޑ֡Ϭࡋૈຫௗ߈ᎃ߈ݤǴЪૈΚ՗ीᇤৡၨեܭᎃ߈ݤǶ Βǵӭӛࡋ CAT Segall(1996)ஒཷ՟ڄኧڗჹኧޑΒ໘ୃ༾ϩ೸ၸϦԄȐ25ȑǴа຤ഓૻ৲ڄኧڗ жǶ ) ș ( ǿ )] ș ( [ ( )  + ( j Ȑ25ȑ ځύǿ(ș)ࢂ຤ഓૻ৲ં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 ΢Ԅ߄Ңڙ၂ޣӧࡼෳֹmঁ၂ᚒࡕǴૈΚ՗ीॶࣁș(m)ޑ຤ഓૻ৲ં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 ύǴ٠ߚ٩ᏵӚൂ΋ӛࡋޑനεॶٰᒧᚒǴԶࢂᡣ຤ഓૻ৲ં ତޑՉӈԄॶനεϯޑ၂ᚒǴӵϦԄȐ28ȑ܌ҢǺ ) , ( ) (ș(m) , ș(m) ui , Ȑ28ȑ ځύ,(ș(m))߄Ңࡼෳֹ߻mᚒϐࡕޑૻ৲ંତǴ,(ș(m),ui)ࢂ߄Ңᚒ৤ϣഭᎩ၂ᚒӧૈ

(27)

Κ՗ीӛໆș(m)΢ޑૻ৲ંତǶ Զ٬Ҕ MAP ਔǴځᒧᚒ฼ౣߡঅ҅ӵϦԄȐ29ȑ܌ҢǺ 1 ) ( ) ( ) ( , ) ( , ) , șm șm ui Ȑ29ȑ КၨϦԄȐ28ȑᆶȐ29ȑǴёаว౜ѝৡӧૈΚӃᡍϩଛӅᡂ౦ኧંତޑϸંତ -1 ) Ƕ

ҴǵෳᡍಖЗచҹ

ෳᡍಖЗచҹޑЬाϩࣁȨനεෳᡍߏࡋȩᆶȨૈΚ՗ीޑനλᡂ୏ໆȩٿᅿ Ȑഋ᜽ӵǴ1998ǹഋཥᙦǴ1999ȑǴȨനεෳᡍߏࡋȩࢂࡰෳᡍޑᚒኧၲډႣ೛ޑ ߏࡋਔǴջଶЗෳᡍǹȨૈΚ՗ीޑനλᡂ୏ໆȩࢂࡰ྽ෳᡍޑૈΚ՗ीޑᡂ୏ໆ λܭႣ೛ॶǴջଶЗෳᡍǶ ٩Ᏽа΢ഋॊޑाન᏾ӝԋ CAT ࡼෳࢬำǴӵკ 3 ܌ҢǺ კ3 CAT ࡼෳࢬำ ೛ۓෳᡍଆᗺ ᒧᚒ฼ౣ ෳᡍ่״ ૈΚ՗ी όԋҥ ԋҥ ᒧ᏷ෳᡍ౛ፕ ಖЗ చҹ

(28)

ಃΟ࿯ ᚼӀ౗௓ᆅ

ӧԜλ࿯ஒϟಏᚼӀ౗௓ᆅϐ࣬ᜢࣴزǴԶᚼӀ౗௓ᆅ܌Ҕᐒ౗ݤޑ୷ҁচ౛ ࢂճҔ၂ᚒᚼӀୖኧٰ௓ᆅ၂ᚒ೏ࡼෳޑᐒ౗Ǵаၲډ၂ᚒᚼӀ౗௓ڋӧႣ೛ጄ ൎǴаΠӃᇥܴ୷ҁޑϦԄӵϦԄȐ30ȑ܌ҢǺ ) | ( ) ( ) (A P S P A S P u Ȑ30ȑ ځύǴP(S)ࣁ၂ᚒ೏ᒧڗޑᐒ౗ǹP(A)ࣁ၂ᚒ೏ࡼෳޑᐒ౗ǹP(A|S)ࣁ၂ᚒӧ೏ᒧ ڗΠЪ೏ࡼෳޑᐒ౗ǴջࣁᚼӀୖኧEPǹrࣁёௗڙ၂ᚒനεᚼӀ౗Ƕ ऩP(S)!rǴ߾з ) (S P r EP d ǴᙖԜٰᓸեଯᚼӀ၂ᚒޑр౜ᐒ౗ǹऩP(S)drǴ ߾зEP 1ǴᙖԜᡣեᚼӀ၂ᚒޑр౜όڙज़ڋǶ ௓ᆅ၂ᚒᚼӀ౗ޑБݤԖࡐӭǴёϩԋߚጕ΢ᚼӀ౗௓ᆅᆶጕ΢ᚼӀ౗௓ᆅǴ ߚጕ΢ᚼӀ౗௓ᆅനԐҗ Sympson ک Hetter(1985)ගрǴᙁᆀ SH ݤǴࢂჴ୍΢த٬ ҔޑБݤǴԖ೚ӭᏢޣஒځբ຾΋؁ۯ՜Ǵаၲډ׳ֹ๓ޑ௓ᆅǴٯӵǺASHCȐഋ

ܹ০Ǵ2007ȑǵSHC(Chang, Ansley, & Twu, 2002)ǴԜᜪБݤᗨૈԖਏ௓ᆅ၂ᚒᚼӀ౗Ǵ

ՠӧჴሞࡼෳϐ߻Ѹ໪ӃॏжኳᔕᚼӀୖኧǴ྽ኳᔕᚼӀୖኧޑ௃ნکჴሞࡼෳ௃ ნԖ܌όӕਔǴ၀Бݤޑ௓ᆅԋਏ൩཮όӵႣයǶ

ќ΋ᅿᚼӀ౗௓ᆅБݤࣁጕ΢ᚼӀ౗௓ᆅޑБԄǴٯӵǺSHOȐԙ܃։Ǵ2005ȑǵ

SHOF(Chen & LiaoǴ2005)ǵSHCOFȐ᝵໡ᑯǴ2006ȑǵASHCOFȐጰᑑ݊Ǵ2008ȑǴ аΠϩࣁߚጕ΢ᚼӀ౗௓ᆅݤᆶጕ΢ᚼӀ౗௓ᆅݤٿᜪϟಏǶ

൘ǵߚጕ΢ᚼӀ౗௓ᆅݤ

΋ǵSHݤ Sympsonᆶ Hetter(1985)ගр SH ݤǴځ؁ᡯӵΠǺȐଷ೛LࣁෳᡍߏࡋǹEPࣁ ᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀ౗Ƕȑ ؁ᡯ΋Ǻ೛ۓ؂΋၂ᚒޑEP߃ۈॶࣁ 1Ƕ

(29)

؁ᡯΒǺଷ೛ڙ၂ޣҞ߻ࡼෳډಃ jᚒǴ٩Ᏽڙ၂ޣҞ߻ૈΚ՗ीॶǴճҔᒧᚒ฼ ౣᒧڗΠ΋ᚒ၂ᚒiǶӆவU(0,1)ύᒧڗ΋ঁ໶ኧxǴऩx dEPiǴ߾ࡼෳԜ ၂ᚒǹऩx !EPiǴ߾όӆࡼෳԜ၂ᚒǶख़ᙟ΢ॊբݤޔډࡼෳֹ΋ᚒǶ ؁ᡯΟǺਥᏵڙ၂ޣࡼෳಃ jᚒޑ่݀՗ीڙ၂ޣૈΚॶǴख़ᙟ؁ᡯΒޔډࡼෳֹL ᚒǶ ؁ᡯѤǺख़ᙟ؁ᡯΒᆶ؁ᡯΟǴޔډ܌Ԗڙ၂ޣ೿ࡼෳֹ౥ǴਥᏵP(S)ٰፓ᏾؂΋ ၂ᚒޑEPǶ ऩP(S)!rǴ߾ ) (S P r EP ǹऩP(S)drǴ߾EP 1Ƕ ؁ᡯϖǺפрLEPനεޑ၂ᚒǴஒP(A|S)ॶ೛ࣁ 1ǶȐԜ؁ᡯࢂӢࣁᚒ৤ϼλǴ ஒ཮Ԗᒧόډࡼෳ၂ᚒޑёૈ܄ȑ ؁ᡯϤǺஒཥౢғޑEPǴख़ᙟ؁ᡯΒԿ؁ᡯϖǴ΋ޔډEPᛙۓЪP(A)λܭrǶ ॏжౢғޑᚼӀୖኧ൩ёၮҔӧჴሞޑ CATǶSH ݤᗨฅёаԖਏ௓ڋᚼӀ౗Ǵ ՠࢂ SH ݤࡼෳϐ߻໪ӃॏжౢғᚼӀୖኧǴ཮઻຤࣬྽ӭޑਔ໔Ƕऩటࡼෳޑ҆ ᡏᆶॏжౢғᚼӀୖኧޑ҆ဂᡏόӕǴࣴزว౜ჹᚼӀ౗ޑ௓ᆅஒόӵႣයȐԙ܃ ։Ǵ2005ȑǶCAT ᒧᚒਔǴ΋૓௦Ҕനεૻ৲ݤǴӢԜ཮೷ԋଯ᠘ձࡋᚒҞၸ෠೏ᒧ

ڗǴԶե᠘ձࡋᚒҞόܰ೏ᒧڗǴᚒ৤ޑ٬Ҕ౗ၨόଯ(Chang & Ying, 1999)ǶԶЪ

SHݤӧཱུᆄૈΚ୔໔Πޑ၂ᚒᚼӀ౗൳ၲ 100%(Chang & Ansley, 2003)Ƕ

ΒǵSHCݤ

Chang, Ansley & Twu(2002)ගр SHC ᚼӀ౗௓ᆅݤǴᆶ SH ᚼӀ౗௓ᆅݤ࣬ ՟ǴሡӃॏжᚼӀୖኧࡕӆ຾ՉࡼෳǴԶ SHC ݤׯؼޑ೽ҽࢂଞჹόӕޑૈΚ୔໔

຾ՉᚼӀୖኧޑॏжǶځ؁ᡯӵΠǺȐଷ೛Nࣁᚒ৤ߏࡋǹMࣁૈΚ୔໔ϩപኧǹEP

ࣁᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀ౗ȑ

؁ᡯ΋Ǻஒڙ၂ޣૈΚϩթጄൎϪപԋMঁ୔໔Ƕ

(30)

ݤॏжౢғӚ୔໔܌ჹᔈޑEPॶǶനࡕ཮׎ԋ΋ঁM uNޑᚼӀୖኧં ତǶ

ஒԜM uNޑᚼӀୖኧંତၮҔӧჴሞޑCATǶᒧ᏷၂ᚒਔǴ྽ڙ၂ޣૈΚ՗

ीॶTˆပӧ୔໔mȐm 1,2,3,,MȑǴ൩٬Ҕ୔໔mޑPKٰ௓ᆅ၂ᚒޑᚼӀ౗Ƕ

SHCݤόፕڙ၂ޣޑ҆ဂϩթࣁՖǴࣣૈஒ؂ঁૈΚ୔໔ޑ၂ᚒᚼӀ౗଺ؼӳ ޑ௓ᆅǴฅԶځനεޑલᗺࢂૈΚ՗ीཞ઻ၸεȐChang, Ansley & Twu, 2002ǹ᝵໡ ᑯǴ2006ȑǶ ΟǵASHCᚼӀ౗௓ᆅݤ ഋܹ০Ȑ2007ȑගр ASHC ݤǴࣁΑׯ຾ SHC ݤౢғૈΚ՗ीޑཞ઻ၸεޑ ୢᚒǴаගଯૈΚॶ՗ीᆒྗࡋǶASHC ᆶ SHC ݤ࣬՟Ǵ໪ӃӧόӕૈΚ୔໔Ӄॏ жᚼӀୖኧࡕӆ຾ՉࡼෳǴԶ ASHC ݤׯؼޑ೽ҽࢂଞჹόӕޑૈΚ୔໔๏ϒόӕ ޑᚼӀ౗௓ᆅǴаගϲૈΚॶ՗ीǴଞჹڙ၂ޣΓኧၨӭޑૈΚ୔໔Ǵ๏ϒၨᝄ਱ ޑᚼӀ౗௓ᆅǴӧ ASHC ݤύǴΞёа٩ྣ߃ۈ೛ۓࢂց٬Ҕ b ॶϩቫᒿᐒᒧᚒݤǴ ϩԋ ASHC1 ᆶ ASHC2ǹڙ၂ޣΓኧၨϿޑૈΚ୔໔Ǵ๏ϒၨቨ᚞ޑᚼӀ౗௓ᆅǶ 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( š T ࣁࢌ၂ᚒ܌ԖᚼӀୖኧճҔϣකݤ܌׎ԋޑᚼӀୖኧԔጕǹrࣁёௗڙ ၂ᚒനεᚼӀ౗ȑ Ȑ΋ȑASHC1 ؁ᡯ΋ǺӃஒڙ၂ޣૈΚϩթጄൎϪപԋMঁ୔໔Ǵ٩Ᏽ؂ঁ୔໔ޑڙ၂ޣΓኧϩ Ѳፓ᏾rॶǶڙ၂ޣΓኧКٯၨଯޑ୔໔ԖၨλޑrॶǴڙ၂ޣΓኧКٯၨ եޑ୔໔ԖၨεޑrॶǶ ؁ᡯΒǺଞჹMঁૈΚ୔໔ǴӚ๏ۓSӜ֡฻ϩթڙ၂ޣǴ٩Ӛ୔໔rॶǴϩձ٬ Ҕ SH ݤǴॏжౢғӚ୔໔܌ჹᔈޑᚼӀୖኧǴനࡕ཮׎ԋ΋ঁM uNޑ ᚼӀୖኧંତǶ

(31)

؁ᡯΟǺଷ೛ڙ၂ޣૈΚ՗ीॶࣁTšǴਥᏵനεૻ৲ݤפډΠ΋ၰࡼෳޑ၂ᚒ ) ... , , (n 123 N n ǴڗрᚼӀୖኧંତޑಃnՉǴճҔϣৡݤפрჹᔈTšޑᚼ ӀୖኧEP_spline( ) š T ȐऩEP_spline( ) š T εܭ 1Ǵ߾зEP_spline( ) š T ࣁ 1ȑǶջ ёճҔԜEP_spline( ) š T ٰ௓ᆅ၂ᚒޑᚼӀ౗Ƕख़ᙟ؁ᡯΟǴޔډڙ၂ޣࡼ ෳֹ܌Ԗ၂ᚒǶ ӧԜБݤύǴ؂၂ᚒύ܌ԖᚼӀୖኧࣣճҔϣකݤ׎ԋᚼӀୖኧԔጕǴ྽ૈΚ ՗ीॶTšόፕပӧՖೀࣣԖόӕޑᚼӀୖኧEP_spline( ) š T ٰ௓ᆅ၂ᚒࡼෳᐒ౗Ƕ ȐΒȑASHC2Ǻ ԜБݤޑEPંତᆶаૈΚϩթࣁ୷ᘵϐ SHC ᚼӀ౗௓ᆅݤ࣬ӕǴБݤޑόӕ ӧڙ၂ޣࡼෳޑ߻kᚒǴ௦Ҕ b ॶϩቫᒿᐒᒧᚒݤٰᒧᚒǶځ؁ᡯӵΠǺ ؁ᡯ΋ǺճҔ ASHC1 ᚼӀ౗௓ᆅݤޑ٣Ӄॏж่݀ǴڗளM uNޑEPંତǶ ؁ᡯΒǺஒᚒ৤٩ b ॶελϩԋkቫǴ kࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ؁ᡯΟǺڙ၂ޣࡼෳ߻kᚒਔǴϩձԾkቫύӚᒿᐒᒧڗ΋၂ᚒǴ຾ՉࡼෳǶ ؁ᡯѤǺ㲱Π(L k)ᚒۘ҂ࡼෳ၂ᚒǴଷ೛ڙ၂ޣૈΚ՗ीॶࣁTšǴਥᏵനεૻ৲ ݤפډΠ΋ၰࡼෳޑ၂ᚒn(n 1,2,3...N)ǴڗрᚼӀୖኧંତޑಃnՉǴճ ҔϣකݤפрჹᔈTšޑᚼӀୖኧEP_spline( ) š T ȐऩEP_spline( ) š T εܭ 1Ǵ߾ зEP_spline( ) š T ࣁ 1ȑǶջёճҔԜEP_spline( ) š T ٰ௓ᆅ၂ᚒޑᚼӀ౗Ƕख़ ᙟ؁ᡯΟǴޔډڙ၂ޣࡼෳֹ܌ԖLၰ၂ᚒǶ

ASHC1ݤᆶ ASHC2 ݤӧૈΚ՗ीᆒྗࡋ΢֡ᓬܭ SHC ݤǹASHC2 ӧᚼӀ౗

௓ᆅ΢Ǵӧ၂ᚒᚼӀ౗ѳ֡ॶǵ҂٬Ҕ၂ᚒኧࡰ኱Ǵ᏾ᡏ΢ਏૈന٫ǹӧڙ၂ޣࣁ தᄊϩթਔǴASHC2 ݤޑ߄౜όᇽܭ SHC ݤȐഋܹ০Ǵ2007ȑǶ

(32)

ॶǴቚуჴሞᔈҔޑ֚ᜤǴЪคݤᗉխࡼෳ߻໪ॏжኳᔕᚼӀୖኧޑၸำǴ΋ѿࡼ ෳ௃ნᆶচӃॏжᚼӀୖኧਔޑ௃ნόӕਔǴᚼӀୖኧߡคݤԖਏ௓ᆅ၂ᚒᚼӀ ౗ǴԜѦӧୃᄊޑ௃ნΠǴASHC ޑനεᚼӀ౗Ԗୃଯޑ౜ຝǶ

ມǵጕ΢ᚼӀ౗௓ᆅݤ

΋ǵSHOݤ ԙ܃։Ȑ2005ȑගр SH_online(SHO)ݤǴᚼӀୖኧаጕ΢ᕇளڗж SH ݤ໪٣ ӃॏжౢғǴҔٰ௓ᆅΠ΋ՏԵғޑ၂ᚒࡼෳᐒ౗ǴаၲډᚼӀ౗௓ᆅǶᚼӀୖኧ ॏжᆶࡼෳӕ؁຾ՉǴځ؁ᡯӵΠǺȐଷ೛ L ࣁෳᡍߏࡋǹEPࣁᚼӀୖኧǹ r ࣁё ௗڙ၂ᚒനεᚼӀ౗Ƕȑ ؁ᡯ΋Ǻ೛ۓ؂΋၂ᚒޑEP߃ۈॶࣁ 1Ƕ ؁ᡯΒǺଷ೛ڙ၂ޣҞ߻ࡼෳډಃ jᚒǴ٩Ᏽڙ၂ޣҞ߻ૈΚ՗ीॶǴճҔനεૻ ৲ݤᒧڗΠ΋ၰࡼෳ၂ᚒiǶவU(0,1)ύᒧڗ΋໶ኧxǴऩx d EPiǴ߾ࡼෳ Ԝ၂ᚒǹऩx !EPiǴ߾όӆࡼෳԜ၂ᚒǶख़ᙟ΢ॊբݤޔډֹԋ΋ᚒࡼෳǶ ؁ᡯΟǺਥᏵڙ၂ޣࡼෳֹ jᚒޑ่݀՗ीڙ၂ޣૈΚॶǴख़ᙟ؁ᡯΒޔډࡼෳֹL ᚒǶ ؁ᡯѤǺਥᏵ߻य़ڙ၂ޣޑᒧᚒ௃׎ǴीᆉрP(S)ٰፓ᏾؂΋၂ᚒޑEPǶ ऩP(S)!rǴ߾ ) (S P r EP ǹऩP(S)drǴ߾EP=1Ƕ ؁ᡯϖǺפрLEPനεޑ၂ᚒǴஒEPॶ೛ࣁ 1ǶȐԜ؁ᡯࢂӢࣁᚒ৤ϼλǴஒ཮ Ԗᒧόډࡼෳ၂ᚒޑёૈ܄ȑ ؁ᡯϤǺஒཥౢғޑEPǴख़ᙟ؁ᡯΒԿ؁ᡯϖǴ΋ޔ܌Ԗڙ၂ޣࡼෳֹ౥Ƕ SHOёᗉխ SH ݤ໪٣ӃॏжᚼӀୖኧǹӧࡼෳ௃ნ౦୏ΠǴ٩ฅૈԖਏ଺ᚼ Ӏ౗ޑ௓ᆅȐԙ܃։Ǵ2005ȑǶSHO ݤޑჴࡼၸำሡ٩ᒘ߻΋Տڙ၂ޣޑᒧᚒ่݀ ٰፓ᏾ᚼӀୖኧǴऩԖ΋ဂڙ၂ޣӕਔௗڙෳᡍǴ߾চԖޑᄽᆉݤஒό፾ҔǶ

(33)

ΒǵSHOFᚼӀ౗௓ᆅݤ

ࣁΑׯ๓ SHO ӧࡼෳ߃යޑᚼӀ௓ᆅԋਏǴChen & Liao(2005)ࡌ᝼ஒ Freeze ำׇ(Revuelta & Ponsoda,1998)уΕ SHO ύǴаගଯᚼӀ౗௓ᆅޑਏૈǴ၀Бݤᆀࣁ The SHO procedure with Freeze(SHOF)ǶFreeze ࢂ΋ঁᝄ਱ޑᚼӀ௓ᆅำׇǴѝा၂

ᚒޑᚼӀ౗εܭrmaxǴFreeze ߡ཮ଶЗࡼෳ၀၂ᚒǴޔډځᚼӀ౗λܭ܈฻ܭrmaxǴ

ωࡠൺ၀၂ᚒޑࡼෳǶ SHOFޑჴࡼࢬำک SHO ࣬՟ǴځനЬाৡ౦ӧܭᚼӀୖኧޑፓ᏾БԄǴӵ߄ 1Ǻ ߄ 1SHO ᆶ SHOF ޑᚼӀୖኧፓ᏾БԄКၨ SHO SHOF ऩP(S)>r Ǵ߾EP= ) (S P rP(S) drǴ߾P(A|S)= 1Ƕ ऩP(A)>rǴ߾EP = 0ȐFreezeȑ ऩP(A)dr ЪP(S)>rǴ߾EP= ) (S P rP(A)dr ЪP(S) drǴ߾EP = 1 ೸ၸ Freeze ޑᝄ਱௓ᆅǴSHOF ׯ๓ጕ΢௓ᆅݤӧࡼෳ߃යᚼӀ௓ᆅόᛙۓޑ ௃׎ǴЪڀԖၨեޑෳᡍख़᠄౗Ϸၨଯޑᚒ৤٬Ҕ౗Ǵ٠ᆢ࡭ؼӳޑૈΚ՗ीྗዴ ܄Ȑֆދ࣓Ǵ2006ȑǶSHOF ᗨฅ᏾ᡏᚼӀ௓ᆅԋਏόᒱǴՠऩଞჹӚঁૈΚНྗٰ ࣮Ǵځԋਏёૈόᅰ౛གྷǶ ΟǵSHCOFݤ ࣁΑჹӚૈΚϩѲ୔໔଺׳ӳޑᚼӀ౗௓ᆅǴ᝵໡ᑯȐ2006ȑගрΑ The Conditional SH online Procedure with Freeze Control(SHCOF)ǴSHCOF ᆶ SHC ࣬՟Ǵ ЬाޑόӕӧܭᚼӀୖኧޑፓ᏾БԄǴځ؁ᡯӵΠǺଷ೛ N ࣁᚒ৤ߏࡋǹM ࣁૈΚ

୔໔ϩപኧǹP(A|S)ࣁᚼӀୖኧǹr ࣁёௗڙ၂ᚒനεᚼӀ౗Ƕ

(34)

ኧંତ PE ޑᚼӀୖኧॶ k Ⴃ೛ॶࣁ 1Ƕ ؁ᡯΒǺа SHC ޑჴࡼБԄჹಃ j ঁڙෳޣࡼෳǶ ؁ᡯΟǺଞჹಃ j ঁڙෳޣࡼෳ่݀Ǵख़ཥीᆉ؂΋၂ᚒӚૈΚ୔໔ޑP(AP(S٠аΠय़ᄽᆉݤፓ᏾ᚼӀୖኧ kǶऩP(A)!rǴ߾EP= 0ǹऩP(A)drЪ r S P( )! Ǵ߾ ) (S P r EP ǹऩP

A drЪP

S drǴ߾EP=1Ƕ ؁ᡯѤǺаፓ᏾ၸޑᚼӀୖኧંତEPǴख़ᙟ؁ᡯΒԿ؁ᡯϖǴ΋ޔډ܌Ԗڙ၂ޣࡼ ෳֹ౥Ƕ SHCOF ݤ࣪ౣΑ SHC ॏжᚼӀୖኧޑ຤ਔၸำǴଞჹӚૈΚ୔໔ޑᚼӀ౗բ Ԗਏޑ௓ᆅǹӧᚒಔ၂ᚒϷӭӛࡋ၂ᚒΠǴ᝵໡ᑯ(2006)ว౜ SHCOF ޑૈΚॶ՗ी ၨ SHC Ԗၨ٫ޑԋਏǴՠӧᚼӀ౗௓ᆅ΢όӵ SHCǶ ѤǵASHCOFᚼӀ౗௓ᆅݤ

ጰᑑ݊Ȑ2008ȑගр ASHC online with freeze(ASHCOF)ᙖԜׯ๓ ASHC ݤǴӢ ࣁ ASHC ݤϩࣁٿ໨ ASHC1 ᆶ ASHC2Ǵ܌а ASHCOF Ψϩࣁ ASHCOF1 ᆶ

ASHCOF2Ǵځ؁ᡯϩॊӵΠǺȐଷ೛Nࣁᚒ৤ߏࡋǹM ࣁૈΚ୔໔ϩപኧǹEPࣁ ᚼӀୖኧǹrࣁёௗڙ၂ᚒനεᚼӀ౗ǶEP_spline( ) š T ࣁࢌ၂ᚒޑMঁᚼӀୖኧճҔ ϣකݤ܌׎ԋޑᚼӀୖኧԔጕǶȑ Ȑ΋ȑASHCOF1 ؁ᡯ΋Ǻஒڙ၂ޣૈΚϩթጄൎϩപԋMঁ୔໔Ǵ٩Ᏽ؂ঁ୔໔ޑڙ၂ޣКٯፓ᏾ rॶǴႣ೛ڙ၂ޣૈΚϩଛ΋໒ۈࣁѳ֡ϩଛǵr=1Ϸ؂΋ঁEPॶ֡ࣁ 1Ƕ ؁ᡯΒǺଷ೛ڙ၂ޣ jૈΚ՗ीॶࣁTšǴਥᏵനεૻ৲ݤפډΠ΋ၰࡼෳޑ၂ᚒ ) ... , , (n 123 N n ǴڗрEPંତޑಃnՉǴճҔϣৡݤפрჹᔈTšޑᚼӀୖኧ ) EP_spline( š T ȐऩEP_spline( ) š T εܭ 1Ǵ߾зEP_spline( ) š T ࣁ 1ȑǶ٩ࡼෳၸ

(35)

ำύཥ՗ीޑૈΚॶTšख़ᙟ٬ҔEP_spline( ) š T ᆅ௓ӚૈΚ୔໔ޑᚼӀ౗Ǵޔ ډڙ၂ޣjࡼෳֹ܌Ԗ၂ᚒǶ ؁ᡯΟǺ٩؁ᡯΒǴ຾Չ j 1ঁڙ၂ޣࡼෳǴ؂႖cঁڙ၂ޣǴ߾ख़ཥीᆉ؂ঁ୔ ໔ޑڙ၂ޣΓኧКٯፓ᏾rॶǶڙ၂ޣКٯၨଯޑ୔໔ԖၨλޑrॶǴڙ၂ ޣКٯၨեޑ୔໔ԖၨεޑrॶǶ؂ࡼෳֹcঁΓ߾٩ᏵόӕૈΚ୔׳ཥࡕ ޑrॶǴፓ᏾ӚૈΚ୔໔ޑ၂ᚒᚼӀୖኧંତޑ؂΋ঁEPॶǶ 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 ؁ᡯѤǺख़ᙟ؁ᡯΒǴޔډ܌Ԗڙ၂ޣڙෳ่״Ƕ ȐΒȑASHCOF2 ԜБݤ ASHCOF1 ᜪ՟Ǵόӕܭڙ၂ޣࡼෳޑ߻kᚒǴ௦Ҕ b ॶϩቫᒿᐒᒧᚒ ݤٰᒧᚒǴځ؁ᡯӵΠǺ ؁ᡯ΋Ǻஒڙ၂ޣૈΚϩթጄൎϩപԋMঁ୔໔Ǵ٩Ᏽ؂ঁ୔໔ޑڙ၂ޣКٯፓ᏾ rॶǴႣ೛ڙ၂ޣૈΚϩଛ΋໒ۈࣁѳ֡ϩଛǵr=1Ϸ؂΋ঁEPॶ֡ࣁ 1Ƕ ؁ᡯΒǺஒᚒ৤٩ b ॶελϩԋ k ቫǴk ࣁ߃ۈ໘ࢤᒧᚒޑᚒኧǶ ؁ᡯΟǺڙ၂ޣjࡼෳ߻ k ᚒਔǴϩձԾ k ቫύӚᒿᐒᒧڗ΋၂ᚒǴ຾ՉࡼෳǶ㲱 Π(L k)ᚒۘ҂ࡼෳ၂ᚒǴଷ೛ڙ၂ޣ jૈΚ՗ीॶࣁTšǴਥᏵനεૻ৲ݤ פډΠ΋ၰࡼෳޑ၂ᚒn(n 1,2,3...N)ǴڗрEPંତޑಃnՉǴճҔϣৡݤ פрჹᔈTšޑᚼӀୖኧEP_spline( ) š T ȐऩEP_spline( ) š T εܭ 1Ǵ߾з ) EP_spline( š T ࣁ 1ȑǶ٩ࡼෳၸำύཥ՗ीޑૈΚॶTšख़ᙟ٬ҔEP_spline( ) š T ᆅ௓ӚૈΚ୔໔ޑᚼӀ౗Ǵޔډڙ၂ޣ jࡼෳֹ܌Ԗ၂ᚒǶ ؁ᡯѤǺ٩؁ᡯΟǴ຾Չ j 1ঁڙ၂ޣࡼෳǴ؂႖cঁڙ၂ޣǴ߾ख़ཥीᆉ؂ঁ୔

(36)

໔ޑڙ၂ޣΓኧКٯፓ᏾rॶǶڙ၂ޣКٯၨଯޑ୔໔ԖၨλޑrॶǴڙ၂ ޣКٯၨեޑ୔໔ԖၨεޑrॶǶ؂ࡼෳֹcঁΓ߾٩ᏵόӕૈΚ୔׳ཥࡕ ޑrॶǴፓ᏾ӚૈΚ୔໔ޑ၂ᚒᚼӀୖኧંତޑ؂΋ঁEPॶǶ 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؁ᡯϖǺख़ᙟ؁ᡯΟǴޔډ܌Ԗڙ၂ޣ ڙෳ่״Ƕ ጰᑑ݊Ȑ2008ȑගр ASHCOF ૈᗉխॏжኳᔕᚼӀୖኧޑ֚ᘋǴᡣࡼෳԋਏό ڙࡼෳ௃ნ౦୏܌ቹៜǴࣴزว౜ǴASHCOF ૈԖਏׯ๓ ASHC ᚼӀ౗௓ᆅǴӧૈ Κॶ՗ෳᆢ࡭ؼӳޑਏૈǴ٠ЪӧᚼӀ౗௓ᆅၨቨ᚞Ϸᚒ৤ၨεޑ௃ݩΠᓬܭ SHOFݤᆶ SHCOF ݤǶ

ಃѤ࿯ س಍໒วБݤ

΋૓ၗૻس಍ޑࡌ࿼ࢂሡा઻຤εໆޑΓΚǵਔ໔ᆶނΚǴԶЪሡा஑཰س಍ ϩ݋ᆶ೛ीΓωǴӢࣁӧس಍ޑࡌ࿼ၸำύǴϩ݋ᆶ೛ीޑ߻࿼բ཰ӵ݀ؒԖዴჴ ଺ӳǴёૈᏤठ᏾ঁس಍ޑѨ௳Ǵ܌аѸ໪Ӹӧ΋ঁБݤǴբࣁس಍ว৖ޑ٩ᏵȐ೚ ϡǴ1998ȑǶว৖ၗૻس಍җ໒ۈډֹԋޑ؁ᡯᆶၸำǴ΋૓ᆀբࣁس಍ว৖ғڮຼ

ය(system development life cycle, SDLC)Ǵҗܭ؂΋ঁس಍೿Ԗځόӕޑ੝܄ǴӢԜ ᜢܭس಍ว৖ғڮຼයޑჄϩᆶೕჄǴ٠ؒԖڰۓޑ኱ྗኳԄǶۭΠ൩ᘣѲԄǵᚉ ࠠԄǵख़ᙟуமԄϷӄфૈԄس಍ว৖ݤϩձ௖૸ӵΠǶ

൘ǵᘣѲԄس಍ว৖ݤ

Royce(1970)ගрǴԜว৖ݤаس಍ቫԛࣁଆᗺǴ࿶җϩ݋ǵ೛ीǵำԄኗቪǵ ෳ၂Ϸᆢៈ฻໘ࢤ຾Չ೬ᡏว৖ำׇǴӵკ 4 ܌ҢǴᘣѲԄس಍ว৖ݤࣁനђԴԶ ЪԿϞϝࣁ٬ҔനቶݱޑБݤǴځӚ໘ࢤޑπբख़ᗺӵΠ܌ॊȐ೚ϡǴ1998ǹ஭ε ໋Ǵ2001ȑǺ

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΋ǵ߃؁ϩ݋ ຾Չᇆ໣πբϷۓကس಍Һ୍ޑҞ኱Ǵפр܌ԖёՉБਢࡕǴ຾Չࣴزᆶ௖૸Ǵ פрന٫БਢǴ٠଺ԋҁਏ੻ϩ݋Ƕ Βǵሡ؃ϩ݋ ଞჹ߃؁ϩ݋ޑሡ؃଺׳ుΕޑࣴزǴ΋૓ԶقǴሡ؃ϩ݋ޑख़ᗺӧܭᕕှس ಍ሡाϙሶǻ೯தѸ໪ዴᇡس಍ޑфૈሡ؃ǵၗ਑ሡ؃ǵ٬Ҕޣϟय़ሡ؃ǵ܄ૈሡ ؃ǵ೬ฯᡏሡ؃ǵӼӄϷ௓ڋሡ؃Ϸس಍ଛ࿼ሡ؃฻Ƕ Οǵ೬ᡏ೛ी ЬाޑҞޑӧܭሡ؃ϩ݋໘ࢤ܌ዴᇡޑӚᅿфૈሡ؃Ǵ຾΋؁ᔕр΋ҽှ،೭ ঁୢᚒޑБਢǶ΋ঁس಍җ೚ӭኳಔ܌ಔԋǴኳಔҁيගٮΑࢌ໨੝ਸфૈǴᙖҗ ኳಔϐ໔ޑᜢᖄ௓ڋǴֹٰԋ٬Ҕޣሡ؃ޑфૈǶ ѤǵำԄኗቪ Ьाπբࣁᒧ᏷ӝ፾ޑำԄᇟقǴճҔ܌ᒧڗޑำԄᇟقஒ٬Ҕޣሡ؃ᙯඤԋ ੿҅ޑำԄዸǶ ϖǵෳ၂ ෳ၂πբЬाଞჹำԄኗቪޑำԄዸǴ຾Չ΋ೱՍޑᡍ᛾Ϸ᛾ჴޑπբǴዴᇡ ࢂց಄ӝس಍ޑሡ؃Ƕ Ϥǵᆢៈ ᆢៈࢂ྽س಍҅ԄၮբࡕǴёૈҗܭᒱᇤǵфૈঅׯǵ೬ฯᡏޑ׳ཥǴԶჹܭ চԖޑำԄϷЎҹ຾ՉঅׯǶѬёૈ຾Չ׳҅܄ᆢៈǵ፾ᔈ܄ᆢៈǵֹ๓܄ᆢៈϷ Ⴃٛ܄ᆢៈ฻Ƕ

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4 ᘣѲԄ໒วݤำׇ

ມǵᚉࠠԄس಍ว৖ݤ

Boar(1984)२ӃගрᚉࠠԄس಍ว৖ݤǴӵკ 5 ܌ҢǴԜᅿБݤࡪྣ٬Ҕޣޑ߃ ؁ሡ؃ǴᏃೲֹԋ΋ঁᚉࠠس಍ٮ٬Ҕޣ٬ҔǴϐࡕӆόᘐӦਥᏵ٬Ҕޣޑཀـ຾ Չس಍ޑঅׯԿ٬ҔޣᅈཀࣁЗϐ೬ᡏس಍໒วБݤǶҗܭӧཥس಍ว৖ਔǴ٬Ҕ ޣ೯தѝૈගр೽ϩޑሡ؃Ǵ܌аऩ௦Ҕᚉࠠݤ߾ёаࡐזٰᕕှ٬Ҕޣޑሡ؃Ǵ ٠ૈᒿਔᆶس಍ว৖ޣ଺፾྽ޑྎ೯ǴԜᅿБݤҭёаҔٰᒣձ٬Ҕޣޑ୏ᄊфૈ ሡ؃Ǵ܈ޣஒπբᚉࠠຑ՗অ҅ԋനಖޑ೬ᡏౢࠔǶᚉࠠس಍ว৖ݤၸำёϩࣁሡ ؃ϩ݋ǵזೲᇙբǵࡌ࿼ᚉࠠǵຑ՗অ҅Ϸֹԋس಍฻໘ࢤǴӚ໘ࢤޑπբख़ᗺӵ Π܌ॊȐ஭ε໋Ǵ2001ȑǺ ΋ǵሡ؃ϩ݋ ໒วޣᆶ٬Ҕޣሡ΋ଆ૸ፕ٠ۓက೬ᡏޑҞ኱Ϸ܌Ԗޑфૈሡ؃ǴӕਔӈрѸ ໪଺ుΕۓကޑӦБǶ Βǵזೲᇙբ ߃؁ϩ݋ ೬ᡏ೛ी ำԄኗቪ ෳ၂ ᆢៈ ሡ؃ϩ݋

(39)

๱ख़ӧ٬Ҕޣё࣮ډޑϟय़ǴӵᒡΕᒡрϐฝय़Ϸൔ߄฻Ǵ໒วޣ໪٬Ҕ౜Ԗ ޑำԄኳހ܈ᔈҔ࣬ᜢπڀǴӵൔ߄Ϸ਱ԄౢғᏔٰၲԋזೲ೛ीޑҞޑǶ Οǵࡌ࿼ᚉࠠ ֹԋё୺Չޑ೬ᡏᚉࠠౢࠔǶ Ѥǵຑ՗س಍܈ֹԋس಍ ೸ၸ٬Ҕޣޑჴሞᏹբᆶሡ؃ຑ՗Ǵගрሡ؃ޑፓ᏾Ƕ ೸ၸ΢ॊޑำׇຼԶൺۈޑ୺ՉǴޔډᅈى٬Ҕޣϐሡ؃Ǵωᝩុ຾Չࡕុϩ ݋Ǵ೛ी…฻໘ࢤǴӢԜ໒วޣӧԜ໘ࢤջૈкϩΑှٗ٤фૈࢂѸ໪೛ीǶ კ5 ᚉࠠԄس಍ว৖ݤำׇ

ୖǵख़ᙟуமԄس಍ว৖ݤ

ख़ᙟуமԄس಍ว৖ݤΞ೏ᆀሀቚԄس಍ว৖ݤǴѬࢂ௦Ҕ؁ᡯቚໆޑБԄٰ ว৖ǴᚐѦޑηس಍фૈࢂӧ؂ԛቚуޑၸำύ೏уΕԿ೬ᡏس಍Ǵ٠ख़ཥ຾Չ೛ ीǵᇙբϷᚉࠠঅ҅ޑπբǴӵԜख़ᙟቚໆޔډ܌Ԗηس಍фૈ೏уΕس಍ࣁЗǴ ӵკ 6 ܌ҢǶ זೲᇙբ ࡌ࿼ᚉࠠ ሡ؃ϩ݋ অ҅ ຑ՗س಍ όঅ҅ ֹԋس಍

(40)

6 ख़ᙟуமԄس಍ว৖ݤำׇ ځπբ؁ᡯԖΟ໨Ǻ1.ࡌ࿼ೀ౛௓ڋమൂǵ2.ቚໆ؁ᡯǵ3.ղᘐೀ౛௓ڋమൂࢂ ց่״ǶਥᏵ೚ϡ(1998)ޑှញǺ२ӃѸሡࡌ࿼ೀ౛௓ڋమൂǴѬёۓက᏾ঁس಍Ѹ ໪ڀഢޑ܌ԖᔈҔس಍фૈǴΨёаᕕှډຯᚆֹԋޑس಍ᗋԖӭᇻǴЪҗቚໆ؁ ᡯύԾೀ౛௓ڋమൂ׀ᆄڗ΋໨ϩ݋πբǴזೲࡌ࿼ᚉࠠǴҗ٬Ҕޣޑຑ՗่݀ᕇ ளঅ҅ޑཀـǴѬх֖೛ीǵᇙբϷϩ݋Ǵځύ೛ी೽ҽёԾᒧ೛ीБݤǴᇙբБ य़߾ሡхࡴำԄޑኗቪϷෳ၂Ǵϩ݋߾ࢂ࿶җ٬Ҕޣ٬ҔࡕǴගٮཀـ٠࿶ၸຑ՗ ޑำׇǴஒ܌ሡޑঅ҅Ǵܫ຾ೀ౛మൂޑ׀ᆄǶനࡕղᘐೀ౛௓ڋమൂࢂց่״Ǵ ऩࢂ߾᏾ঁس಍ֹԋǴऩࣁց߾ख़ᙟ຾Չቚໆ؁ᡯǶ೸ၸԜᅿၸำख़ᙟόᘐӦჴՉ ϐࡕǴૈֹ๓Ӧஒ܌ሡޑфૈߕуӧس಍ύǶ

စǵӄфૈԄس಍ว৖ݤ

஭ԭ੫(2003)ගрӄфૈԄس಍໒วБԄࢂࡰ؂΋ঁၗૻس಍ޑ໒ว೿Ѹ໪࿶

җȨس಍ϩ݋ȩ(system analysis)ǵȨس಍೛ीȩ(system design)ǵȨس಍ࡌ࿼ȩ(system

development)ǵȨس಍ჴࡼȩ(system implementation)ǵȨس಍ຑ᠘ȩ(system evaluation)

฻ϖঁำׇǴ᏾ঁس಍ޑ໒วωᆉֹ᏾ֹԋǶඤѡ၉ᇥǴ໒วس಍Ѹ໪ӃΑှس಍ ޑҞޑϷሡ؃Ǵௗ๱೛ीس಍ޑϣ৒ᆶࢬำǴฅࡕ໒ۈኗቪำԄǴനࡕҬ๏٬Ҕޣ ٬Ҕᆶຑ՗Ǵҗ٬Ҕޣ຾Չຑ᠘πբϐࡕǴ൩ֹԋ΋঺ֹ๓ޑၗૻس಍ǴӄфૈԄ س಍໒วำׇӵკ 7 ܌ҢǶ ೛ी 0 ᇙբ 0 ϩ݋ 0

Ǿ

ቚໆ؁ᡯ ೛ी 1 ᇙբ 1 ϩ݋ 1 ೛ी 2 ᇙբ 2 ϩ݋ 2 ೛ी n ᇙբ n ϩ݋ n ቚໆ؁ᡯ

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7 ӄфૈԄس಍ว৖ݤำׇ வа΢Ѥᅿس಍ว৖БݤύǴ᏾౛рӚᅿس಍ว৖Бݤޑ܌޸຤ਔ໔ǵᓬᗺᆶ લᗺǴӵΠ߄ 2Ǻ ߄ 2 س಍ว৖БݤޑКၨ س಍ว৖Бݤ ޸຤ਔ໔ ᓬᗺ લᗺ ᘣѲԄ ၨߏ ൻׇᅌ຾Ǵ৒ܰඓඝ᏾ঁس ಍ࢎᄬǶ ऩԖᒱᇤǴёૈा޸࣬ ྽ӭޑਔୢٰঅ҅Ƕ ᚉࠠԄ ၨอ זೲӦᇙ଺рᚉࠠǴӆ٩٬ Ҕޣሡ؃ǴόᘐӦঅ҅Ǵᗉ խε൯ᒱᇤޑঅׯǶ ሡाόᘐෳ၂Ǵ܌޸຤ ޑෳ၂ΓΚ࣬ჹቚуǶ ख़ᙟуமԄ ၨอ ёаᕕှຯᚆس಍ֹԋᗋԖ ӭᇻǶ ሡाόᘐෳ၂Ǵ܌޸຤ ޑෳ၂ΓΚ࣬ჹቚуǶ ӄфૈԄ ၨอ ᙁዅޑ೛ीࢬำ ؒԖঅ҅ޑำׇ வ߄ 2 ޑКၨύǴёаޕၰѤᅿس಍ว৖БݤӚԖځᓬલᗺǶԶҁࣴزज़ܭਔ ໔ޑୢᚒǴคݤ௦ҔᘣѲԄޑس಍ว৖ݤǴЪӧΓΚϷ׆ఈس಍ӧֹԋࡕૈ಄ӝ٬ Ҕޣሡ؃ޑԵໆΠǴҁࣴزޑس಍໒วБݤǴஒ٩ᚉࠠԄس಍ว৖ݤٰว৖а MIRT ࣁ୷ᘵޑ CAT س಍Ƕ

ಃϖ࿯ ႝတᆛၡמೌ

ࡌ࿼س಍ନΑሡा౛ፕЍ࡭ϐѦǴᗋሡाᙖҗႝတᆛၡБय़ޑמѯஒཷۺჴᡏ ϯǶҁس಍ޑࡌҥၸำࢂ୷ܭӼӄ܄ǵჴҔ܄Ϸ࿶ᔮਏᔈ΢ޑԵໆǴ܌аჹܭբ཰ س಍ޑᒧ᏷ǴࢂаၨӼӄǵᛙۓޑ Linux س಍ࣁѳѠǴځᎩ࣬ᜢ໒วπڀΨаխ຤ǵ س಍ϩ݋ س಍೛ी س಍ࡌ࿼ س಍ჴࡼ س಍ຑ᠘

(42)

ᛙۓࣁᓬӃԵໆǶԜѦҁس಍ࢂࡌ࿼ӧᆛሞᆛၡᕉნύǴӢԜ௦ҔᆛၡΟቫԄЬவ ࢎᄬၗ਑৤מೌǴаΠϩձᇥܴ࣬ᜢπڀǺ

൘ǵΟቫԄЬவࢎᄬၗ਑৤מೌ

೭ঁࢎᄬЬाӧҔЊᆄک՛ܺᏔᆄϐ໔у΢ύϟቫǴԋࣁΟቫԄޑЬவࢎᄬ (Client/Server)Ƕӧ೭ᅿࢎᄬΠǴҔЊᆄ٬Ҕ኱ྗޑ೯ૻڐۓ(ٯӵǺTCP/IP)ᆶύϟቫ ྎ೯ǹύϟቫ٬Ҕ኱ྗޑၗ਑৤೯ૻڐۓ܈ၗ਑৤ύϟ೬ᡏᆶࡕᆄޑၗ਑৤ྎ೯Ƕ ΟቫԄЬவࢎᄬᡄᒠቫޑ่ᄬӵკ 8 ܌ҢǴӚቫޑҺ୍Ԗх֖٬Ҕޣϟय़ޑၗ਑և ౜ ቫ (Presentation Tier) ǵ ᏹ բ ၗ ਑ ೀ ౛ ޑ ᡄ ᒠ ቫ Ǵ Ξ ᆀ ୘ ཰ ᡄ ᒠ ቫ (Functionality/Business Tier)аϷٮᔈၗ਑ޑӸڗ୍ܺޑၗ਑୍ܺቫ(Data Tier)Ȑ໳ර ৰǴ2000ȑǶ

җკ 8 ளޕǴᡄᒠೀ౛ቫ೸ၸ PHP(Hypertext Preprocessor)ೀ౛ၗ਑Ǵ٠ճҔ่ ᄬϯࢗ၌ᇟق(Structure Query Language, SQL)ٰᆅ౛ၗ਑৤ǶSQL ࣁߚำׇ܄ᇟق (non-procedural)ǴѬҁيόૈᐱҥӸӧǴሡा٩ྣ؂΋ঁำׇೀ౛೚ӭޑ୏բٰӸ ڗၗ਑৤Ȑ໳රৰǴ2000ȑǶ კ8 ΟቫԄЬவࢎᄬᡄᒠკ

ມǵ໒วπڀ

PHP(Hypertext Preprocessor)ࢂ΋ᅿ೏ቶݱ٬ҔǵӭҔ೼ޑ໒ܫচۈዸဌҁᇟق (Script Language)ǴΜϩ፾ӝܭᆛ।ޑ໒วǴ٠ё൪Ε HTML ᆛ।ύǶନԜϐѦᗋё ᘤំᏔ Apache/PHP ၗ਑৤ȐMySQLȑ ၗ਑և౜ቫ ᡄᒠೀ౛ቫ ၗ਑Ӹڗቫ

(43)

аᔈҔӧ໒วำԄǴࢂ࣬྽ڀԖ໒วቸ܄ޑᇟقǶPHP Ьा٬Ҕܭ՛ܺᏔ(Server) ᆄޑ୏ᄊᆛ।ޑ໒วǴфૈᆶ ASP(Active Serve Page)ǵJSP(Java Server Pages)ǵCold

Fusion฻࣬՟ǶќѦ PHP ޑᇟݤᜪ՟ܭ C/C++ե໘ᇟقǴ܌а΋૓ၗૻΓ঩܈ࢂዕ

஼ځдำԄᇟقޣࣣ࣬྽৒ܰ΢ЋǶ܌аӧჴբၠѳѠس಍ਔࢂߚதӳҔޑπڀǴ ٠ЪЍජӭᅿၗ਑৤Ƕځд࣬ᜢၗૻፎୖྣ۔Бᆛઠ(http://www.php.net/)Ƕ

ୖǵၗ਑৤س಍

MySQL ࢂ΋঺ڀԖזೲǵӭ୺Չᆣ(multithread)ǵӭ٬ҔޣЪфૈமεޑᜢᖄ

Ԅၗ਑৤ᆅ౛س಍(relational database management system, RDBMS)ǴаЬவԄࢎᄬޑ БԄٰჴ౜Ǵ٠Ъ೸ၸ΋ঁ՛ܺᏔᆄޑ MySQL ᆶ೚ӭόӕҔЊᆄޑڄԄ৤ޑಔ ԋǶу΢୺Չ୷ҁ SQL ࡰзޑਏ౗ߚதِೲǴᆶ༾೬ SQL(MS-SQL)ϷҘମЎ(Oracle) ฻୘཰Ҕၗ਑৤ٰКၨࢂడόᇽՅǴ׳ख़ाޑ΋ᗺࢂ MySQL Ҕӧߚ୘཰Ҕ೼ࢂխ ຤Ǵ٠ЪЍජύЎεϖዸ(Big5)ǴќѦଞჹ೚ӭόӕޑѳѠΨ೿ԖჹᔈޑЍජǴӧӼ း೛ۓ΢य़Ψࢂ࣬྽৒ܰǶӢԜҁࣴزޑࡕᆄၗ਑৤،ۓ௦Ҕ MySQLǶځд࣬ᜢၗ ૻፎୖྣ۔Бᆛઠ(http://www.mysql.com/)Ƕ

စǵᆛၡ՛ܺᏔ

Apache ࢂ΋঺Ծҗ೬ᡏǴΨࢂ΋঺ଯਏૈޑᆛઠ՛ܺᏔ(Web Server)ǴҞ߻೏

ቶݱၮҔӧӚᅿբ཰ѳѠ΢य़ǴᛙۓЪ੃઻ၨϿޑၗྍǴӧᆛሞᆛၡޑ՛ܺᏔѳѠ ΢य़ࢂε൯ሦӃځдቷ୘ǶԶЪ Apache ᆛၡ՛ܺᏔҁيගٮΑ࣬྽ӭኬϯޑኳಔǴ س಍೛ीޣёаவύࡷᒧ፾ӝޑ೽ϩ๏ϒӼး٬ҔǴᘉк܄࣬྽மεǴԶЪڀԖЍ ජ PHP ޑኳಔǶځд࣬ᜢၗૻፎୖྣ۔Бᆛઠ(http://www.apache.org /)Ƕ

Ҵǵ᏾ӝԄᆛၡ՛ܺᏔ

XAMPPࢂ᏾ӝԄᆛၡ՛ܺᏔǴх֖ ApacheǵMySQLǵPHP ᆶ PerlǴҞ߻խ຤

ගٮѤᅿހҁ(LinuxǵWindowsǵMac OS X Ϸ Solaris)Ƕૈᡣᆛၡس಍ࢎઠޣБߡֹ ԋ୷ҁޑࢎઠ೛ۓǶ

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ಃΟക ࣴزБݤ

ҁࣴزЬाҞޑࢂࡌ࿼аMIRTࣁ୷ᘵޑCATس಍Ǵ٠уΕᚼӀ౗௓ᆅޑᐒڋǴ аᆢៈෳᡍᚒ৤ޑӼӄ܄ᆶჴҔ܄Ƕ ਥᏵҁࣴزޑҞޑ຾Չࣴز೛ीǴҁകЬाϩࣁΟঁ೽ϩٰᇥܴ᏾ঁࣴزࢎ ᄬǶϩձࢂࣴزࢬำǵس಍ϩ݋ᆶ೛ीǵኳᔕMCATჴᡍ೛ीᆶࣴزπڀǶ

ಃ΋࿯ ࣴزࢬำ

ࣴزࢬำӵკ9܌ҢǴ२Ӄ຾Չس಍ࡌ࿼ᆶෳᡍ࣬ᜢ౛ፕޑЎ᝘௖૸Ǵ،ۓࣴز ЬᚒࡕǴ΋Бय़Ӄଞჹࣴزޑس಍ሡ؃຾Չϩ݋ᆶ೛ीǴௗ๱໒ว٬ҔޣኳಔǴฅ ࡕኗቪMCATਡЈำԄǴќ΋Бय़җჴቻၗ਑ჹኧᏢࣽᚒ৤຾ՉӭӛࡋኳԄޑୖኧ ϩ݋Ǵӆҗ՗ीֹԋޑ၂ᚒୖኧᆶڙ၂ޣբเϸᔈٰኳᔕMCAT٠ϩ݋่݀Ǵӆஒ ኳᔕϩ݋่݀ӣ㎸๏س಍Ǵӆவ୺Չس಍ෳ၂ၸำ܌ว౜ޑୢᚒ຾Չঅ҅Ǵനࡕኗ ቪࣴز่݀ᆶࡌ᝼Ƕ

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9 ࣴزࢬำ

ಃΒ࿯ س಍ϩ݋ᆶ೛ी

൘ǵس಍ࢎᄬϩ݋

ҁࣴزࡌ࿼ޑMCATس಍௦ҔЬவԄࢎᄬǴӵკ10܌ҢǶس಍ё୔ϩࣁҔЊᆄ ȐClient SideȑϷ՛ܺᏔᆄȐServer SideȑǺҔЊᆄࣁ٬Ҕޣᏹբϟय़೽ҽǴ٬Ҕޣ ೸ၸᆛ।ᘤំᏔ࿶җHTMLᇻᆄฦΕس಍ǹ՛ܺᏔᆄޑբ཰س಍௦ҔCentOS 5ȐLinux ހҁȑǴࡕᆄၗ਑৤՛ܺᏔ௦ҔMySQLǴҔٰ୺ՉำׇᆶӸܫҁس಍ޑ٬Ҕޣၗ਑ǵ ԋᕮǵᚒ৤฻Ǵᆛ।՛ܺᏔ೬ᡏࣁApacheǴᆛ।՛ܺᏔᆄޑำԄᇟقࣁPHPǴᙖҗ PHPٰว৖Ӛ໨ኳಔфૈำԄ٠ᆶၗ਑৤຾Չೱ่ǴќѦ٩ྣჴሞޑሡ؃ǴӧPHP Ў᝘௖૸ س಍ሡ؃ϩ݋೛ी ٬Ҕޣϟय़໒ว ኳᔕ! ႝတϯ፾܄ෳᡍ! ኗቪ MCAT ਡЈำԄ ෳᡍ߃ۈ೛ۓ ᒧᚒ฼ౣ ૈΚ՗ीݤ ᚼӀ౗௓ᆅ س಍ෳ၂ᆶঅ҅ ϩ݋่݀! ኧᏢࣽᚒ৤! ୖኧϩ݋! ่݀ᆶࡌ᝼!

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ޑำԄύΨ཮่ӝHTMLǵJavaScript ฻ځдᆛ।ำԄᇟقǴӅӕֹԋӚኳಔޑфૈ ሡ؃Ƕ კ10 س಍ࢎᄬኳԄ

ມǵ፾܄ෳᡍࢬำ೛ी

ҁࣴز܌ೕჄ፾܄ෳᡍࢬำӵკ11܌ҢǴ؂Տڙ၂ޣୖуෳᡍࡕǴ೿཮Ӄ೛ۓ Ӛӛࡋޑ߃ۈૈΚॶᆶ၂ᚒǴ྽ڙ၂ޣ଺ֹ߃ۈ೛ۓޑ၂ᚒࡕǴӧૈΚ՗ीБय़ё ᒧ᏷MLEᆶEAPٿᅿૈΚ՗ीޑБݤǴ٩ྣ೛ۓޑૈΚ՗ीݤ຾ՉૈΚ՗ीǴӧᒧ ᚒ฼ౣБय़ёᒧ᏷നεૻ৲ݤǴ٠٩ྣ՗ीޑૈΚॶᆶ೛ۓᒧᚒ฼ౣǴவᚒ৤ύࡷ ᒧ၂ᚒǴ؂ᚒ೏ࡷᒧޑ၂ᚒ೿཮࿶ၸᚼӀ౗௓ᆅǴа،ۓࡷᒧ၂ᚒࢂցёаࡼෳǴ ऩόૈࡼෳǴ߾Ԝ၂ᚒჹӕ΋Տڙ၂ޣόૈӆ೏ᒧڗǴӧᒧᚒ฼ౣБय़ёᒧ᏷ SHCOǵSHCOFǵASHCOϷASHCOFǴऩς࿶ၲډനεෳᡍߏࡋ܈ૈΚ՗ीനλᡂ ୏ໆਔǴ߾่״ෳᡍౢғᏢಞບᘐൔ֋Ǵց߾ᝩុࡼෳᆶૈΚ՗ीޔډ಄ӝෳᡍύ ЗచҹǶ Request HTML Document ࠼Њᆄ Internet HTML Document ՛ܺᏔᆄ CentOS 5 HTML JavaScript ᘤំᏔ! ٬Ҕޣ PHP ၗ਑৤ ȐMySQLȑ ᆛၡ ՛ܺᏔ ȐApacheȑ

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11 ፾܄ෳᡍࢬำ೛ी

ୖǵس಍ኳಔ೛ी

ҁࣴز܌೛ीޑس಍ኳಔᆶ٬ҔޣϷၗ਑৤ޑᜢ߯ӵკ12܌ҢǴନΑගٮ፾܄ ෳᡍኳಔϐѦǴᗋԖځдфૈޑኳಔǶჹڙ၂ޣԶقǴёа೸ၸ፾܄ෳᡍኳಔǴ٩ Ᏽόӕޑ၂ᚒϸᔈኳԄǵᒧᚒ฼ౣǵૈΚ՗ीݤǵᚼӀ౗௓ᆅᆶෳᡍύЗ೛ۓ຾Չ ԋҥ ೛ۓӚӛࡋ ߃ۈૈΚᆶ၂ᚒ ᒧᚒ฼ౣ Ȑനεૻ৲ݤȑ ౢғᏢಞບᘐൔ֋ ૈΚ՗ी ȐMLE ᆶ EAPȑ όԋҥ ಖЗచҹ Ȑനεෳᡍߏࡋ܈ ૈΚ՗ीനλᡂ୏ໆȑ ڙ၂ޣ ᚒ৤ ᚼӀ౗௓ᆅ ȐSHCOǵSHCOFǵ ASHCOϷ ASHCOFȑ ԋҥ όԋҥ

(48)

፾܄ෳᡍǴΨёа೸ၸԋ݀ࢗ၌ኳಔǴࢗ၌؂ԛෳᡍᐕำǹჹᆅ౛ޣԶقǴёа೸ ၸ஦ဦᆅ౛ኳಔǴཥቚ܈մନڙ၂ޣ஦ဦᆶஏዸǴΨёа೸ၸᚒ৤ᆢៈኳಔǴ຾Չ ᚒ৤ޑཥቚ܈অׯǴΨёа೸ၸෳᡍࡼෳኳಔǴ೛ۓӚڙ၂ޣ܌ឦ੤ભޑෳᡍᜪࠠǴ х֖ᒧ᏷όӕޑᚒ৤ᆶ೛ۓόӕޑ፾܄ෳᡍБԄǴᗋёа೸ၸԋ݀ࢗ၌ኳಔǴࢗ၌ ܌Ԗڙ၂ޣޑ܌ԖෳᡍᐕำǶ კ12 MIRT ኳಔࢎᄬ Ӛኳಔޑಒ೽ᇥܴӵΠǺ ΋ǵ஦ဦᆅ౛ኳಔ ӵკ 13 ܌ҢǴڙ၂ޣѝૈჹԾρޑ஦ဦၗ਑຾Չঅׯǹᆅ౛ޣёаଞჹࢌՏ٬ Ҕޣཥቚ܈অׯ஦ဦၗ਑ǴΨёа΋ԛ༊Ε܈༊рӭ฽஦ဦၗ਑ǴΨёаץԛঅׯ ੝ۓၗ਑Ǵᗋёаࢗ၌ၗ਑৤ύ܌Ԗ٬Ҕޣޑ஦ဦǶ ᚒ৤ᆢៈኳಔ ஦ဦᆅ౛ኳಔ ፾܄ෳᡍኳಔ ᆅ౛ޣ ڙ၂ޣ ஦ဦၗ਑ ၂ᚒၗ਑ ෳᡍԋ݀ ෳᡍࡼෳኳಔ ෳᡍၗ਑ ᒧᚒၗ਑ ԋ݀ࢗ၌ኳಔ ٬Ҕޣ س಍ኳಔ ၗ਑৤

(49)

13 ஦ဦᆅ౛ኳಔ Βǵᚒ৤ᆢៈኳಔ ӵკ 14 ܌ҢǴᚒ৤ޑᆢៈޣёаཥቚ܈ጓঅᚒ৤ӜᆀϷᚒ৤࣬ᜢၗ਑ǴΨёа ଞჹᚒ৤ޑ၂ᚒ຾Չཥቚǵጓঅ܈մନǴᗋёа༊Ε܈༊р၂ᚒୖኧȐ᠘ձࡋୖኧǵ ᜤࡋୖኧǵ౒ෳࡋୖኧȑǶ კ14 ᚒ৤ᆢៈኳಔ Οǵෳᡍࡼෳኳಔ ӵკ 15 ܌ҢǴӧҁس಍ύԵໆၗ਑৤ޑॄ಻ᆶჴሞ౜൑ޑၮҔǴஒෳᡍࡰࢴа ੤ભࣁൂՏǴ܌аෳᡍޑᆅ౛ޣёаᒧ᏷టࡼෳޑ੤ભǴӆᒧ᏷གྷाࡼෳޑᚒ৤Ǵ നࡕӆᒧ᏷ࡼෳᅿᜪȐ၂ᚒϸᔈኳԄǵᒧᚒ฼ౣǵૈΚ՗ीݤǵᚼӀ౗௓ᆅᆶനε ෳᡍߏࡋȑǴ൩ёаࡰࢴෳᡍ๏੤ભࡼෳǴ࣬ჹΨёаڗ੃ෳᡍǶ ᚒ৤ᆢៈኳಔ ᚒ৤! ཥቚǵጓঅ ၂ᚒཥቚ! ጓঅ܈մନ ၂ᚒୖኧ! ༊Εǵ༊р ஦ဦᆅ౛ኳಔ ஦ဦ! ༊Εǵ༊р ஦ဦ! ץԛঅׯ ஦ဦࢗ၌ ൂ΋஦ဦ! ཥቚǵঅׯ

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15 ෳᡍࡼෳኳಔ Ѥǵ፾܄ෳᡍኳಔ ӵკ 16 ܌ҢǴڙ၂ޣ໒ۈෳᡍࡕǴ཮җόӕޑ၂ᚒϸᔈኳԄᆶૈΚ՗ीݤ՗ी ૈΚǴӆҗኩਔ՗ीૈΚᆶᒧᚒ฼ౣᒧ᏷፾܄ᚒҞǴӧ࿶ၸᚼӀ౗௓ᆅǴ،ۓࢂց ෳᡍԜᚒǴޔډၲԋෳᡍಖЗచҹֹԋ፾܄ෳᡍǶ ࿶җЎ᝘௖૸ޑКၨᆶჴሞज़ڋԵໆΠǴҁس಍ӧ၂ᚒϸᔈኳԄ໒วΑൂӛࡋ ၂ᚒϸᔈኳԄᆶӭӛࡋ၂ᚒϸᔈኳԄǹӧᒧᚒ฼ౣ໒วΑനεૻ৲ݤǹӧૈΚ՗ी ݤ໒วΑ MLE ᆶ EAPǹӧᚼӀ౗௓ᆅ໒วΑ SHCOǵSHCOFǵASHCO ᆶ ASHCOFǶ

16 ፾܄ෳᡍኳಔ ϖǵԋ݀ࢗ၌ኳಔ ӵკ 17 ܌ҢǴڙ၂ޣёа࣮ډҁيޑ୷ҁၗ਑ǵൂϡᏢಞइᒵϷෳᡍບᘐൔ ֋ǹᆅ౛ޣёаଞჹ܌Ԗڙ၂ޣޑෳᡍ่݀Ƕ ፾܄ෳᡍኳಔ ၂ᚒ ϸᔈኳԄ ૈΚ ՗ीݤ ᒧᚒ฼ౣ ᚼӀ౗ ௓ᆅ ෳᡍࡼෳኳಔ ࡼෳ੤ભ! ޑ௓ᆅ ࡼෳᚒ৤! ޑ௓ᆅ ࡼෳᅿᜪ! ޑ௓ᆅ

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17 ԋ݀ࢗ၌ኳಔ

ಃΟ࿯ ኳᔕMCATჴᡍ೛ी

ҁࣴزޑჴቻၗ਑ࢂҗ୯ҥᆵύ௲ػεᏢ௲ػޑෳᡍ಍ीᆶ፾܄ᏢಞࣴزύЈ ගٮǴෳᡍ၂ᚒਥᏵ୯λϖԃભኧᏢࣽૈΚࡰ኱ࣴวǴ٠ஒځ୔ϩࣁኧᆶໆǵ൳Ֆǵ жኧ฻ΟঁӛࡋǶෳᡍᚒ৤Ӆх֖ 238 ᚒǴࡼෳኬҁ 775 ΓǴԶჴᡍ೛ीϩࣁٿঁ ೽ҽǴ΋ঁࢂૈΚ՗ीޑຑ՗Ǵќ΋ঁࢂᚼӀ౗௓ᆅޑຑ՗ǴаΠϩձᇥܴǺ

൘ǵૈΚ՗ी

ӧኳᔕ MCAT ၸำύǴԾᡂ໨ࣁૈΚ՗ीݤ(MLE, EAP)Ǵᒿ๱ෳᡍߏࡋቚуǴ ຑ՗Ӛӛࡋޑ֡Бਥৡ(root mean squared error, RMSE)ޑΠफ़௃׎Ƕ

ມǵᚼӀ౗௓ᆅ

ϩձӧૈΚ՗ीݤύǴٰຑ՗ѤᅿᚼӀ౗௓ᆅᆶคᚼӀ౗௓ᆅޑԋਏǴԜѤᅿ ᒧᚒБݤޑжဦӵΠǺ ΋ǵSHCOǺSHC ጕ΢ᚼӀ౗௓ᆅݤǶ ΒǵSHCOFǺSHC ጕ΢ᚼӀ౗௓ᆅݤǴ֖ᚼӀ౗এ่(freeze)Ƕ ΟǵASHCOǺаૈΚϩթࣁ୷ᘵϐ SHC ጕ΢ᚼӀ౗௓ᆅݤǶ ѤǵASHCOFǺаૈΚϩթࣁ୷ᘵϐ SHC ጕ΢ᚼӀ౗௓ᆅݤǴ֖ᚼӀ౗এ่(freeze)Ƕ όӕޑᚼӀ౗௓ᆅݤǴ཮೛ۓόӕޑനεᚼӀ౗ୖኧ(r)Ǵځ೛ۓࢂԵ᝵໡ᑯ Ȑ2006ȑǵഋܹ০Ȑ2007ȑᆶጰᑑ݊Ȑ2008ȑᆶԵቾჴቻၗ਑ޑज़ڋǴӵΠᇥܴǺ ԋ݀ࢗ၌ኳಔ ڙ၂ޣ! ஦ဦև౜ ෳᡍ่݀! և౜

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參考文獻

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