題組測驗等化效果於不同等化設計之比較

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୯ҥᆵύ௲ػεᏢ௲ػෳᡍ಍ीࣴز܌౛ᏢᅺγፕЎ

ࡰᏤ௲௤Ǻ೾դԽ റγ

ᚒಔෳᡍ฻ϯਏ݀ܭόӕ฻ϯ೛ीϐ

Кၨ

ࣴزғǺᚑذԹ ኗ

!

ύ

๮

҇

୯ ΐ

Μ

Ζ

ԃ

Ϥ

Д!

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ᖴ ᜏ

ҁፕЎளа໩ճֹԋǴ२ӃाགᖴךޑࡰᏤ௲௤ɡ೾դԽ௲௤ǴҗܭԴৣ஼ Јޑ௲ᏤǴ٬ך೭ٿԃٰڙ੻ؼӭǴό໻ӧᏢೌ΢Ԗ܌ԏᛘǴ׳Ꮲ཮Α೚ӭࡑΓ ೀШޑၰ౛ǹགᖴα၂ہ঩ࡼቼᡕ௲௤аϷමࡌሎ௲௤ǴӧᕷԆϐύኘޜຑ᎙ፕ ЎǴόսࡰрךࣴز΢ޑόىϐೀаϷගٮ೚ӭᝊ຦ޑࡌ᝼Ǵ٬ளፕЎϣ৒Ϸࢎ ᄬૈ୼׳уֹ๓Ƕ གᖴች㧌ᏢۆǵཫറᏢߏǵڂՙᏢߏǵ៼࣑Ꮲۆǵ☰ॳᏢۊ๏ϒךӧፕЎ΢ ޑڐշǴ੝ձགᖴཫറᏢߏӧࣴز΢௲ΑךࡐӭǴჹܭךӧፕЎ΢ޑᅪൽǴਔத ගٮ஑཰΢ޑᢀᗺǴЪᕴૈӧך଎ைਔࣁךှൽǴӢࣁԖգޑᔅԆǴ٬ளךૈ୼ ໩ճޑֹԋፕЎǹགᖴࡹଈᏢߏǵඵࣁᏢߏǵػໜᏢߏǵЎߪᏢߏаϷ໋๔Ꮲߏ ೭ٿԃٰޑྣ៝ǹགᖴ٫ᑉǵ٫ᐇǵҺῑǵნጩǵሎᇬǵϘണǵדയکγര೭ٿ ԃٰޑᜢЈᆶႴᓰǴόᆅࢂӧᏢ཰΢ᗋࢂғࢲ΢೿ᔅԆΑךࡐӭǴΨӢࣁԖգ ॺǴࣴز࠻္кᅈΑ៿ઢǴ஥๏Αך೚ӭऍӳޑӣᏫǶᗋԖёངޑᏢ׌ۂॺǴቼ ࣤǵۏ։ǵ܃զǵٍػаϷችۇǴᖴᖴգॺᕴࢂ஥๏ך೚ӭ៿ઢǶ നाགᖴޑࢂךനᒃངޑৎΓǴᖴᖴݿ༰ගٮך΋ঁคኁคቾޑ᠐ਜᕉნǴ ᡣךόѸᏼЈᏢ຤ޑ٣Ǵᕴࢂค࡜ค৷ޑࣁךбрǴ๏ךޭۓᆶᜢᚶǹᖴᖴঢঢǵ ۊۊჹך΋ၡ΢ޑЍ࡭ϷႴᓰǴ٬ךԖ୲࡭Πѐޑ߿਻ǴᖴᖴգॺǶ നࡕǴाᖴᖴ܌ԖᜢЈךǵම࿶ᔅշၸךޑΓǴӢࣁԖգॺޑႴᓰǴךωள аᕇளᅺγᏢՏޑᄪᝬǶӧԜǴ໻аԜፕЎ᝘๏܌ԖᜢЈךǵᔅշךޑΓǶ ᚑذԹ ໻ठ ύ๮҇୯ΐΜΖԃϤД

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ᄔा

೚ӭεࠠ኱ྗϯԋ൩ෳᡍ٬ҔᚒಔԄෳᡍຑ՗ᏢғޑᏢಞԋਏǴ೭٤εࠠ኱ ྗϯԋ൩ෳᡍத٬Ҕ၂ᚒϸᔈ౛ፕࡌҥӅӕໆЁǴՠᚒಔԄෳᡍၗ਑ऩ٬Ҕ၂ᚒ ϸᔈ౛ፕϩ݋Ǵ߾཮۹ౣᚒಔϣ၂ᚒ໔ޑ࣬ᜢԶቹៜୖኧ՗ीϐਏ݀Ƕ ҁࣴزаᚒಔϸᔈ౛ፕϩ݋ᚒಔԄෳᡍၗ਑Ǵ೸ၸኳᔕࣴز௖૸ӧۓᗕό฻ ಔ೛ीᆶѳᑽόֹӄ୔༧೛ीٿᅿ฻ϯ೛ीΠϐ฻ϯਏ݀Ǵ٠ଞჹόӕڙ၂Γ ኧǵᚒಔኧǵᚒಔਏ݀ᡂ౦ኧаϷۓᗕКٯѤᅿᡂ໨ǴКၨ၂ᚒୖኧϷڙ၂ޣૈ Κୖኧϐ՗ीᆒྗࡋǶ ҁࣴز่݀ว౜Ǻ 1. аڙ၂Γኧٰ࣮Ǵ၂ᚒୖኧ՗ीᇤৡ཮ᒿ๱ቚуԶ෧Ͽǹ 2. аᚒಔኧٰ࣮Ǵ྽ڰۓෳᡍߏࡋਔǴڙ၂ޣૈΚୖኧ՗ीᇤৡ཮ᒿ๱ᚒಔኧޑ ቚуԶ෧Ͽǹ 3. аᚒಔਏ݀ᡂ౦ኧٰ࣮Ǵڙ၂ޣૈΚୖኧ՗ीᇤৡ཮ᒿ๱ᚒಔਏ݀ᡂ౦ኧᡂε Զቚуǹ 4. аۓᗕКٯٰ࣮Ǵ྽ڰۓෳᡍߏࡋਔǴڙ၂ޣૈΚୖኧᆶ၂ᚒୖኧ՗ीᇤৡ཮ ᒿ๱ۓᗕКٯޑቚуԶ෧Ͽǹ 5. аόӕ฻ϯ೛ीٰ࣮ǴNEAT ฻ϯ೛ीܭ၂ᚒ᠘ձࡋୖኧϷڙ၂ޣૈΚୖኧ՗ ीᆒྗࡋᓬܭ BIB ฻ϯ೛ीǶ ᜢᗖӷǺෳᡍ฻ϯǵᚒಔǵᚒಔϸᔈ౛ፕǵѳᑽόֹӄ୔༧೛ीǵۓᗕό฻ಔ೛ ी

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Abstract

Testlet items are widely used in large-scale standardized achievement tests to evaluate the learning achievements of the students. Generally, the item response models are used to establish the common scales in these large-scale tests; nevertheless, fitting standard item response models to testlet responses ignores the local dependence between the items within a testlet, the item parameters estimate may be biased.

The purpose of this paper is to use to evaluate the linking performances of balanced incomplete block (BIB) design and non-equivalent groups with anther test design (NEAT) for horizontal equating designs based on the testlet model by using the simulation data. The factors taken into consideration include the following: the sample sizes, the number of the testlets, the variances of the testlet effects, and the ratios of anchor items.

The results of simulation study show that:

1. The root mean square error (RMSE) of the item parameters decrease as the sample sizes increase.

2. The RMSE of the ability parameters decrease as the number of the testlets increase. 3. The RMSE of the ability parameters increase as the variances of testlet effects

increase.

4. The RMSE of the item parameters decrease as the ratios of the anchor items increase.

5. The NEAT design outperforms the BIB design in estimating the item discrimination parameters and the ability parameters.

Keywords: test equating, testlet, testlet response theory, balanced incomplete block design, nonequivalent groups with anchor test design

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Ҟᒵ

ಃ΋ക ᆣፕ... 1 ಃ΋࿯ ࣴز୏ᐒᆶҞޑ...1 ಃΒ࿯ ࡑเୢᚒ...3 ಃΟ࿯ Ӝຒှញ...4 ಃΒക Ў᝘௖૸... 5 ಃ΋࿯ ᚒಔᆶֽ೽၂ᚒ٩ᒘޑཷۺ ...5 ಃΒ࿯ ᚒಔϸᔈ౛ፕ...12 ಃΟ࿯ ෳᡍ฻ϯޑཀကᆶᅿᜪ...19 ಃѤ࿯ ෳᡍ฻ϯ೛ी...21 ಃΟക ࣴز೛ीᆶБݤ... 24 ಃ΋࿯ ࣴزࢬำ...24 ಃΒ࿯ ኳᔕჴᡍϐᡂ໨೛ी...25 ಃΟ࿯ ෳᡍ฻ϯ೛ी...27 ಃѤ࿯ ኳᔕჴᡍ؁ᡯ...31 ಃϖ࿯ ຑ՗Бݤ...31 ಃϤ࿯ ࣴزπڀ...32 ಃѤക ࣴز่݀... 34 ಃ΋࿯ BIB ฻ϯ೛ीϐୖኧ՗ी่݀...34 ಃΒ࿯ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀...41 ಃΟ࿯ BIB ᆶ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀Кၨ ...48 ಃϖക ่ፕᆶࡌ᝼... 57 ಃ΋࿯ ่ፕ...57 ಃΒ࿯ ࡌ᝼...59 ୖԵЎ᝘... 61 ύЎ೽ϩ...61 मЎ೽ϩ...62 ߕᒵ΋ όӕᡂ໨ϐୖኧ՗ीᇤৡ... 69 ߕᒵΒ NEAT ฻ϯ೛ी฻ϯࡕ՗ी่݀ ...73

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߄Ҟᒵ!

߄ 2-1 NEAT ฻ϯ೛ी...23 ߄ 3-1 ኳᔕၗ਑ᡂ໨೛ۓ...25 ߄ 3-2 BIB ฻ϯ೛ीᚒҁଛ࿼߄...28 ߄ 3-3 ۓᗕ၂ᚒኧᆶᕴ၂ᚒኧჹྣ߄ ...29 ߄ 3-4 BIB ฻ϯ೛ीΓኧჹྣ߄...29 ߄ 3-5 NEAT ฻ϯ೛ीᚒҁଛ࿼߄...29 ߄ 3-6 NEAT ฻ϯ೛ीӧόӕۓᗕКٯϐ࣬ᜢᚒኧჹྣ߄...30 ߄ 3-7 NEAT ฻ϯ೛ीΓኧჹྣ߄...30 ߄ 4-1 BIB ฻ϯ೛ीϐୖኧ՗ी่݀...35 ߄ 4-2 NEAT ฻ϯ೛ीϐୖኧ՗ी่݀ ...42 ߄ 4-3 NEAT ฻ϯ೛ीܭۓᗕᚒᆶߚۓᗕᚒϐ၂ᚒୖኧ՗ी่݀ ...51

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კҞᒵ

კ 3-1 ࣴزࢬำკ...24 კ 4-1 BIB ฻ϯ೛ीΠǴόӕڙ၂Γኧჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ ...37 კ 4-2 BIB ฻ϯ೛ीΠǴόӕڙ၂Γኧჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ ...37 კ 4-3 BIB ฻ϯ೛ीΠǴόӕڙ၂Γኧჹܭ၂ᚒ౒ෳࡋୖኧϐ՗ीᇤৡ ...37 კ 4-4 BIB ฻ϯ೛ीΠǴόӕڙ၂ΓኧჹܭૈΚୖኧϐ՗ीᇤৡ ...38 კ 4-5 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ ...39 კ 4-6 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ ...39 კ 4-7 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭ၂ᚒ౒ෳࡋୖኧϐ՗ीᇤৡ ...39 კ 4-8 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭૈΚୖኧϐ՗ीᇤৡ ...40 კ 4-9 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ...46 კ 4-10 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ...46 კ 4-11 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭ၂ᚒ౒ෳࡋୖኧϐ՗ीᇤৡ...47 კ 4-12 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭૈΚୖኧϐ՗ीᇤৡ...47 კ 4-13 όӕ฻ϯ೛ीჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ...48 კ 4-14 όӕ฻ϯ೛ीჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ...49 კ 4-15 όӕ฻ϯ೛ीჹܭ၂ᚒ౒ෳࡋୖኧϐ՗ीᇤৡ...49 კ 4-16 όӕ฻ϯ೛ीჹܭૈΚୖኧϐ՗ीᇤৡ...50

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ಃ΋കʳ ᆣፕ

ಃ΋࿯ʳ ࣴز୏ᐒᆶҞޑ

җܭᒧ᏷ᚒ܈ࢂߚᚒޑෳᡍᚒࠠѝૈෳໆڙ၂ޣޑ૶ᏫૈΚǴᐽഓఘȐ2009ȑ ࡰрᒧ᏷ᚒᆶ໒ܫԄୢᚒ࣬КǴၨᜤෳໆډᏢғਜቪ߄ၲǵ಍᏾کಔᙃޑૈΚǴ ᆶჴբຑໆȐperformance assessmentȑ࣬КǴᒧ᏷ᚒคݤෳໆډȨ଺ȩȐdoingȑ ޑૈΚǴԶࢂߚᚒکᒧ᏷ᚒ΋ኬǴࡐᜤෳໆډᏢғਜቪ߄ၲǵ಍᏾ǵಔᙃکȨ଺ȩ ޑૈΚǴࡺ EbelȐ1951ȑගра௃ნ٩ᒘޑ၂ᚒ໣Ȑcontext-dependent item setȑ ٰှ،೭ᜪޑୢᚒǶԶ HaladynaȐ1992ȑᔠຎ೚ӭ࣬ᜢࣴزࡕǴᇡࣁ೭ᜪࠠޑෳ ᡍό໻ёаԖਏෳໆډόӕᜪࠠޑଯቫԛࡘԵȐhigher order thinkingȑǴЪ፾Ҕܭ ӚᅿෳᡍᜪࠠǴٯӵǺᒧ᏷ᚒ܈ࡌᄬϸᔈᚒȐconstructed-response itemsȑǶ

௃ნ٩ᒘޑ၂ᚒ໣Ǵࢂࡰ΋ಔᏱԖӅӕڈᐟȐstimuliȑ܈ૻ৲ٰྍޑ၂ᚒ ȐAllen & Sudweeks, 2001; Haladyna, 1992; Lee, 2000ȑǴٯӵǺ᎙᠐ෳᡍǵკТǵ ኧᏵ߄฻ǹWainerᆶKielyȐ1987ȑஒԜᅿᜪࠠޑ၂ᚒᆀࣁᚒಔȐtestletȑǶ

җܭᚒಔԄෳᡍό໻ёаԖਏෳໆډόӕᜪࠠޑଯቫԛࡘԵǴЪ፾ҔܭӚᅿ ෳ ᡍ ᜪ ࠠ Ǵ Ӣ Ԝ Ǵ ୯ ϣ Ѧ ޑ ௲ ػ Ј ౛ ෳ ᡍ а Ϸ ೚ ӭ ε ࠠ ኱ ྗ ϯ ԋ ൩ ෳ ᡍ Ȑstandardized achievement educational testȑࣣ٬ҔᚒಔԄෳᡍٰຑໆᏢғޑᏢಞ ԋਏǴٯӵǺԎᅽෳᡍȐThe Test of English as a Foreign Language, TOFELȑǵᏢೌ ຑໆෳᡍȐScholastic Assessment Test, SATȑǵऍ୯୯ৎ௲ػ຾৖ຑໆȐNational Assessment of Educational Progress, NAEPȑǵ୯ሞᏢғຑໆȐThe Programme for International Student Assessment, PISAȑ Ϸ ୯ ሞ ᎙ ᠐ ว ৖ ࣴ ز Ȑ Progress of International Reading Literacy Study, PIRLSȑǵ୯ϣޑ୯ύ୷ҁᏢΚෳᡍϷεᏢᏢ ࣽૈΚෳᡍ฻Ƕ

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ᡍޑၗ਑ϩ݋Ǵ೚ӭ୯ϣѦޑεࠠ኱ྗϯԋ൩ෳᡍࣣ٬Ҕ၂ᚒϸᔈ౛ፕ຾Չၗ਑ ϩ݋аࡌҥӅӕໆЁǶฅԶǴа၂ᚒϸᔈ౛ፕٰϩ݋ෳᡍၗ਑ǴѸ໪಄ӝൂӛࡋ ȐunidimensionalityȑаϷֽ೽ᐱҥ܄Ȑlocal independenceȑ೭ٿঁ୷ҁଷ೛Ǵՠ ӧRosenbaumȐ1988ȑޑࣴزᡉҢᚒಔԄෳᡍ่ᄬၴϸΑֽ೽ᐱҥ܄ޑଷ೛ǴӢ ԜǴ྽ᚒಔԄෳᡍၗ਑٬Ҕ၂ᚒϸᔈ౛ፕٰϩ݋ਔǴ۹ౣᚒಔ၂ᚒϣޑ࣬ᜢǴ߾ ཮ଯ՗ڙ၂ޣૈΚୖኧЪ၂ᚒୖኧ཮ౢғୃ՗ޑ௃׎ȐWainer, 1995; Wainer & Lukhele, 1997; Wainer, Sireci, & Thissen, 1991; Wainer & Thissen, 1996; Wainer & Wang, 2000; Yen, 1993ȑǶҗܭ΢ॊϐୢᚒǴԖᏢޣࡌ᝼ஒᚒಔຎࣁ΋ঁӭᗺीϩ ၂ᚒǴаӭᗺीϩޑБԄٰीᆉ၀ᚒಔޑளϩǴ٠аӭᗺीϩኳԄٰϩ݋ᚒಔԄ ෳᡍၗ਑ǴWainerȐ1995ȑᇡࣁԜБݤӧ᏾ҽෳᡍх֖ၨଯКٯޑᐱҥ၂ᚒЪڀ Ԗ፾ࡋޑᚒಔਏ݀ਔΨ೚፾ҔǶՠࢂǴऩஒᚒಔຎࣁ΋ঁӭᗺीϩ၂ᚒٰϩ݋Ǵ ߾཮഼Ѩࢌ٤ૻ৲ǴЪคݤߥ੮؂΋၂ᚒୖኧޑཷۺȐWang & Wilson, 2005ȑǶ ӢԜǴᏢޣගраᚒಔϸᔈ౛ፕȐtestlet response theory, TRTȑٰϩ݋ᚒಔԄ ෳᡍၗ਑Ƕᚒಔϸᔈ౛ፕࢂ၂ᚒϸᔈ౛ፕϐۯ՜ǴځኳԄуΕ΋ঁᒿᐒਏ݀ǴҔ ٰ߄Ңڙ၂ޣᆶӚᚒಔ၂ᚒ໔ޑҬϕբҔǴԶԜᒿᐒਏ݀ޑᡂ౦ኧǴջж߄ᚒಔ ϣ၂ᚒ࣬٩ޑำࡋǶ٬Ҕᚒಔϸᔈ౛ፕٰϩ݋ᚒಔԄෳᡍၗ਑Ǵёᗉխаӭᗺी ϩኳԄٰϩ݋ΒϡीϩᚒಔԄෳᡍၗ਑܌೷ԋޑલѨǴ٠ߥ੮၂ᚒୖኧޑཷۺǴ ளډ׳ᆒྗޑୖኧ՗ीȐBradlow, Wainer, & Wang, 1999; Wainer, Bradlow, & Du, 2000; Wainer, Bradlow, & Wang, 2007; Wang & Wilson, 2005ȑǶ

ԜѦǴ೚ӭεࠠ኱ྗϯԋ൩ෳᡍࣣ٬ҔᚒಔԄෳᡍٰຑໆᏢғޑᏢಞԋਏǴ ਥᏵၸѐޑࣴزᡉҢǴεࠠ኱ྗϯԋ൩ෳᡍࣣ٬Ҕ၂ᚒϸᔈ౛ፕ຾Չၗ਑ϩ݋а ࡌҥӅӕໆЁǴځෳᡍᚒҁೱ่೛ीε೽ϩ௦Ҕѳᑽόֹӄ୔༧೛ीȐbalanced incomplete block design, BIBȑϷۓᗕό฻ಔ೛ीȐnonequivalent groups with anchor test design, NEATȑ ٿ ᅿ ฻ ϯ ೛ ी Ƕ ٯ ӵ Ǻ ഞ Ԁ ᆕ ӝ ෳ ᡍ Ȑ Massachusetts comprehensive assessment system, MCASȑ௦ҔNEAT฻ϯ೛ीǴԶ಻ើޑPPON

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Ȑ Periodiek Peilingsonderzoek van het Onderwijs ȑ ǵ ऍ ୯ ୯ ৎ ௲ ػ ຾ ৖ ຑ ໆ ȐNational Assessment of Educational Progress, NAEPȑаϷѠ᡼ᏢғᏢಞԋ൩ຑໆ ၗ਑৤ȐTaiwan Assessment of Student Achievement, TASAȑϐࡌ࿼ीฝࣣ௦ҔBIB ฻ϯ೛ीȐЦཫറǴ2006ȑǹฅԶǴᚒಔԄෳᡍၗ਑ऩ٬Ҕ၂ᚒϸᔈ౛ፕٰϩ݋Ǵ ཮ቹៜୖኧ՗ीޑᆒྗࡋǴЪ࣬ᜢЎ᝘ϿԖଞჹεࠠ኱ྗϯԋ൩ෳᡍ٬Ҕᚒಔϸ ᔈ౛ፕ຾Չ฻ϯԋਏϐ௖૸Ƕ Ԗ᠘ܭԜǴҁࣴزϐҞޑట٬Ҕᚒಔϸᔈ౛ፕٰϩ݋ᚒಔԄෳᡍၗ਑Ǵ೸ၸ ኳᔕࣴزޑБԄ௖૸ӧBIBᆶNEATٿᅿ฻ϯ೛ीΠϐ฻ϯਏ݀Ǵ٠ଞჹόӕڙ၂ Γኧǵᚒಔኧǵᚒಔਏ݀ᡂ౦ኧаϷۓᗕКٯѤᅿᡂ໨ǴКၨ၂ᚒୖኧᆶڙ၂ޣ ૈΚୖኧϐ՗ीᆒྗࡋǶ

ಃΒ࿯ʳ ࡑเୢᚒ

ਥᏵ΢ॊޑࣴزҞޑǴҁࣴزஒ௖૸аΠୢᚒǺ ΋ǵʳόӕڙ၂Γኧࢂց཮ቹៜᚒಔԄෳᡍၗ਑ܭBIBᆶNEAT฻ϯ೛ीϐ฻ϯਏ ݀ǻ Βǵʳόӕᚒಔኧࢂց཮ቹៜᚒಔԄෳᡍၗ਑ܭBIBᆶNEAT฻ϯ೛ीϐ฻ϯਏ ݀ǻ Οǵʳόӕᚒಔਏ݀ᡂ౦ኧࢂց཮ቹៜᚒಔԄෳᡍၗ਑ܭBIBᆶNEAT฻ϯ೛ीϐ ฻ϯਏ݀ǻ ѤǵʳόӕۓᗕКٯࢂց཮ቹៜᚒಔԄෳᡍၗ਑ܭNEAT฻ϯ೛ीϐ฻ϯਏ݀ǻ ϖǵʳόӕ฻ϯ೛ीࢂց཮ቹៜୖኧ՗ीϐᆒྗࡋǻ

(13)

ಃΟ࿯ʳ Ӝຒှញ

൘ǵᚒಔ

ᚒಔࢂࡰᏱԖӅӕڈᐟޑ΋ಔ၂ᚒǴ΋૓தـޑ᎙᠐ෳᡍ൩ࢂᚒಔԄ၂ᚒǴ ڙ၂ޣѸ໪᎙᠐ֹ΋ጇЎകǴӆӣเ΋ಔᆶЎക࣬ᜢޑ၂ᚒǶ

ມǵֽ೽၂ᚒ٩ᒘ

၂ᚒϸᔈ౛ፕύޑ୷ҁଷ೛ɡֽ೽ᐱҥ܄Ǵࢂࡰӧ࣬ӕૈΚНྗޑ௃ݩΠǴ ڙ၂ޣբเӚ၂ᚒޑเჹᐒ౗ࢂ࣬ϕᐱҥޑǴҭջڙ၂ޣό཮Ӣࣁเჹಃ΋ᚒԶ ቹៜಃΒᚒޑբเ௃׎Ƕऩڙ၂ޣӧբเࢌ၂ᚒਔڙډځд၂ᚒޑբเ௃׎Զቹ ៜǴջၴϸΑֽ೽ᐱҥ܄ޑଷ೛Ǵ೭ਔ൩ౢғֽ೽၂ᚒ٩ᒘȐlocal item dependence, LIDȑǶ

ୖǵۓᗕό฻ಔ೛ी

NEAT฻ϯ೛ीࢂஒటೱ่ޑόӕෳᡍǴ๏ϒόӕڙ၂ޣဂᡏ຾ՉࡼෳǴЪ ؂ဂڙ၂ޣ֡໪ќѦࡼෳ΋ҽۓᗕෳᡍǴԶۓᗕෳᡍӧόӕڙ၂ޣဂᡏޑෳᡍ໩ ׇࢂ΋ኬޑǴаᗉխ໩ׇӢનޑቹៜǴЪۓᗕ၂ᚒޑෳᡍϣ৒کᜤࡋѸ໪ᆶటೱ ่ޑόӕෳᡍ࣬՟ȐDorans & Holland, 2000; von Davier, Holland, & Thayer, 2004ȑǶ

စǵѳᑽόֹӄ୔༧೛ी

BIB฻ϯ೛ीࢂஒᚒ৤ύޑ၂ᚒϩԋኧঁ၂ᚒ୔༧ǴЪ୔༧໔ᆶ୔༧ϣޑ၂ ᚒࣣόख़ፄǴӆஒऩυঁ၂ᚒ୔༧ጓᇙԋᚒҁǴ؂ঁᚒҁύޑ၂ᚒ୔༧ёૈ೽ҽ ࣬ӕ܈ֹӄόӕǴԶӧ܌ԖޑෳᡍᚒҁύǴ؂ঁ၂ᚒ୔༧р౜ޑԛኧࢂ΋ኬޑȐම ҏฑǵЦཫറǵ೾դԽǵ೚ϺᆢǴ2006ǹKuehl, 2000ȑǶ

(14)

ಃΒകʳ Ў᝘௖૸

ҁࣴزЬा௖૸ᚒಔԄෳᡍӧόӕ฻ϯ೛ीΠǴ຾Չ฻ϯਏ݀ϐКၨǶӢ ԜǴҁകஒଞჹȨᚒಔᆶֽ೽၂ᚒ٩ᒘޑཷۺȩǵȨᚒಔϸᔈ౛ፕȩǵȨෳᡍ฻ ϯޑཀကᆶᅿᜪȩᆶȨෳᡍ฻ϯ೛ीȩϐ࣬ᜢࣴز຾Չϩ݋᏾౛Ƕ

ಃ΋࿯ʳ ᚒಔᆶֽ೽၂ᚒ٩ᒘޑཷۺ

൘ǵᚒಔޑว৖ᆶۓက

җܭᒧ᏷ᚒ܈ࢂߚᚒޑෳᡍᚒࠠѝૈෳໆڙ၂ޣޑ૶ᏫૈΚǴᐽഓఘȐ2009ȑ ࡰрᒧ᏷ᚒ܈ࢂߚᚒޑෳᡍᚒࠠࡐᜤෳໆډᏢғਜቪ߄ၲǵ಍᏾ǵಔᙃکȨ଺ȩ ޑૈΚǴӢԜǴEbelȐ1951ȑගра௃ნ٩ᒘޑ၂ᚒ໣ٰှ،೭ᜪޑୢᚒǴᇡࣁ ௃ნ٩ᒘޑ၂ᚒ໣ёаෳໆډၨଯቫԛޑᏢಞԋ݀ǴԶ௃ნ٩ᒘޑ၂ᚒ໣ջ΋ಔ ᏱԖӅӕڈᐟ܈ૻ৲ٰྍޑ၂ᚒȐAllen & Sudweeks, 2001; Haladyna, 1992; Lee, 2000ȑǴٯӵǺ᎙᠐ෳᡍǵკТǵኧᏵ߄฻ǹWainer ᆶ KielyȐ1987ȑஒ΋ಔᏱ ԖӅӕڈᐟޑ၂ᚒᆀࣁᚒಔǶHaladynaȐ1992ȑᔠຎ೚ӭόӕሦୱޑᚒಔ࣬ᜢࣴ زࡕǴٯӵǺᇟЎෳᡍύޑ᎙᠐౛ှǵኧᏢෳᡍύ٩Ᏽ܌ᡉҢޑኧᏵ߄բเޑᚒ ࠠϷ٩ᏵणМკȐVenn diagramȑ຾Չϩ݋௢౛ޑᚒࠠǵࣽᏢୢᚒှ،Ǵᇡࣁ೭ ᜪޑᚒࠠό໻ёаԖਏෳໆډόӕᜪࠠޑଯቫԛࡘԵǴЪ፾ҔܭӚᅿෳᡍᜪࠠǴ ٯӵǺᒧ᏷ᚒ܈ࡌᄬϸᔈᚒǹќѦǴHaladynaȐ1992ȑҭᇡࣁ೭ᜪޑෳᡍǴёа ᡣෳᡍว৖ޣᕇள׳ӭԖᜢڙ၂ޣޑᏢಞၗૻǶ ന߃ǴᚒಔࢂҔٰጓᇙ֖ԖεڈᐟȐlarge stimuliȑޑෳᡍǴᒿ๱ႝတϯ፾܄ ෳᡍȐcomputerized adaptive testing, CATȑޑว৖ǴԖᏢޣගраᚒಔޑ่ᄬٰ ׯ๓ႝတϯ፾܄ෳᡍύൂ΋၂ᚒ่ᄬ܌ౢғޑୢᚒȐWainer & Kiely, 1987;

(15)

Wainer & Lewis, 1990ȑǶႝတϯ፾܄ෳᡍࢂᙖҗႝတس಍٩Ᏽ؂Տڙ၂ޣޑૈ ΚǴᒧڗന፾ӝ၀ڙ၂ޣޑ၂ᚒϒаբเǴҗܭڙ၂ޣ܌բเޑ၂ᚒ೿ࡐௗ߈ځ ૈΚНྗǴӢԜǴК໺಍ર฽ෳᡍ෧Ͽεऊ΋ъޑ၂ᚒջёᆒዴӦෳໆрڙ၂ޣ ૈΚǶฅԶǴӧႝတϯ፾܄ෳᡍύǴൂ΋၂ᚒޑ่ᄬ཮Ԗે๎ਏ݀Ȑcontext effectsȑǵ၂ᚒᜤࡋԛׇȐitem difficulty orderingȑϷϣ৒ѳᑽȐcontent balancingȑ ޑୢᚒౢғǴаϣ৒ѳᑽ೭ঁୢᚒٰᖐٯᇥܴǺаᆉኧෳᡍٰᇥǴෳᡍว৖ޣ׆ ఈуǵ෧ǵ४ǵନ೭ѤᅿၮᆉБԄޑ၂ᚒӧ᏾ҽෳᡍӚ՞25ʘǴՠႝတϯ፾܄ෳ ᡍӧ຾ՉᒧᚒਔǴԖёૈ཮ᒧډၨӭуݤၮᆉޑ၂ᚒǴԶؒԖᒧډନݤၮᆉޑ၂ ᚒǴӵԜჹܭዕግуݤၮᆉޑڙ၂ޣԶقၨ՞ᓬ༈Ǵՠჹܭନݤၮᆉၨዕግޑڙ ၂ޣࠅࢂόϦѳޑǶ၂ᚒᜤࡋԛׇ೭ঁୢᚒࢂࡰǴӧ΋૓ෳᡍ่ᄬޑ၂ᚒᔈҗᙁ ൂډ֚ᜤ଺௨ׇǴԶႝတϯ፾܄ෳᡍࠅၴϸΑ೭ঁೕ߾ǹҗܭ؂ঁᚒಔϣޑ၂ᚒ ёаҗᙁൂډ֚ᜤ଺௨ׇǴӧ᏾ҽෳᡍύ໻ᚒಔᆶᚒಔ໔཮Ԗ၂ᚒᜤࡋԛׇ೭ঁ ୢᚒౢғǴࡺႝတϯ፾܄ෳᡍऩ௦ҔᚒಔԄෳᡍ߾ёа٬ځ၂ᚒᜤࡋԛׇਏ݀फ़ եǶ ќѦǴෳᡍว৖ಔᙃӧ໒วϷࡷᒧ၂ᚒ೭Бय़઻຤࣬྽ӭޑਔ໔аϷߎᒲǴ ࣗԿКෳᡍጓᇙޑၸำ܌઻຤ޑၗྍᗋाӭǶҗܭڙ၂ޣӧௗڙᚒಔԄෳᡍਔε ೽ϩޑਔ໔೿ӧೀ౛೭٤ڈᐟǴऩ΋ঁڈᐟΠѝጓᇙ΋ঁ၂ᚒࢂࡐੁ຤ޑǴЪᚒ ಔԄෳᡍёаᡣෳᡍว৖ޣᕇள׳ӭԖᜢڙ၂ޣޑᏢಞၗૻǴӢԜǴӭኧޑڈᐟ ೿Քᒿ΋ಔ၂ᚒǶԜѦǴᚒಔԄෳᡍό໻ૈԖਏෳໆډڙ၂ޣޑଯቫԛࡘԵǴᡣ ෳᡍว৖ޣᕇள׳ӭԖᜢڙ၂ޣޑᏢಞၗૻǴᗋёаׯ๓ႝတϯ፾܄ෳᡍύൂ΋ ၂ᚒ่ᄬ܌ౢғޑୢᚒǴҗԜёـǴᚒಔޑ٬Ҕࢂຫٰຫख़ाΑȐLee, Brennan, & Frisbie, 2000ȑǶ

ᒿ๱ᚒಔෳᡍ่ᄬޑว৖ǴόӕޑᏢޣΨ๏ϒᚒಔόӕޑӜᆀǴٯӵǺEbel Ȑ1951ȑ܌ගрޑှញ܄၂ᚒȐinterpretive exercisesȑǵCuretonȐ1965ȑ܌ගр ޑຬભ၂ᚒȐsuperitemsȑǵWainerᆶKielyȐ1987ȑ܌ගрޑᚒಔȐtestletsȑǵ

(16)

HaladynaȐ1992ȑ܌ගрޑ၂ᚒ໣Ȑitem clustersȑǵYenȐ1993ȑ܌ගрޑࢤပ ȐpassagesȑǵWilsonᆶAdamsȐ1995ȑ܌ගрޑ၂ᚒ״Ȑitem bundlesȑ฻ǶਥᏵ ፏӭࣴزᡉҢǴҞ߻നቶڙᏢޣ܌ௗڙᆶ٬ҔޑӜຒࣁȨᚒಔȐtestletsȑȩǶ ନΑӜᆀԖ܌όӕϐѦǴᚒಔޑۓကΨӢӚᏢޣޑᢀᗺό΋ኬԶԖ܌όӕǶ Wainer ᆶ KielyȐ1987ȑ܌ගрޑᚒಔཷۺࢂࣁΑှ،ႝတϯ፾܄ෳᡍޑᒧᚒୢ ᚒǴஒȨᚒಔȩۓကࣁ΋ಔᆶൂ΋ϣ৒ሦୱԖᜢޑ၂ᚒǴ٠ஒԜຎࣁ΋ঁൂՏǴ ځх֖ڰۓኧໆޑႣۓၡ৩Ȑpredetermined pathsȑǴڙ၂ޣѸ໪٩ൻԜႣۓၡ৩ ٰ຾ՉෳᡍǶٯӵǺ᎙᠐౛ှෳᡍǵ΋ಔਥᏵკ߄຾ՉբเޑኧᏢ၂ᚒǶෳᡍว ৖ޣਥᏵෳᡍೕ਱ஒ΋ಔ၂ᚒጓᇙԋ΋ঁᚒಔǴҗܭᚒಔϣޑ၂ᚒڀԖ࣬ӕޑᚒ ༸Ǵࡺڙ၂ޣѸ໪բเᚒಔϣޑ܌Ԗ၂ᚒǴനࡕਥᏵڙ၂ޣբเࢌᚒಔޑ่݀ӆ ،ۓΠ΋ঁाࡼෳޑᚒಔǶWainer ᆶ LewisȐ1990ȑ຾΋؁ගр΋ঁ׳දၹޑۓ ကǴஒᚒಔຎࣁ΋ঁλෳᡍǴλډى୼ᡣෳᡍว৖ޣளаᏹ׋ǴࠅΞεډىа఼ ᇂ၀ᚒಔҁيޑϣ৒ǶWainerǵSireci ᆶ ThissenȐ1991ȑஒᚒಔۓကࣁ΋ঁёඹ жෳᡍޑൂՏǴࢂ΋ಔ࣬ϕԖᜢᖄޑ၂ᚒǴΨ൩ࢂᇥǴஒᚒಔຎࣁ΋ঁКঁձ၂ ᚒᗋεޑෳᡍ่ᄬ୷ҁൂՏǶ

ມǵᚒಔޑᜪࠠ

ᚒಔޑϩᜪࢂ࣬྽ख़ाޑǴӢࣁόӕᜪࠠޑᚒಔёૈ཮٬Ҕόӕޑϩ݋Б ԄǴ຾Զளډόӕޑ่݀ᆶ่ፕǶᚒಔޑᅿᜪё٩ෳᡍጓᇙȐtest constructionȑǵ ෳᡍჴࡼȐtest administrationȑᆶෳᡍीϩȐtest scoringȑٰϩᜪǴ૟ϟಏӵΠǶ ΋ǵෳᡍጓᇙ

೭ᜪࠠޑᚒಔӧෳᡍ่ᄬ΢х֖΋ಔᆶڈᐟ׷਑Ԗᜢޑ၂ᚒǴ؂΋ၰ၂ᚒ೿ ࢂ٩ᒘܭ܌٬Ҕޑڈᐟ׷਑ǶӃ߻ࣴز܌ගϷޑȨᚒಔȩ൳Я೿ࢂ๱ख़ܭԜᅿᜪ ࠠޑᚒಔǶ

(17)

Βǵෳᡍჴࡼ җܭӧႝတϯ፾܄ෳᡍύǴൂ΋၂ᚒޑ่ᄬ཮ౢғે๎ਏ݀ǵ၂ᚒԛׇϷϣ ৒ѳᑽ฻ୢᚒǶӢԜǴWainerᆶKielyȐ1987ȑࡌ᝼ஒ΋ಔ၂ᚒຎࣁ΋ঁൂՏǴځ х֖ڰۓኧໆޑႣۓၡ৩Ȑpredetermined pathsȑǴڙ၂ޣѸ໪٩ൻԜႣۓၡ৩ٰ ຾ՉෳᡍǶԶ೭٤၂ᚒ״Ȑbundles of itemsȑᆀࣁаၡ৩ࣁ୷ᘵޑᚒಔȐpath-based testletsȑǶ Οǵෳᡍीϩ ߈൳ԃٰǴҗܭ໺಍ᒧ᏷ᚒෳᡍѝૈෳрڙ၂ޣ܌ᏢǴคݤෳрڙ၂ޣၨଯ ቫԛޑࡘԵૈΚǴӢԜ٬Ҕჴբຑໆжඹ໺಍ᒧ᏷ᚒෳᡍǴᡣ௲ৣૈ୼׳ᕕှڙ ၂ޣჹୢᚒᕕှำࡋǵୢᚒှ،ૈΚǵϩ݋ǵᘜયаϷ߄ၲԾךޑૈΚǶ

ӧჴբຑໆک࠼ᢀीϩෳᡍȐobjectively scored testȑϐ໔ޑৡձӧܭǴа۳ ࠼ᢀीϩෳᡍा؃ຑϩޣ٬Ҕ΋ᅿຑϩ኱ྗჹڙ၂ޣޑ߄౜຾ՉຑϩǴՠคݤዴ ᇡ࣬ӕޑϩኧࢂցࢂ٬Ҕόӕຑϩ኱ྗ܈җόӕຑϩޣຑϩԶளǶ൩ჴբຑໆԶ قǴε೽ϩޑ၂ᚒࣣҗӕ΋Տຑϩޣ܈࣬ӕޑຑϩ኱ྗٰຑϩǴӧ೭ٿᅿ௃ݩ ΠǴёૈᏤठϩኧ໔ࢂ࣬ϕ٩ᒘޑǹऩঁձ၂ᚒ܈բ཰ࢂ٬Ҕόӕޑຑϩ኱ྗ܈ όӕຑϩޣٰຑϩǴ߾ό཮Ԗ೭ᅿ௃׎วғȐFerrara, Huynh, & Baghi, 1997; Yen, 1993ȑǶ

ୖǵֽ೽၂ᚒ٩ᒘޑۓကϷচӢ

ӧђڂෳᡍ౛ፕȐclassical test theory, CTTȑύǴځύ΋໨୷ҁଷ೛ࣁෳໆᇤ ৡᆶڙ၂ޣ੿ჴϩኧϐ໔և႟࣬ᜢǶԶӧ၂ᚒϸᔈ౛ፕύޑ୷ҁଷ೛ɡֽ೽ᐱҥ

܄Ǵࢂࡰӧ๏ۓૈΚНྗTޑ௃ݩΠǴڙ၂ޣբเӚ၂ᚒޑเჹᐒ౗ࢂ࣬ϕᐱҥ

ޑǴҭջڙ၂ޣό཮Ӣࣁเჹಃ΋ᚒԶቹៜಃΒᚒޑբเ௃׎Ƕֽ೽ᐱҥ܄ޑଷ ೛ё߄ҢࣁǺ

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) | ( P ) | ( P ) | , ( P X₁ x₁ X₂ x₂ T X₁ x₁ T X₂ x₂ T Ȑ2-1ȑ ऩڙ၂ޣӧբเࢌ၂ᚒਔ཮ڙډځд၂ᚒޑբเ௃׎ԶቹៜǴջၴϸΑֽ೽ ᐱҥ܄ޑଷ೛Ǵ೭ਔ൩ౢғΑֽ೽၂ᚒ٩ᒘǶӧ೚ӭ௲ػǵЈ౛ෳᡍύ࿶த཮Ԗ ᚒಔԄޑ၂ᚒǴٯӵǺ᎙᠐ෳᡍǴҗܭӧӕ΋ঁᚒಔϣޑ၂ᚒࢂ٬Ҕ࣬ӕ΋ࢤЎ ӷૻ৲Ǵࡺ၂ᚒ໔ёૈ࣬ϕԖᜢᖄǴڙ၂ޣӧբเࢌ၂ᚒਔ཮ڙډځд၂ᚒޑբ เ௃׎ԶቹៜǶ ԜѦǴֽ೽၂ᚒ٩ᒘගډ၂ᚒϩኧ໔ޑచҹ࣬ᜢ܄Ȑconditional correlationȑ ёϩࣁ҅य़ޑȐpositiveȑаϷॄय़ޑȐnegativeȑٿᅿǴ҅य़ޑֽ೽၂ᚒ٩ᒘࢂ ࡰǴऩࢌڙ၂ޣӧࢌ΋၂ᚒޑ߄౜КႣයޑӳȐ܈߄౜КႣයޑόӳȑǴٗሶд\ Ӵӧځд၂ᚒΨԖёૈ཮߄౜ޑКႣයޑӳȐ܈߄౜КႣයޑόӳȑǹԶॄय़ޑ ֽ೽၂ᚒ٩ᒘࢂࡰǴࢌڙ၂ޣӧࢌ΋၂ᚒޑ߄౜ؼӳǴՠд\Ӵӧځд၂ᚒޑ߄౜ ΢ԖёૈߚதৡǶ

YenȐ1993ȑᇡࣁֽ೽၂ᚒ٩ᒘёૈࢂҗѦӧڐշ܈υᘋȐexternal assistance or interferenceȑǵเᚒೲࡋȐspeedenessȑǵੲമȐfatigueȑǵግಞȐpracticeȑǵ ၂ᚒ܈ϸᔈ׎ԄȐitem or response formatȑǵࢤပ٩ᒘȐpassage dependenceȑǵ ၂ᚒՍȐitem chainingȑǵჹӃ߻ޑเਢ଺ှញȐexplanation of previous answerȑǵ ຑϩೕ߾܈ຑϩޣȐscoring rubrics or ratersȑᆶޕ᛽ǵϣ৒аϷૈΚȐcontent, knowledge, and abilitiesȑ೭٤Ӣન܌೷ԋǶаΠ૟ଞჹ೭٤Ӣન၁ಒᇥܴǺ ΋ǵѦӧڐշ܈υᘋ

ჹܭ΋٤၂ᚒǴऩڙ၂ޣவԴৣ܈ӕᏆ໔ளډԖਏޑڐշǴ߾ڙ၂ޣӧբเ ೭٤၂ᚒਔஒ཮߄౜ؼӳǴԶౢғֽ೽၂ᚒ٩ᒘǶ࣬ϸޑǴऩڙ၂ޣڙډѦӧυ ᘋ཮٬ෳᡍϩኧफ़եǴٯӵǺ௲࠻ઇᚯǵόؼ׷਑ǵவԴৣ܈ӕᏆ໔ளډόᆒዴ ޑߞ৲Ƕ

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Βǵเᚒೲࡋ ऩڙ၂ޣคݤӧೕۓਔ໔ϣֹԋ᏾ҽෳᡍǴЪ҂բเޑ၂ᚒ೯தวғӧෳᡍ ҃ᆄǴ೭ᅿ௃׎ࢂ҅य़ޑȐpositivelyȑֽ೽၂ᚒ٩ᒘǶӵ݀ӧ຾ՉෳᡍਔǴਔ໔ ޑӼ௨ࢂ΋ঁख़ाޑӢનǴ߾ॄय़ޑȐnegativeȑֽ೽၂ᚒ٩ᒘΨԖёૈ཮วғǹ ऩᏢғᒧ᏷޸ਔ໔ѐբเ᏾ҽෳᡍࢌ೽ҽޑ၂ᚒǴ߾ڙ၂ޣӧ೭೽ҽ཮ளډၨଯ ޑϩኧǴԶӧځд೽ϩޑளϩ཮ၨեǶ Οǵੲമ ӧଯा؃ޑෳᡍȐdemanding testȑύǴࢤပȐpassageȑр౜ӧ᏾ҽෳᡍޑՏ ࿼཮ڙډڙ၂ޣੲമӢનԶቹៜځ၂ᚒᜤࡋǴٯӵǺࢤပр౜ӧෳᡍ߻ъࢤਔǴ ೭٤၂ᚒჹܭڙ၂ޣԶقࢂၨᙁൂޑǴՠऩр౜ӧෳᡍࡕъࢤǴڙ၂ޣёૈ཮Ӣ ࣁགډੲമԶቹៜځբเ௃׎ǶԶӧࢤပύޑ၂ᚒǴӢӅ٦ӕ΋ঁڈᐟЪӅӕڙ ډڙ၂ޣੲമޑӢનቹៜԶౢғ҅य़ޑֽ೽၂ᚒ٩ᒘǶ Ѥǵግಞ ऩڙ၂ޣӢࣁख़ፄግಞ܈၂ᚒᚼӀޑӢનԶׯ๓ӧ၂ᚒ΢ޑ߄౜Ǵ߾཮ౢғ ֽ೽၂ᚒ٩ᒘǶ ϖǵ၂ᚒ܈ϸᔈ׎Ԅ ၂ᚒёа٬Ҕόӕޑ׎Ԅٰෳໆ࣬ӕޑϣ৒ǶԶ၂ᚒޑ׎Ԅࢂ࣬྽ӭኬϯ ޑǴх֖ᒧ᏷ᚒ܈ࡌᄬϸᔈᚒǶࡌᄬϸᔈᚒࢂ٩Ᏽځߏࡋ܈ᜪࠠԶԖ܌ᡂϯǴٯ ӵǺ྽ڙ၂ޣёаᙖҗቪࡺ٣ǵฝკ܈ࡌҥኳԄբрϸᔈǴ೭٤ᡂϯࣣ཮ౢғֽ ೽၂ᚒ٩ᒘǶ Ϥǵࢤပ٩ᒘ ऩࢌ٤၂ᚒឦܭ࣬ӕޑࢤပǴ߾཮ౢғֽ೽၂ᚒ٩ᒘǶ೭ᅿֽ೽၂ᚒ٩ᒘࢂ җڙ၂ޣჹܭࢤပޑङඳޕ᛽܌ౢғǴаᇟЎࣽޑ᎙᠐ෳᡍԶقǴෳᡍύх֖΋ ጇᆶཥࠠࢬགԖᜢޑЎകǴऩڙ၂ޣ A ჹܭཥࠠࢬགޑ࣬ᜢޕ᛽Ԗ܌ੋᘪǴԶڙ

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၂ޣ B ჹܭ೭Бय़ޑ࣬ᜢޕ᛽ࣗϿǴٗሶڙ၂ޣ A ӧբเ೭ጇЎകޑ၂ᚒਔǴ Ԗёૈ཮߄౜ၨӳǴϸϐǴڙ၂ޣ B ൩Ԗёૈ߄౜ό٫Ƕ Ύǵ၂ᚒՍ ӵ݀΋ೱՍޑ၂ᚒࢂҗܰԶᜤ܌ಔԋޑǴ߾ڙ၂ޣ཮Ӣࣁเჹಃ΋ᚒԶቚу ಃΒᚒޑเჹޑᐒ౗Ƕ ΖǵჹӃ߻ޑเਢ଺ှញ ӧኧᏢჴբຑໆёаว౜ԖКၨ੝ਸޑ၂ᚒՍǹࢌ΋၂ᚒा؃ڙ၂ޣբเǴ ᒿࡕޑ၂ᚒ߾ा؃ڙ၂ޣჹӃ߻ޑเਢ଺ှញǴٯӵǺࢌڙ၂ޣӧբเ၂ᚒ 1 ਔ ᒧ᏷ A ೭ঁเਢǴௗΠٰޑ၂ᚒ཮ा؃дଞჹಃ΋ᚒ܌ᒧ᏷ޑเਢ຾ՉှញǴᒧ ᏷೭ঁᒧ໨ޑ౛җ܈ޣӈрှᚒၸำǶ೭ঁှញၸำёаගٮᆶڙ၂ޣ߄౜Ԗᜢ ޑᚐѦૻ৲Ǵᆶ߻΋ၰ၂ᚒڀԖଯࡋޑ࣬ᜢ܄Ƕ ΐǵຑϩೕ߾܈ຑϩޣ ӧჴբຑໆύޑ၂ᚒёҗόӕޑຑϩ኱ྗ܈όӕຑϩޣٰຑϩǴฅԶǴऩҗ ӕ΋Տຑϩޣ܈࣬ӕޑຑϩೕ߾ٰຑϩǴёૈ཮Ꮴठ؂΋၂ᚒ໔ޑϩኧࢂ࣬ϕ٩ ᒘޑǶ Μǵޕ᛽ǵϣ৒аϷૈΚ ڂࠠޑԋ൩ෳᡍ܌х֖ޑ၂ᚒࢂෳໆ΋ঁጄൎޑϣ৒ሦୱǶऩѝෳໆൂ΋ϣ ৒ሦୱǴٗሶ೭٤၂ᚒᡉҢԖֽ೽၂ᚒ٩ᒘǶٯӵǺ୯λΟԃભޑኧᏢཷۺෳᡍǴ ෳໆڙ၂ޣࢂց཮࣮ਔដ᠐ڗਔ໔Ǵ߾೭٤၂ᚒ཮Ԗֽ೽٩ᒘޑ௃׎Ƕ Ҟ߻ςว৖рኧᅿόӕຑ՗ֽ೽၂ᚒ٩ᒘޑБݤǴനத೏٬ҔޑБݤࣁ Yen Ȑ1984ȑ܌ගрޑQ3಍ीໆȐQ3 statisticȑǶQ3಍ीໆޑीᆉБԄࢂ௨ନ௞ڙ

၂ޣૈΚޑቹៜࡕीᆉٿٿ၂ᚒ໔ූৡޑ࣬ᜢǶKellerǵSwaminathan ᆶ SireciȐ2003ȑ

ջ௦ҔQ₃಍ीໆຑ՗ᚒಔ၂ᚒࢂցԖֽ೽၂ᚒ٩ᒘޑ੝܄ǴਥᏵࣴزᡉҢόӕᚒ

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ಃΒ࿯ʳ ᚒಔϸᔈ౛ፕ

൘ǵᚒಔϸᔈኳԄϐว৖

җܭᚒಔԄෳᡍڀԖֽ೽၂ᚒ٩ᒘޑ੝܄Ǵऩ٬Ҕ၂ᚒϸᔈ౛ፕኳԄϩ݋ၗ ਑ǴӢࣁ၂ᚒϸᔈ౛ፕޑֽ೽ᐱҥଷ೛Զ۹ౣᚒಔ၂ᚒϣޑ࣬ᜢǴ߾཮ଯ՗ڙ၂ ޣૈΚୖኧЪ၂ᚒୖኧ཮ౢғୃ՗ޑ௃׎ȐWainer, 1995; Wainer & Lukhele, 1997; Wainer, Sireci, & Thissen, 1991; Wainer & Thissen, 1996; Wainer & Wang, 2000; Yen, 1993ȑǶќѦǴҭԖᏢޣගрஒ΋ঁᚒಔຎࣁ΋ঁӭᗺीϩ၂ᚒǴаӭᗺीϩޑ БԄٰीᆉ၀ᚒಔޑளϩǴ٠аӭᗺीϩኳԄٰϩ݋ᚒಔԄෳᡍၗ਑ǴٯӵǺ΋ ঁᚒಔϣԖ5ᚒΒϡीϩޑᒧ᏷ᚒǴเჹ1ᚒள1ϩǴ߾ڙ၂ޣӧբเ၀ᚒಔ܌ள ޑϩኧനեࣁ0ϩǴനଯள5ϩǹԜБݤ፾ҔܭBockȐ1972ȑ܌ගрޑӜကϸᔈኳ ԄȐnominal response model, NRMȑǵMastersȐ1982ȑගрޑ೽ҽ๏ϩኳԄȐpartial credit model, PCMȑǵSamejimaȐ1969ȑගрޑ฻ભϸᔈኳԄȐgrade-response model, GRMȑ܈MurakiȐ1992ȑගрޑ΋૓ϯ೽ҽ๏ϩኳԄȐGeneralized Partial Credit Model, GPCMȑǶWainerȐ1995ȑᇡࣁ྽᏾ҽෳᡍх֖ၨଯКٯޑᐱҥ၂ᚒЪᚒಔ ਏ݀ࣁ፾ࡋਔǴΨ೚ё٬ҔӭᗺीϩኳԄٰϩ݋ᚒಔԄෳᡍၗ਑ǶՠࢂǴऩஒᚒ ಔຎࣁ΋ঁӭᗺीϩ၂ᚒǴ߾཮഼Ѩࢌ٤ૻ৲ȐWang & Wilson, 2005ȑǴᖐٯٰ ᇥǴ΋ঁᚒಔϣԖ5ᚒΒϡीϩޑᒧ᏷ᚒǴڙ၂ޣAเჹಃ1ǵ2ǵ5ᚒǴڙ၂ޣB เჹಃ2ǵ3ǵ4ᚒǴᗨฅٿՏڙ၂ޣӧ၀ᚒಔޑளϩࣣࣁ3ϩǴՠჴሞ΢дॺӧӚ ᚒޑ߄౜ࠅόᅰ࣬ӕǶ

ӢԜǴBradlowǵWainerᆶWangȐ1999ȑගрᚒಔϸᔈ౛ፕϐኳԄǴ၂კှ ،ၸѐа၂ᚒϸᔈ౛ፕϩ݋ᚒಔԄෳᡍ܌೷ԋޑୢᚒǶBradlow฻ΓȐ1999ȑஒ BirnbaumȐ1968ȑ܌ගрޑΒୖኧኳԄȐtwo-parameter logistic model, 2PLMȑу Ε΋ঁᒿᐒਏ݀Ȑ܈ᆀᚒಔਏ݀ȑۯ՜ԋΒୖኧᚒಔኳԄȐtwo-parameter testlet

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model, 2PTMȑǴЪଷ೛Ԝᚒಔਏ݀ޑᡂ౦ኧࣁ΋தኧǴջ؂ঁᚒಔڀԖ࣬ӕޑᚒ ಔਏ݀ᡂ౦ำࡋȐ 2 2 ) ( VJ Vrd j ȑǴՠӧ੿ჴၗ਑ύᡉҢ؂ঁᚒಔڀԖόӕޑᚒಔਏ ݀ᡂ౦ำࡋǴࡺWainerǵBradlowᆶDuȐ2000ȑஒΒୖኧᚒಔኳԄуΕ౒ෳࡋୖ ኧۯ՜ԋΟୖኧᚒಔኳԄȐthree-parameter testlet model, 3PTMȑǴЪଷ೛ᚒಔਏ݀ ᡂ౦ኧᒿ๱ᚒಔԶᡂ୏ǶΟୖኧᚒಔኳԄޑीᆉБԄӵϦԄȐ2-2ȑǺ ] ) ( [ exp 1 ] ) ( [ exp ) 1 ( ) | 1 ( P ) ( ) ( j id j i j j id j i j j j i j b a b a c c x J T J T T Ȑ2-2ȑ ) 1 , 0 ( N ~ i T Ȑ2-3ȑ ) , 0 ( N ~ 2 ) ( ) (j rd j id V J Ȑ2-4ȑ ځύǴP(x_j 1|T_i)ж߄ಃi Տڙ၂ޣӧբเᚒಔ၂ᚒಃ j ᚒள 1 ϩޑᐒ౗ǹTiж߄ ಃ i Տ ڙ ၂ ޣ ૈ Κ ୖ ኧ ǹa ǵj b ǵj c ϩ ձ ж ߄ ಃ j ᚒ ၂ ᚒ ޑ ᠘ ձ ࡋ ୖ ኧj

Ȑdiscrimination parameterȑǵᜤࡋୖኧȐdifficulty parameterȑǵ౒ෳࡋୖኧȐguessing parameterȑǹJid(j)ж߄ڙ၂ޣբเᚒಔd(j)ਔޑᚒಔਏ݀Ƕ 2 ) (j rd V ߄Ңᚒಔd(j)ޑᚒಔਏ݀ᡂ౦ำࡋǴ 2 ) (j rd V ຫε߄Ңᚒಔϣ၂ᚒޑֽ೽ ၂ᚒ٩ᒘ௃׎ຫᝄख़Ƕ྽c_j 0Ъ 2 2 ) ( VJ Vrd j Ȑ؂ঁᚒಔޑᚒಔਏ݀ᡂ౦ኧࣣ࣬฻ȑ ਔǴϦԄȐ2-2ȑ߾ᕭ෧ԋ Bradlow ฻ΓȐ1999ȑ܌ගрޑΒୖኧᚒಔኳԄǶ྽c_j 0 Ъa_j 1ਔǴϦԄȐ2-2ȑ߾ᕭ෧ԋ Wang ᆶ WilsonȐ2005ȑ܌ගрޑ Rasch ᚒಔ ኳԄȐRasch testlet modelȑǺ

) exp( 1 ) exp( 1) ( P ) ( ) ( j id j i j id j i ij b b y J T J T Ȑ2-5ȑ ྽J_id₍_j₎ 0ȐؒԖᚒಔਏ݀ȑǴ߄Ң၂ᚒ໔ࢂ࣬ϕᐱҥޑǴϦԄȐ2-5ȑ߾ᕭ

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෧ࣁ RaschȐ1960ȑ܌ගрޑൂୖኧኳԄȐone-parameter logistic model, 1PLMȑǶ ΢ॊޑኳԄ໻፾ҔܭΒϡीϩ၂ᚒǴ຾΋؁КၨᚒಔኳԄᆶӭᗺीϩኳԄǴ ᚒಔኳԄԖаΠޑᓬᗺǺ ΋ǵऩஒᚒಔຎࣁ΋ঁӭᗺीϩ၂ᚒ຾Չϩ݋Ǵ཮഼Ѩ΋٤ϸᔈಔࠠޑૻ৲Ǵՠ ҔᚒಔኳԄٰϩ݋ᚒಔ၂ᚒǴϩ݋ޑൂՏࣁ၂ᚒǴࡺёаߥ੮؂΋၂ᚒୖኧ ޑཷۺǹ Βǵ၂ᚒीϩޑ኱ྗؒԖׯᡂǴเჹीࣁ1Ǵเᒱीࣁ0ǹ Οǵ၂ᚒୖኧȐ᠘ձࡋୖኧǵᜤࡋୖኧǵ౒ෳࡋୖኧȑޑཷۺϝฅ፾ҔǶ ᗨฅ΢ॊޑᚒಔኳԄԖ೭٤ᓬᗺǴՠ໻ज़ܭΒϡीϩ၂ᚒǶ΋૓ԶقǴᚒಔ ёૈх֖Βϡीϩ၂ᚒϷӭᗺीϩ၂ᚒǶٯӵǺኧᏢࣽෳᡍ܈Ծฅࣽෳᡍޑᚒಔ х֖ࡌᄬϸᔈᚒǴ٠аӭᗺीϩ߄ҢǶԜѦǴ׵լ੝Ԅໆ߄ȐLikert-type scaleȑ Ϸຑۓໆ߄Ȑrating scaleȑ၂ᚒࣣࢂӭᗺीϩ၂ᚒǴӢԜǴว৖р፾ӝӭᗺीϩ ၂ᚒޑᚒಔኳԄǶ WangǵBradlowᆶWainerȐ2002ȑӧ฻ભϸᔈኳԄύуΕᒿᐒਏ݀Զԋࣁ฻ ભϸᔈᚒಔኳԄȐgraded-response testlet model, GRTMȑǶӧीᆉڙ၂ޣޑ੿҅ϸ ᔈᐒ౗ਔǴϩࣁٿঁ؁ᡯǴ२Ӄीᆉᏹբ੝ቻԔጕȐoperating characteristic curvesȑǺ ] ] ) ( [ exp 1 ) ( [ exp ) ( P ) ( ) ( i d ij i i d ij i * ij a a J E T J E T T Ǵ j 0,1,2,....,m_i Ȑ2-6ȑ ځύǴP*(T) ij ж߄ૈΚॶࣁT ޑڙ၂ޣբเᚒಔ၂ᚒಃ i ᚒள j ϩа΢ޑϸᔈᐒ ౗ǹTж߄ڙ၂ޣૈΚୖኧǹa ж߄ಃi ᚒ၂ᚒޑ᠘ձࡋୖኧǹ_i E ж߄ಃi ᚒ၂ᚒij ಃ j ঁޑ⸣ॶୖኧȐthreshold parameterȑǹJd(i)ж߄ڙ၂ޣբเᚒಔd(i)ਔޑᚒಔ ਏ݀ǹЪP*( ) 1 0 T i کP ( ) 0 * ) 1 (mi T i Ƕ

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ӆᙖҗϦԄȐ2-6ȑीᆉᜪձϸᔈԔጕȐcategory response curveȑǺ ) ( P ) ( P ) ( P * ) 1 ( * T T T ij i j ij Ȑ2-7ȑ ځύǴP_ij(T)ж߄ૈΚॶࣁT ޑڙ၂ޣբเᚒಔ၂ᚒಃi ᚒள j ϩޑϸᔈᐒ౗Ƕ WangǵChengᆶWilsonȐ2005ȑаϷWangᆶWilsonȐ2005ȑࡰрǴ೽ϩ๏ϩ ᚒಔኳԄȐpartial credit testlet model, PCTMȑࢂӧ೽ϩ๏ϩኳԄуΕᒿᐒਏ݀Զ ளǴځीᆉБԄӵΠǺ 1 0 ) ( 0 ) ( ] ) ( [ exp ] ) ( [ exp ) ( P

¦

i m r r j i d ij x j i d ij ix J G T J G T T Ǵځύ

¦

{ 0 0 ) ( ) 0 ( j i d ij J G T Ȑ2-8ȑ ځύǴP_ix(T)ж߄ૈΚॶࣁT ޑڙ၂ޣբเᚒಔ၂ᚒಃ i ᚒள x ϩޑᐒ౗ǹ x ж߄ ڙ၂ޣޑӣเ܌ឦᜪձǴவ0,1,2,...,m_iǹm ж߄ಃ i ᚒ܌Ԗޑᜪձኧǹ_i Tж߄ ڙ၂ޣޑૈΚॶǹG_ij ж߄ಃ i ᚒ၂ᚒಃ j ঁޑ၂ᚒ؁ᡯᜤࡋୖኧȐitem step difficultyȑǹJd(i)ж߄ڙ၂ޣբเᚒಔd(i)ਔޑᚒಔਏ݀Ƕ

ມǵୖኧ՗ीБݤ

җܭҁࣴزࢂ௦Ҕ SCORIGHT 3.0 ೬ᡏȐWang, Bradlow, & Wainer, 2005ȑჹ ኳᔕၗ਑຾Չୖኧ՗ीǴԶԜ೬ᡏޑୖኧ՗ीБݤࢂ௦Ҕଭёϻ᜘ᆾӦьᛥ ȐMarkov chain Monte Carlo, MCMCȑ՗ीБݤǶӢԜǴଞჹ MCMC ՗ीำׇ၁ ॊӵΠǶ

MCMCࢂ΋ᅿنМ՗ीݤޑۯ՜ǴԜᄽᆉݤޑᓬᗺࢂ΋ԛૈೀ౛ӭঁᡂኧޑ

՗ीǶԜБݤѸ໪࿶ၸӭԛख़ፄܜڗኬҁǴࡌᄬр΋ߏՍޑଭёϻ᜘ȐMarkov chainȑǴ຾Զᕇள΋ᛙۓϩթȐstationary distributionȑǴ೸ၸଭёϻ᜘ύޑᒿᐒ

(25)

ᡂኧёΑှᡂኧޑ੝܄Ƕࡌᄬଭёϻ᜘ޑБݤεӭࢂճҔ Metropolis-Hastings ᄽ ᆉݤϷӓМܜኬݤȐGibbs samplerȑٰ຾ՉኳԄޑୖኧܜኬϷ՗ीǶԶᚒಔϸᔈ ౛ፕࢂࡌᄬӧֹ᏾ޑ໘ቫنМࢎᄬύǴSCORIGHT 3.0 ೬ᡏջ௦ҔӓМܜኬݤ຾ ՉኳԄޑୖኧܜኬϷ՗ीǶ ߈ԃٰǴຫٰຫӭᏢޣ٬Ҕ MCMC ٰ௢ፕࡕᡍϩթǴЬाޑচӢࢂ΋ѿᕇ ளࡕᡍኬҁϩթǴ߾ࡐ৒ܰջёֹԋ௢ፕǶЪ MCMC όሡा٩ᒘᅌ߈౛ፕ Ȑasymptotic theoryȑǴΨ൩ࢂεኬҁ౛ፕȐlarge sample theoryȑǴջёᕇள኱ྗᇤǹ ࣬ჹܭനεཷ՟ݤȐmaximum likelihood methodȑǴMCMC Ϣ೚ჹԖज़ኬҁ຾Չ ௢ፕǶќѦǴҗܭ໒วр୷ܭنМۓ౛բኳࠠୖኧ՗ीޑխ຤೬ᡏٮࣴزޣБߡ ٬ҔǴٯӵǺWinBUGSǴӢԜว৖р SCORIGHT 3.0 ೭ঁխ຤೬ᡏǴ٬ள IRT ኳԄΨૈ٬Ҕ MCMC ຾Չ௢ፕǶ WainerǵBradlow ᆶ WangȐ2007ȑаΒୖኧᚒಔኳԄٰᔠຎ MCMC ޑၮᆉ ၸำǶ೛ۓ/ ࣁኳԄύޑ܌ԖୖኧǴх֖၂ᚒ᠘ձࡋୖኧ(a₁,...,a_J)ǵ၂ᚒᜤࡋ ୖኧ(b₁,...,b_J)ǵڙ၂ޣૈΚୖኧ(T₁,...,T_I)ǵᚒಔୖኧJ1d(1),...,JId(J)ǴаϷቹ ៜୖኧϩթޑ( , 2) a a V P ǵ( , 2) b b V P ᆶ 2 J V Ǵځύ J ߄Ң၂ᚒኧǴ I ߄Ңڙ၂ΓኧǶа Πࣁଭёϻ᜘ᆾӦьᄽᆉݤϐܜኬำׇǶ ؁ᡯ 1. ᒧ᏷΋ঁ߃ۈӛໆ_/ _/(t 0) Ǵt ߄ҢॏжኧǴ೛ۓt =0ǶਥᏵ Wainer ฻Γ ޑ࿶ᡍࡰр MULTILOG ک BILOG ೬ᡏޑ՗ी่݀ёаගٮ๏ MCMC ྽ ଺߃ۈॶǴӢࣁ٬Ҕ೭٤೬ᡏޑ՗ी่݀྽଺ MCMC ޑ߃ۈॶǴёау זԏᔙޑೲࡋǶ ؁ᡯ 2. ᒧ᏷ࢌୖኧޑη໣O1Ǵ٠ᙖҗచҹϩթ ( | , ) ) ( 1 1 t Y p O /O ύܜڗ׳ཥॶ ) 1 ( 1 t O Ƕ ځύ () 1 t O / ж߄/ ೭ঁӛໆх֖O1೭٤ୖኧǴीᆉO1ಃ t ԛॏжޑॶǹԶY ߄ Ң܌ᢀჸޑෳᡍၗ਑Ƕ

(26)

؁ᡯ 3. ᒧ᏷ࢌୖኧޑη໣O2Ǵ٠ᙖҗచҹϩթ ( | , , ) ) 1 ( 1 ) ( , 2 1 2 /t t Y p O O O O ύܜڗ׳ཥ ॶ ( 1) 2 t O Ƕځύ () , 2 1 t O O / ΋ಔୖኧх֖O1کO2ǴीᆉO2ಃ t ԛॏжޑॶǹԶ ) 1 ( 1 t O ࢂҗ؁ᡯ 2 ׳ཥO1܌ளډޑॶǶ ؁ᡯ 4. வచҹϩթ ( | , , ( 1)) 2 ) 1 ( 1 , 2 1 / t t Y p O O O O ܜڗኬҁ ( 11), 2 /t O O Ǵ೛ۓt t1Ƕ ؁ᡯ 5. ऩt dMȐࡰۓޑॏжኧȑǴ߾ӣډ؁ᡯ 2 ख़ፄ຾Չ೭٤ำׇǴޔډt !M ωଶЗǶ ќѦǴाଞჹ MCMC ӧॏжኧ M ΢ޑᒧ᏷຾Չ௖૸ǴM ёϩࣁ M'کM-M' ٿঁ೽ҽǶM'ӧ MCMC ύᆀࣁȨႣᐨȐburn-inȑਔයȩǴջ໒ۈॏжޔډԏᔙᕇ ளᛙۓϩթࣁЗǴࣁΑᕇளԖਏޑ௢ፕǴӢԜाஒ߻य़҂ԏᔙޑॏжၗ਑մନǴ ߥ੮M-M'ٰ଺ϩ݋ǴҗܭM-M'໔ޑၗ਑ڀԖଯࡋ࣬ᜢǴӢԜǴ٬ҔޣёԾु ໔ຯ kǴѝܜڗр໔႖ k ޑၗ਑ٰև౜ǴٯӵǺॏж M=4000 ԛǴմନ߻य़ M'=2000 ޑॏжၗ਑ǴഭΠM-M'=2000Ȑ2001~4000ȑޑॏжၗ਑ǴҗܭഭΠޑၗ਑ڀԖ ଯࡋ࣬ᜢǴ٬ҔޣԾु໔ຯ 10Ǵࡺѝ૶ᒵಃ 2001ǵ2011ǵ2021ǵ……ǵ3081ǵ 3091 ԛޑॏжၗ਑Ƕᔠຎ M'ԛॏжࢂցԏ⻃ǴЬाࢂ٬Ҕ F ᔠۓٰຑ՗ࢂցၲ ډԏᔙǴځύࣴزޣѸ໪ᏹ׋ Q ঁଭёϻ᜘Ȑ೯த೛ۓ Q ࣁ 3 Կ 5 ঁ᜘ȑǴωૈ ٬Ҕ F ᔠۓٰຑ՗ࢂցၲډԏᔙǹၲډԏᔙࡕǴܜڗ Q ×(M-M')฽ၗ਑຾Չࡕᡍ ௢ፕǶ

ୖǵᚒಔϸᔈ౛ፕϐ࣬ᜢࣴز

BradlowǵWainerᆶWangȐ1999ȑаኳᔕࣴزޑБԄ௖૸ᚒಔ၂ᚒ௦Ҕ Bilog-MG೬ᡏȐZimowski, Muraki, Mislevy & Bock, 2003ȑǵGibbsܜኬݤȐؒԖԵ

(27)

຾Չୖኧ՗ीϐᆒྗࡋǶӧڰۓෳᡍߏࡋࣁ60ᚒȐх֖30ᚒᐱҥ၂ᚒϷ30ᚒᚒಔ ၂ᚒȑޑ௃ݩΠǴᏹ׋ޑᡂ໨ԖᚒಔኧϷᚒಔਏ݀ᡂ౦ኧǴځύᚒಔኧϩࣁ3܈6 ঁᚒಔǴᚒಔਏ݀ᡂ౦ኧϩࣁ0.5ǵ1ǵ2Οᅿ௃׎Ƕ่݀ᡉҢǴ೭Οᅿ՗ीБݤޑ ၂ᚒୖኧϷڙ၂ޣૈΚୖኧ՗ीᇤৡࣣ཮ᒿ๱ᚒಔਏ݀ᡂ౦ኧᡂεԶቚуǴЪ௦ ҔGibbs_Jܜኬݤ຾Չୖኧ՗ीനࣁᆒྗǶ Wang ᆶ WilsonȐ2005ȑаኳᔕၗ਑຾ՉࣴزǴ٬ҔᚒಔϸᔈኳԄᏹ׋όӕ ၂ᚒᜪࠠǵᚒಔኧǵڙ၂Γኧǵᚒಔਏ݀ᡂ౦ኧѤᅿᡂ໨ჹڙ၂ޣૈΚୖኧǵᚒ ಔਏ݀ᡂ౦ኧǵ၂ᚒᜤࡋୖኧ՗ीޑቹៜǶځύ၂ᚒᜪࠠϩࣁΒϡीϩ၂ᚒȐ40 ᚒȑǵӭϡीϩ၂ᚒȐ24 ᚒȑаϷషӝ၂ᚒȐх֖ 20 ᚒΒϡीϩ၂ᚒᆶ 12 ᚒӭ ϡीϩ၂ᚒȑΟᅿǴᚒಔኧϩձᏹ׋ 4 ܈ 8 ঁᚒಔǴڙ၂Γኧϩࣁ 200 ܈ 500 ΓǴ Զᚒಔਏ݀ᡂ౦ኧϩࣁ 0.25ǵ0.5ǵ0.75ǵ1 Ѥᅿ௃׎Ƕ่݀ᡉҢǴ၂ᚒᜤࡋୖኧ аϷᚒಔਏ݀ᡂ౦ኧϐ՗ीᇤৡࣣᒿ๱ΓኧቚуԶ෧λǹόӕᚒಔኧჹܭ၂ᚒᜤ ࡋୖኧ՗ीᇤৡ٠ค΋ठޑ่݀ǴԶڙ၂ޣૈΚୖኧ՗ीᇤৡ཮ᒿ๱ᚒಔኧቚу Զ෧λǶ

LiǵBolt ᆶ FuȐ2005ȑ໒ว፾ҔܭᚒಔኳԄޑෳᡍ੝ቻԔጕȐtest characteristic curve, TCCȑ฻ϯБݤǴ຾Զаኳᔕၗ਑ٰ຾ՉࣴزǴ௖૸٬Ҕ NEAT ฻ϯ೛ी ܭ໺಍ IRT ኳԄکᚒಔኳԄӧᚒಔၗ਑ϐ฻ϯਏ݀ǹᏹ׋ޑᡂ໨ԖۓᗕᚒಔኧϷ ᚒಔਏ݀ᡂ౦ኧٿᅿǴځύۓᗕᚒಔኧϩࣁ 2 ܈ 4 ঁᚒಔǴᚒಔਏ݀ᡂ౦ኧϩࣁ 0ǵ0.5ǵ1 Οᅿ௃׎ǹќѦǴаჴቻၗ਑ࣁٯٰᇥܴࣴزޣ܌ගрϐ፾Ҕܭᚒಔ ኳԄޑ฻ϯБݤǶਥᏵኳᔕၗ਑่݀ᡉҢǴаᚒಔኳԄϩ݋ޑ฻ϯ߯ኧ՗ीၨࣁ ᆒྗǶჴቻၗ਑่݀ᡉҢǴ؂ঁᚒಔޑᚒಔਏ݀ѳ֡ኧࣣόࣁ႟ǴЪٿဂڙ၂ޣ ޑᚒಔਏ݀ѳ֡ኧԖёૈόӕǴҗԜ่݀ᡍ᛾Αᚒಔၗ਑ӧ຾Չ฻ϯਔѸሡ௦Ҕ ፾ӝᚒಔኳԄޑ฻ϯБݤǶ ೚ࡘ໥Ȑ2008ȑаኳᔕࣴز௖૸ᚒಔෳᡍӧόӕीϩኳԄȐ၂ᚒीϩ IRT ኳ

(28)

Ԅǵᚒಔीϩ IRT ኳԄǵTRT ीϩኳԄȑჹڙ၂ޣૈΚୖኧ՗ीϐቹៜǹќѦǴ аჴቻࣴزɡ2006 ԃ PISA ᎙᠐౛ှෳᡍǴୀෳӚᚒಔֽ೽၂ᚒ٩ᒘޑำࡋǴ٠ КၨόӕीϩኳԄჹڙ၂ޣૈΚୖኧ՗ीޑৡ౦௃׎ǶӧኳᔕࣴزБय़Ǵᏹ׋ό ӕ၂ᚒᜪࠠǵᚒಔኧǵᚒಔਏ݀ᡂ౦ኧΟᅿ௃׎ǹځύ၂ᚒᜪࠠϩࣁΒϡीϩ၂ ᚒȐх֖ 50 ᚒᐱҥ၂ᚒǵ24 ᚒᚒಔ၂ᚒȑǵӭϡीϩ၂ᚒȐх֖ 50 ᚒᐱҥ၂ᚒǵ 24ᚒᚒಔ၂ᚒȑٿᜪǴᚒಔኧϩձᏹ׋ 4 ܈ 8 ঁᚒಔǴԶᚒಔਏ݀ᡂ౦ኧϩࣁ 0ǵ 0.25ǵ0.5ǵ0.75ǵ1ǵ1.5 Ϥᅿ௃׎Ƕኳᔕၗ਑่݀ᡉҢǴа TRT ीϩኳԄჹڙ၂ ޣૈΚ՗ीޑᆒዴ܄ന٫ǹคፕӧՖᅿᚒಔਏ݀ᡂ౦ำࡋΠǴᒿ๱ᚒಔኧໆቚ уǴΟᅿीϩኳԄځڙ၂ޣૈΚ՗ीޑᆒዴ܄཮ᒿϐගଯǹᒿ๱ᚒಔਏ݀ᡂ౦ำ ࡋቚуǴΟᅿीϩኳԄځڙ၂ޣૈΚ՗ीޑᆒዴ܄཮ᒿϐफ़եǶჴቻၗ਑่݀ᡉ ҢǴPISA ᎙᠐ຑໆύޑӚঁᚒಔڀԖό฻ำࡋޑֽ೽၂ᚒ٩ᒘǴќѦǴ࣬ၨܭ ᚒಔीϩޑӭᗺ IRT ኳԄǴൂ΋၂ᚒीϩ IRT ኳԄᆶ TRT ीϩኳԄӧૈΚ՗ी ΢ޑ࣬ᜢၨଯǴЪځ Bias ᆶ RMSE ޑৡ౦ॶҭၨࣁ࣬߈Ƕ

ಃΟ࿯ʳ ෳᡍ฻ϯޑཀကᆶᅿᜪ

΋૓ԶقǴٿҽෳᡍޑϩኧόૈ୼ޔௗ຾ՉКၨǴЬाࢂӢࣁٿҽෳᡍޑϩ ኧόӧӕ΋ໆЁ΢ǴٯӵǺڙ၂ޣAӧXෳᡍޑளϩࣁ50ϩǴڙ၂ޣBӧYෳᡍޑ ளϩࣁ50ϩǴՠคݤዴᇡXෳᡍکYෳᡍޑᜤࡋࢂց࣬ӕǴԖёૈXෳᡍޑ၂ᚒࢂ җၨᜤޑ၂ᚒ܌ಔԋǴԶYෳᡍࢂҗၨᙁൂޑ၂ᚒ܌ಔԋǴࡺؒԖᒤݤޔௗКၨ ٿҽෳᡍޑϩኧǶ ෳᡍ฻ϯࢂճҔ಍ीБݤǴஒڙ၂ޣӧࢌ΋ෳᡍޑϩኧᙯඤԿќ΋ෳᡍޑϩ ኧໆЁ΢ǴаКၨٿҽෳᡍϩኧᜢ߯ޑၸำǹᙁൂٰᇥǴ൩ࢂஒόӕෳᡍϩኧܫ ࿼ܭӕ΋ঁໆЁ΢຾ՉКၨޑБݤǶෳᡍ฻ϯޑҞޑӧܭፓ᏾ෳᡍᜤࡋϐৡ౦Զ ߚෳᡍϣ৒ϐৡ౦ǴЪ೭٤ෳᡍ܌ෳໆޑ੝፦܈ૈΚ࣬ӕǴᜤࡋϷϣ৒೿ཱུࣁ࣬

(29)

՟ȐKolen & Brennan, 1995ȑǶෳᡍϩኧ໔ޑ฻ϯѸ໪಄ӝ࣬฻܄Ȑequityȑǵჹ ᆀ܄Ȑsymmetry propertyȑǵიᡏόᡂ܄Ȑgroup invariance propertyȑϷෳᡍѸ໪ ࢂൂӛࡋȐunidimensionality of the testsȑ฻܄፦ωૈ୼຾ՉȐAngoff, 1971; Hambleton & Swaminathan, 1985; Kolen & Brennan, 2004; Lord, 1980ȑǶ

HambletonᆶSwaminathanȐ1985ȑࡰрෳᡍ฻ϯޑᅿᜪё୔ϩࣁНѳ฻ϯ Ȑhorizontal equatingȑϷࠟޔ฻ϯȐvertical equatingȑٿᅿǴ૟ϟಏӵΠǺ ΋ǵНѳ฻ϯ Нѳ฻ϯࢂࡰஒٿҽ܈ٿҽа΢ෳᡍϣ৒Ϸᜤࡋ೿ཱུࣁ࣬՟ޑෳᡍ຾Չೱ ่฻ϯǶНѳ฻ϯࣁΑᆢ࡭ෳᡍӼӄ܄ǴԶஒࢌෳᡍϩԋӭᅿόӕ׎Ԅϐෳᡍᚒ ҁǴ೭٤ෳᡍᚒҁࢂҗᚒ৤ύޑ၂ᚒ܌ጓᇙԶԋޑፄҁෳᡍǴᗨฅ೭٤ෳᡍᚒҁ όӕǴՠෳᡍޑϣ৒Ϸᜤࡋ೿ཱུࣁ࣬՟ǶԜѦǴऩा຾ՉНѳ฻ϯǴ߾Ѹ໪ଷ೛ όӕڙ၂ޣဂᡏޑૈΚϩթࢂ΋ኬޑǶ

೚ӭεࠠෳᡍȐlarge-scale testȑ܈ଯ॥ᓀෳᡍȐhigh stake testȑࣁΑᗉխ၂ ᚒၸࡋᚼӀǴࡺஒෳᡍጓᇙԋፄҁෳᡍǴٯӵǺᏢೌຑໆෳᡍکࣴزғΕᏢԵ၂ ȐGraduate Record Examination, GREȑ೿ԖӭᅿፄҁෳᡍǴԶ೭٤ෳᡍԖ΋ԃӭ ԛޑԵ၂ᐒ཮ǴѸ໪೸ၸНѳ฻ϯБݤஒόӕፄҁෳᡍޑϩኧᙯඤԿӕ΋ໆЁ΢ ωૈ຾ՉෳᡍϩኧޑКၨǶ Βǵࠟޔ฻ϯ ࠟޔ฻ϯࢂࡰஒٿҽ܈ٿҽа΢ޑෳᡍ຾Չೱ่฻ϯǴԶ೭٤ෳᡍޑᜤࡋό ӕЪόӕԃស܈ԃભޑڙ၂ޣဂᡏૈΚϩթΨό࣬฻Ǵՠ܌ෳໆޑϣ৒Ϸ੝፦ࢂ ࣬ӕޑǶε೽ϩޑԋ൩ෳᡍࣣ٬Ҕࠟޔ฻ϯБݤஒόӕෳᡍޑϩኧᙯඤԿӕ΋ໆ Ё΢຾ՉෳᡍϩኧޑКၨǴٯӵǺऍ୯ޑуԀԋ൩ෳᡍȐCalifornia Achievement Tests, CATȑǵང༫๮୷ҁמૈෳᡍȐIowa Test of Basic Skillsȑ฻ǴջճҔࠟޔ ฻ϯ຾Չෳᡍϩኧ໔ϐೱ่Ƕ

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ӢԜǴҁࣴز໻௖૸Нѳ฻ϯϐԋਏǶ

ಃѤ࿯ʳ ෳᡍ฻ϯ೛ी

ෳᡍ฻ϯ೛ीࢂࡰԏ໣ၗ਑ޑБݤǴा຾Չෳᡍ฻ϯǴѸ໪٩ᏵځҞޑᒧ᏷ ΋ঁ಄ӝޑ฻ϯ೛ीǶ฻ϯ೛ीᒧ᏷ޑӳᚯ཮ቹៜ฻ϯᇤৡǴࡺӧᒧ᏷฻ϯ೛ी ਔѸ໪ߚதޑλЈᙣ཈ǶதҔޑෳᡍ฻ϯ೛ीࣁǺൂಔ೛ीȐsingle group designȑǵ ฻ဂಔ೛ीȐequivalent group designȑǵѳᑽόֹӄ୔༧೛ीǵۓᗕό฻ಔ೛ी฻ ȐЦᝊ❲Ǵ1995ǹKolen & Brennan, 1995ȑǶаΠϟಏҁࣴز܌௦Ҕޑѳᑽόֹӄ ୔༧೛ीᆶۓᗕό฻ಔ೛ीǺ ΋ǵѳᑽόֹӄ୔༧೛ी BIB฻ϯ೛ीࢂҗYatesȐ1936ȑගрǴԜ೛ीࢂஒᚒ৤ύޑ၂ᚒ֡ϩԋऩυ ঁ၂ᚒ୔༧Ǵ୔༧໔ᆶ୔༧ϣޑ၂ᚒࣣόख़ፄǴ٠ճҔ೭٤၂ᚒ୔༧ጓᇙԋऩυ ঁᚒҁǶӢԜǴڙ၂ޣѝሡௗڙऩυ၂ᚒ୔༧ޑ၂ᚒǴЪόӕڙ၂ޣёૈௗڙ೽ ϩ࣬ӕǵֹӄ࣬ӕǵ܈ֹӄόӕޑ၂ᚒ୔༧ǶԜ೛ीӧคբเϸᔈਔ໔Ȑresponse timeȑޑज़ڋ௃׎ΠǴѸ໪ᅈىΠӈޑज़ڋԄǺ

¦

t i is k s S x 1 , .... , 1 , Ȑ2-8ȑ

¦

S d s is r i t x 1 , .... , 1 , Ȑ2-9ȑ

¦

S t s ijs i j t z 1 , .... , 1 , O Ȑ2-10ȑ S s , t j i z x xis js t2 ijs, 1,...., 1,...., Ȑ2-11ȑ ځύǴ t Ǻ၂ᚒ୔༧ኧ s ǺᚒҁжဦǴs 1,....,S k Ǻ؂ঁᚒҁଛ࿼ޑ၂ᚒ୔༧ኧ

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r Ǻ၂ᚒ୔༧ӧ܌Ԗᚒҁύр౜ޑԛኧ i Ǻᚒ৤ύঁձ୔༧жဦǴi 1,....,t j Ǻᚒ৤ύԋჹ୔༧ύಃΒঁ୔༧жဦǴ j 1,....,t OǺԋჹ၂ᚒ୔༧ӧ܌Ԗᚒҁύр౜ޑԛኧ is x Ǻ၂ᚒ୔༧ᆶᚒҁޑଛ࿼ಔࠠǴځύxis

^

0,1

`

, i 1,...,t, s 1,....,S ijs z Ǻ ԋ ჹ ၂ ᚒ ୔ ༧ ᆶ ᚒ ҁ ޑ ଛ ࿼ ಔ ࠠ Ǵ ځ ύ zijs

^

0,1

`

, i 1,...,t , S s 1,...., ϦԄȐ2-8ȑж߄؂΋ঁᚒҁଛ࿼ޑ၂ᚒ୔༧ኧҞǹϦԄȐ2-9ȑж߄؂΋ঁ ၂ᚒ୔༧ӧ܌Ԗᚒҁύр౜ޑԛኧǹϦԄȐ2-10ȑж߄ԋჹ၂ᚒ୔༧ӧ܌Ԗᚒҁ ύр౜ޑԛኧǹϦԄȐ2-11ȑж߄ԋჹ၂ᚒ୔༧ᆶಔࠠޑ΋ठ܄ǶBIB ฻ϯ೛ी ໪಄ӝϦԄȐ2-8ȑԿȐ2-11ȑޑा؃Ǵа؃р಄ӝޑന٫ှǶ ฅԶǴӧ୔ϩ၂ᚒ୔༧ޑၸำѸ໪Եໆڙ၂ޣԖى୼ޑਔ໔ૈ୼ֹԋ܌Ԗޑ ᚒҞǴЪ၂ᚒ୔༧ኧΨा٣ӃዴۓǶനࡕ௦Ҕᖥ௽Ԅޑ௨ӈБԄஒ၂ᚒ୔༧ᆶᚒ ҁ଺ଛ࿼Ǵ٬؂΋ঁ၂ᚒ୔༧ޑࡼෳԛኧ࣬฻ȐNemhauser & Wolsey, 1999; van der Linden, Veldkamp, & Carlson, 2004ȑǶӢԜǴBIB฻ϯ೛ीԖΠӈΟ໨୷ҁज़ڋǺ

1. ؂΋ঁᚒҁϣޑ၂ᚒ୔༧ኧा࣬ӕ

2. ࿶җ၂ᚒ୔༧ޑ่ӝǴҗ΢ॊϦԄ؃рനλᚒҁኧ

3. ؂΋ঁ၂ᚒ୔༧ӧ܌Ԗᚒҁύр౜ޑԛኧा࣬ӕ

ќѦǴਥᏵNAEP 1998ԃޑמೌ܄ൔ֋ύࡰрǴ؂΋၂ᚒӧ຾ՉࡼෳਔǴε ऊሡा500ঁෳ၂ኬҁȐAllen, Donoghue, & Schoeps, 2001ȑǶ

Βǵۓᗕό฻ಔ೛ी

NEAT฻ϯ೛ीࢂஒటೱ่ޑෳᡍ๏ϒٿಔόӕڙ၂ኬҁP1کQ1຾Չࡼ ෳǴځύǴP1کQ1ϩձவٿಔڙ၂҆ဂᡏPکQύᒿᐒܜڗԶளǴЪٿಔڙ၂ኬ

(32)

ҁࡼෳޑਔ໔όӕǶٿಔڙ၂ኬҁࣣ໪ќѦௗڙ΋ҽۓᗕෳᡍAǴࣁΑᗉխڙ၂ ޣڙډࡼෳ໩ׇӢનޑቹៜǴࡺۓᗕෳᡍӧٿڙ၂ኬҁޑෳᡍ໩ׇࢂ΋ኬޑǴЪ ෳᡍᜤࡋکϣ৒Ѹ໪ᆶXǵYෳᡍཱུࣁ࣬՟Ǵځෳᡍߏࡋ࣬྽ܭ΋ঁϩෳᡍǶNEAT ฻ϯ೛ीӵ߄2-1ȐKolen etal.,1995ǹէ҇ჱǴ1993ȑǶ ߄2-1 NEAT฻ϯ೛ी ڙ၂ޣဂᡏ Xෳᡍ Yෳᡍ Aෳᡍ P1 V V Q1 V V ຏǺVࣁڙ၂ޣѸ໪ڙෳϐෳᡍ NEAT฻ϯ೛ीࣁၨதҔǵΨၨёՉޑෳᡍ฻ϯ೛ीǴѬѝሡଷ೛ڙ၂ኬҁ ࢂᒿᐒܜڗޑǴόѸଷ೛όӕڙ၂ኬҁԖ࣬ӕޑૈΚॶǶӧNEAT฻ϯ೛ीǴ؂ ঁᚒҁѸ໪ࡼෳ࣬ӕޑۓᗕ၂ᚒǴӢԜǴۓᗕ၂ᚒᒧڗޑӳᚯஒ཮ቹៜೱ่ਏ ݀Ǵऩۓᗕ၂ᚒᒧ᏷࡞྽Ǵ߾ёаᗉխڙډግಞǵੲമቹៜǶԜѦǴNEAT฻ϯ ೛ीޑۓᗕ၂ᚒϣ৒ाᅰёૈ࣬՟Ъ၂ᚒᜤࡋा࣬ӕǴӢࣁۓᗕ၂ᚒࢂҔٰፓ᏾ ٿঁόӕૈΚϐဂᡏ܌೷ԋޑό฻ȐPetersen, Kolen, & Hoover,1993ǹЦཫറǴ 2006ȑǶ

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ಃΟകʳ ࣴز೛ीᆶБݤ

ҁകϩࣁϤঁ೽ҽǴ२ӃϟಏࣴزࢬำǴځԛϟಏҁࣴزϐᡂ໨೛ीǵჴᡍ ೛ीǵኳᔕჴᡍ؁ᡯϷຑ՗БݤǴനࡕϟಏࣴزπڀǶ

ಃ΋࿯ʳ ࣴزࢬำ

ҁࣴزਥᏵᚒಔϸᔈ౛ፕύΟୖኧᚒಔኳԄࣁ୷ᘵٰϩ݋ᚒಔԄෳᡍၗ ਑Ǵట೸ၸኳᔕࣴزޑБԄ௖૸ӧόӕ฻ϯෳᡍ௃ნϐ฻ϯਏ݀Ƕࣴزࢬำӵ კ3-1܌ҢǶ კ3-1 ࣴزࢬำკ Ў᝘ᇆ໣ᆶ௖૸! ኗቪࣴزൔ֋! ೛ۓࣴزЬᚒ! BIBᚒҁ! ೱ่೛ी! ٬Ҕ SCORIGHT 3.0 ೬ᡏ຾Չୖኧ՗ी ࣴزᡂ໨೛ۓ! NEATᚒҁ! ೱ่೛ीʳ Кၨόӕᡂ໨ϐୖ ኧ՗ीᆒྗࡋ

(34)

२Ӄࢂ೛ۓࣴزЬᚒǴௗ๱຾ՉᆶࣴزЬᚒϐ࣬ᜢЎ᝘ᇆ໣ᆶ௖૸Ǵ຾Զ೛ ۓࣴز௃ნϷෳᡍᚒҁϐ฻ϯ೛ीǴ٠٩Ᏽ܌೛ۓϐόӕࣴز௃ნౢғኳᔕၗ਑ ࡕǴаSCORIGHT 3.0೬ᡏ຾Չୖኧ՗ीǴ؃рόӕᡂ໨ϐ՗ीᆒྗࡋ٠ኗቪࣴ ز่݀Ƕ җܭ SCORIGHT 3.0 ೬ᡏёჹෳᡍၗ਑຾Չӕਔ՗ीǴӢԜǴҁࣴز௦Ҕӕ ਔ՗ीݤ຾Չෳᡍ฻ϯǹӆޣǴڙज़ܭᚒಔϸᔈኳԄज़ڋڙ၂ޣૈΚୖኧܺவ኱ ྗதᄊϩթޑᜢ߯Ǵࡺҁࣴز໻௖૸ᚒಔԄෳᡍ௦Ҕ BIB ฻ϯ೛ीᆶ NEAT ฻ϯ ೛ी຾ՉНѳ฻ϯϐԋਏǶ

ಃΒ࿯ʳ ኳᔕჴᡍϐᡂ໨೛ी

൘ǵࣴزᡂ໨೛ۓ

ҁࣴزኳᔕᚒಔԄෳᡍၗ਑Ǵ௖૸ BIB ک NEAT ٿᅿ฻ϯ೛ी຾ՉНѳ฻ϯ Πϐෳᡍ฻ϯਏ݀Ƕ૟ஒҁࣴزޑӅӕᡂ໨೛ۓ᏾౛ӵ߄ 3-1Ƕ ߄ 3-1 ኳᔕၗ਑ᡂ໨೛ۓ ࣴزᡂ໨ ᡂ໨೛ۓ ฻ϯ೛ी NEATǵBIB ڙ၂Γኧ 3570Γǵ5460Γǵ7560Γ ෳᡍߏࡋ ؂ঁᚒҁࡼෳᚒኧࣁ 60 ᚒ Ӛᚒҁଛ࿼ޑ၂ᚒ୔༧ኧ 3ঁ ᚒಔኧȐᚒಔߏࡋȑ 12ঁᚒಔȐ5ᚒȑǵ6ঁᚒಔȐ10ᚒȑ ᚒಔਏ݀ᡂ౦ኧ 0ǵ0.25ǵ0.5ǵ1ǵmixȐషӝȑ ۓᗕᚒКٯ 1/3ǵ1/6 ኳᔕԛኧ 50 ԛ

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΋ǵڙ၂Γኧ

ਥᏵ NAEP 1998 ԃޑמೌ܄ൔ֋ύࡰрǴ؂΋၂ᚒӧ຾ՉࡼෳਔǴεऊሡ ा 500 ঁෳ၂ኬҁȐAllen, Donoghue, & Schoeps, 2001ȑǴӢԜǴҁࣴزΓኧ೛ ۓаԜࣁ୷ྗǴࣁΑଛӝӚᅿ฻ϯ೛ीᚒҁኧޑόӕǴ೛ۓࣁ 3570 Γǵ5460 Γǵ 7560ΓΟᅿ௃׎Ƕ Βǵᚒಔኧ ҁࣴز೛ۓ؂ҽෳᡍࣁ 60 ᚒǴ؂ঁᚒҁх֖ 3 ঁ၂ᚒ୔༧Ƕӧڰۓෳᡍߏ ࡋޑ௃ݩΠǴϩࣁ؂ҽෳᡍԖ 12 ঁᚒಔ܈ 6 ঁᚒಔǴҭջ؂ঁᚒಔϣԖ 5 ᚒ܈ 10ᚒ၂ᚒǶ Οǵᚒಔਏ݀ᡂ౦ኧ ҁࣴزట௖૸όӕ၂ᚒ٩ᒘำࡋჹڙ၂ޣૈΚୖኧ՗ीϐቹៜǴЪਥᏵၸѐ ޑࣴزᡉҢǴӧ੿ჴෳᡍύ؂ঁᚒಔޑ၂ᚒ٩ᒘำࡋёૈ཮ό࣬ӕǴӢԜǴҁࣴ زᏹ׋ᚒಔਏ݀ޑᡂ౦ኧࣁ 0ǵ0.25ǵ0.5ǵ1ǵmixȐషӝȑ೭ϖᅿ௃׎Ƕ߻Ѥᅿ ௃׎ࢂࡰ᏾ҽෳᡍϣ؂ঁᚒಔޑᚒಔਏ݀ᡂ౦ኧࣣ࣬ӕǹќѦǴషӝᚒಔਏ݀ࢂ ࡰऩ΋ҽෳᡍԖ 12 ঁᚒಔǴ߾ಃ 1ǵ5ǵ9 ঁᚒಔޑᚒಔਏ݀ᡂ౦ኧࣁ 0Ǵಃ 2ǵ 6ǵ10 ঁᚒಔޑᚒಔਏ݀ᡂ౦ኧࣁ 0.25Ǵ٩Ԝᜪ௢Ƕ ѤǵۓᗕᚒКٯ ҁࣴزӧڰۓෳᡍߏࡋࣁ 60 ᚒޑ௃ݩΠǴ௖૸όӕۓᗕᚒКٯჹୖኧ՗ी ϐቹៜǴᏹ׋ޑۓᗕᚒКٯࣁ 1/3 ܈ 1/6 ٿᅿǴҭջۓᗕᚒኧࣁ 20 ᚒ܈ 10 ᚒǶ ฅԶǴBIB ฻ϯ೛ीϐ؂΋၂ᚒ୔༧ύޑ၂ᚒኧѸ໪ा࣬฻Ǵࡺҁࣴز໻ଞჹ NEAT฻ϯ೛ी௖૸όӕۓᗕᚒКٯჹୖኧ՗ीϐቹៜǶ ԜѦǴӧ΢ॊӚᅿόӕᡂ໨ΠǴ֡ኳᔕౢғ50฽ၗ਑Ǵ՗ीڙ၂ޣૈΚୖኧ ک၂ᚒୖኧ٠ीᆉӚୖኧϐਥ֡БৡȐroot mean square error, RMSEȑǴа؃ࣴز ่݀ޑᆒዴᆶᛙۓǶ

(36)

ມǵୖኧ೛ۓ

ᜢܭҁࣴز၂ᚒୖኧϷڙ၂ޣૈΚୖኧϐ೛ۓǴ૟ϩॊӵΠǶ ΋ǵ၂ᚒୖኧϩթ೛ۓ 1. ᠘ձࡋୖኧǺਥᏵMislevyȐ1986ȑࣴزࡰр᠘ձࡋୖኧ߈՟ܭlognormalϩթǴ ࡺҁࣴز᠘ձࡋୖኧኳԄ௦Ҕlognormal(1.13,0.6)Ǵஒጄൎࣚۓ ܭ0.5ɴ1.5Ƕ 2. ᜤࡋୖኧǺb~N(0,1)Ǵஒጄൎࣚۓܭ-3ɴ3Ƕ

3. ౒ෳࡋୖኧǺਥᏵ Swaminathan & GiffordȐ1986ȑࣴزࡌ᝼౒ෳࡋୖኧኳԄ௦ Ҕ beta ӃᡍϩթǴࡺҁࣴز౒ෳࡋୖኧ௦Ҕbeta(4,16)Ǵஒጄൎ ࣚۓܭ 0ɴ0.25Ƕ ΒǵૈΚୖኧϩթ೛ۓ ڙ၂ޣૈΚϩթࣁ኱ྗதᄊϩթǴT ~ N(0,1)Ǵஒጄൎࣚۓܭ-3ɴ3Ƕڙ၂ᕴ ΓኧԖ3570Γǵ5460Γǵ7560ΓΟᅿ௃ݩǶ२Ӄኳᔕ7560ΓޑૈΚୖኧǴӆவύ ܜڗ5460ঁբࣁ5460ΓޑૈΚୖኧǴ3570ΓޑૈΚୖኧҭࢂவ5460ΓޑૈΚୖኧ ύܜڗԶٰޑǶ

ಃΟ࿯ʳ ෳᡍ฻ϯ೛ी

ҁࣴز܌௦Ҕෳᡍ฻ϯ೛ीࣁ BIB ᆶ NEAT ٿᅿǴ૟ଞჹ೭ٿᅿ฻ϯ೛ी၁ ॊӵΠǶ

൘ǵBIB ฻ϯ೛ी

ਥᏵҁࣴز೛ۓ؂ঁᚒҁᕴᚒኧࣁ60ᚒǴ3ঁ၂ᚒ୔༧Ǵ΋ঁ၂ᚒ୔༧ϣԖ 20ᚒ၂ᚒǴ૟ஒBIB฻ϯ೛ी໪಄ӝϐచҹ᏾౛ӵΠȐKuehl, 2000ȑǺ t r k bu u Ȑ3-1ȑ

(37)

) 1 ( ) 1 ( u u k t r O , where Orb Ȑ3-2ȑ ځύǴ b Ǻᚒҁኧǹ k Ǻ؂ঁᚒҁଛ࿼ޑ၂ᚒ୔༧ኧǹ t Ǻ၂ᚒ୔༧ኧǹ r Ǻ၂ᚒ୔༧ӧᚒҁύр౜ޑԛኧǹ OǺԋჹ၂ᚒ୔༧р౜ӧ࣬ӕ୔༧Տ࿼ޑԛኧ ҁࣴزҗ΢ॊޑϦԄפр಄ӝޑ BIB ฻ϯ೛ीǴӧԜ೛ीύǴӅԖ 7 ঁᚒҁ Ȑ b ɨ7ȑǵ7 ঁ၂ᚒ୔༧Ȑt ɨ7ȑǴ؂ঁᚒҁх֖ 3 ঁ၂ᚒ୔༧Ȑ k ɨ3ȑǴЪ ؂΋၂ᚒ୔༧ӧ܌Ԗᚒҁύр౜ޑԛኧࣁ 3 ԛȐ r ɨ3ȑǵԋჹ၂ᚒ୔༧ӧᚒҁύ р౜ޑԛኧѝԖ 1 ԛȐOɨ1ȑǶҗԜёޕǴ؂ঁᚒҁύ၂ᚒ୔༧ޑಔӝόख़ፄǴ ٯӵǺᚒҁ S1 ޑ၂ᚒ୔༧ଛ࿼ࣁ M1ǵM2ǵM4Ǵ߾ S2 Կ S7 ᚒҁύό཮ӆр౜ ၂ᚒ୔༧ M1ǵM2ǵM4 ޑಔӝǹ၂ᚒ୔༧ӧ܌Ԗᚒҁଛ࿼ύ཮ख़ፄр౜ 3 ԛǴ ٯӵǺ၂ᚒ୔༧ M1 р౜ӧᚒҁ S1ǵS5ǵS7 ύǴ٩Ԝᜪ௢Ǵ၁ـ߄ 3-2Ȑමҏฑǵ Цཫറǵ೾դԽǵ೚ϺᆢǴ2006ȑǶ ߄ 3-2 BIB ฻ϯ೛ीᚒҁଛ࿼߄ ᚒҁׇဦ ୔༧Ȑk1ȑ ୔༧Ȑk2ȑ ୔༧Ȑk3ȑ S1 M1 M2 M4 S2 M2 M3 M5 S3 M3 M4 M6 S4 M4 M5 M7 S5 M5 M6 M1 S6 M6 M7 M2 S7 M7 M1 M3 ҁࣴزኳᔕ؂ঁᚒҁ၂ᚒኧࣁ60ᚒǴ၂ᚒ୔༧ኧ3ঁǴࡺ؂ঁ၂ᚒ୔༧ϐ၂ ᚒኧࣁ20ᚒǶӢԜǴҁ೛ीԖ7ঁ၂ᚒ୔༧Ǵᕴ၂ᚒኧࣁ140ᚒǶ૟ஒҁࣴزۓᗕ

(38)

၂ᚒኧᆶᕴ၂ᚒኧ᏾౛ԋ߄3-3Ǻ ߄ 3-3 ۓᗕ၂ᚒኧᆶᕴ၂ᚒኧჹྣ߄ ฻ϯ ೛ी ୔༧ኧ ؂ঁᚒҁ ᕴᚒኧ ؂ঁᚒҁ ၂ᚒ୔༧ ኧ ؂ঁᚒҁ ۓᗕ၂ᚒ Кٯ ؂ঁᚒҁ ۓᗕ၂ᚒ ኧ ᚒ৤ᕴ၂ ᚒኧ BIB 7 60 3 1/3 20 140 ਥᏵҁࣴزϐࣴزᡂ໨Ǵஒڙ၂ᕴΓኧ೛ۓࣁ 3570 Γǵ5460 Γǵ7560 ΓΟ ᅿ௃׎Ǵ၁ӵ߄ 3-4Ƕ ߄3-4 BIB฻ϯ೛ीΓኧჹྣ߄ ฻ϯ೛ी ᕴڙ၂Γኧ ؂ঁᚒҁ ڙ၂Γኧ ؂ঁ၂ᚒ ڙ၂Γኧ 3570 510 1530 5460 780 2340 BIB 7560 1080 3240

ມǵNEAT ฻ϯ೛ी

NEAT฻ϯ೛ीࣁ΋૓ෳᡍ฻ϯதҔޑ೛ीǴҁࣴزࣁΑКၨNEAT฻ϯ೛ी ᆶBIB฻ϯ೛ीϐ฻ϯਏ݀ǴӢԜǴҗ΢ॊޑBIB฻ϯ೛ी௨ӈрҁࣴزϐNEAT1 ฻ϯ೛ीǶԜ೛ीӅԖ3ঁᚒҁǴ7ঁ၂ᚒ୔༧Ǵ؂ঁᚒҁх֖3ঁ၂ᚒ୔༧ǴЪ ஒಃ΋ঁ၂ᚒ୔༧೛ۓࣁۓᗕ၂ᚒǴځᚒҁଛ࿼ӵ߄3-5Ƕ ߄3-5 NEAT฻ϯ೛ीᚒҁଛ࿼߄ ᚒҁׇဦ ୔༧Ȑk1ȑ ୔༧Ȑk2ȑ ୔༧Ȑk3ȑ S1 M1 M2 M3 S2 M1 M4 M5 S3 M1 M6 M7

(39)

ќѦǴࣁΑКၨۓᗕᚒКٯჹୖኧ՗ीޑቹៜǴӢԜ೛ीΑNEAT2฻ϯ೛ ीǹԜ೛ीᆶ΢ॊޑNEAT1฻ϯ೛ी࣬ӕǴ؂ঁᚒҁᕴᚒኧࣁ60ᚒǴӅԖ3ঁᚒ ҁǴ7ঁ၂ᚒ୔༧Ǵ؂ঁᚒҁх֖3ঁ၂ᚒ୔༧ǴЪಃ΋ঁ၂ᚒ୔༧ࣁۓᗕ၂ᚒǴ ՠᆶNEAT1฻ϯ೛ीόӕϐೀࣁNEAT2฻ϯ೛ीϐಃ΋ঁ၂ᚒ୔༧ϣ၂ᚒኧ೛ ۓࣁ10ᚒǴԶಃΒǵΟঁ၂ᚒ୔༧ϣ၂ᚒኧӚࣁ25ᚒǶ૟ஒҁࣴزۓᗕ၂ᚒኧᆶ ᕴ၂ᚒኧ᏾౛ԋ߄3-6Ǻ ߄3-6 NEAT฻ϯ೛ीӧόӕۓᗕКٯϐ࣬ᜢᚒኧჹྣ߄ ฻ϯ ೛ी ୔༧ኧ ؂ঁᚒҁ ᕴᚒኧ ؂ঁᚒҁ ၂ᚒ୔༧ ኧ ؂ঁᚒҁ ۓᗕ၂ᚒ Кٯ ؂ঁᚒҁ ۓᗕ၂ᚒ ኧ ᚒ৤ᕴ၂ ᚒኧ NEAT1 7 60 3 1/3 20 140 NEAT2 7 60 3 1/6 10 160 ਥᏵҁࣴزϐࣴزᡂ໨Ǵஒڙ၂ᕴΓኧ೛ۓࣁ 3570 Γǵ5460 Γǵ7560 ΓΟ ᅿ௃׎Ǵ၁ӵ߄ 3-7Ƕ ߄3-7 NEAT฻ϯ೛ीΓኧჹྣ߄ ฻ϯ೛ी ᕴڙ၂Γኧ ؂ঁᚒҁ ڙ၂Γኧ ۓᗕ၂ᚒ ڙ၂Γኧ ځᎩ၂ᚒ ڙ၂Γኧ 3570 1190 3570 1190 5460 1820 5460 1820 NEAT1 7560 2520 7560 2520 3570 1190 3570 1190 5460 1820 5460 1820 NEAT2 7560 2520 7560 2520

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ಃѤ࿯ʳ ኳᔕჴᡍ؁ᡯ

ҁࣴزࣁኳᔕჴᡍǴჴᡍޑำׇӵΠǺ ΋ǵࡌҥ၂ᚒᚒ৤Ǵ٠வᚒ৤ύࡷᒧ၂ᚒಔԋᚒҁǹ Βǵኳᔕڙ၂ޣૈΚϩթϷӚᚒಔϐᚒಔਏ݀Ǵڙ၂ޣૈΚϩթܺவ኱ྗதᄊϩ թǴӚᚒಔϐᚒಔਏ݀ܺவதᄊϩթǹ ΟǵճҔϦԄȐ2-2ȑжΕ؁ᡯ΋ޑ၂ᚒୖኧǵ؁ᡯΒޑڙ၂ޣૈΚୖኧϷᚒಔਏ ݀Ǵीᆉڙ၂ޣբเӚ၂ᚒޑเჹᐒ౗ॶP(T)ǹ ѤǵஒU(0,1)ᒿᐒౢғϐॶᆶ؁ᡯΟ܌ౢғϐڙ၂ޣբเӚᚒޑเჹᐒ౗ॶ ) P(T ଺КၨǴऩP(T)εܭҗU(0,1)ᒿᐒౢғϐॶǴ߾ຎࣁเჹǴϸϐ߾ຎ ࣁเᒱǴаԜБԄౢғڙ၂ޣբเϸᔈǹ ϖǵ٬Ҕ؁ᡯѤ܌ౢғϐڙ၂ޣբเϸᔈǴճҔ SCORIGHT 3.0 ೬ᡏ຾Չୖኧ՗ ीǹ ϤǵਥᏵа΢ޑჴᡍำׇǴख़ፄ຾Չ 50 ԛǴаКၨόӕᡂ໨೛ीޑ՗ीᆒྗࡋǶ

ಃϖ࿯ʳ ຑ՗Бݤ

ҁࣴزஒচۈౢғϐୖኧຎࣁ੿ॶǴӆа੿ॶౢғϐբเϸᔈ຾Չୖኧ՗ी ࡕளډ՗ीॶǴीᆉ੿ॶᆶ՗ीॶ໔ϐ RMSEǴ؃ኳᔕ 50 ԛޑѳ֡ॶբࣁୖኧ ՗ीᇤৡǴ٩Ԝٰຑᘐୖኧ՗ीϐਏ݀Ƕ ଞჹڙ၂ޣૈΚୖኧϷ၂ᚒୖኧȐ᠘ձࡋୖኧǵᜤࡋୖኧǵ౒ෳࡋୖኧȑϩ ձीᆉځ RMSEǶځीᆉϦԄӵΠǺ ΃ǵڙ၂ޣૈΚୖኧ N N i i i i i

¦

1 2 ) ˆ ( ) ˆ , ( RMSE T T T T Ȑ3-3ȑ

(41)

ځύǴ N Ǻڙ၂ޣΓኧ i T ǺಃiՏڙ၂ޣૈΚ੿ॶ i Tˆ ǺಃiՏڙ၂ޣૈΚ՗ीॶ Βǵ၂ᚒୖኧȐ᠘ձࡋୖኧǵᜤࡋୖኧǵ౒ෳࡋୖኧȑ n n j j j j j

¦

1 2 ) ˆ ( ) ˆ , ( RMSE [ [ [ [ Ȑ3-4ȑ ځύǴ n Ǻ၂ᚒኧ j [ Ǻಃ jᚒ၂ᚒୖኧ੿ॶ j [ˆ Ǻಃ jᚒ၂ᚒୖኧ՗ीॶ

ಃϤ࿯ʳ ࣴزπڀ

ҁࣴز٬ҔޑπڀԖMATLAB೬ᡏǵSCORIGHT 3.0೬ᡏϷSPSS 12.0ύЎຎ ืހ೬ᡏǴ૟ϩॊӵΠǶ

൘ǵMATLAB೬ᡏ

MATLAB ࢂ΋ঁଯਏ౗ޑኧॶीᆉȐnumerical computationȑکёຎϯ Ȑvisulationȑ঺း೬ᡏǴᇟݤᙁൂЪගٮϣࡌޑڄኧ৤ǴѬૈ୼٬Ҕᙁൂޑࡰз ຾Չኧॶीᆉǵኳᔕǵᛤკ฻ǶӢԜǴҁࣴزճҔԜ೬ᡏኳᔕ၂ᚒୖኧᆶڙ၂ޣ ૈΚୖኧϐ੿ॶаϷڙ၂ޣբเϸᔈǴ٠຾Չၗ਑ᔞਢᙯඤᆶीᆉୖኧ՗ीᇤ ৡǶ

(42)

ມǵSCORIGHT 3.0೬ᡏ

SCORIGHT 3.0೬ᡏࢂ΋ঁխ຤ޑႝတำԄǴ፾ҔܭΒϡीϩǵӭᗺीϩޑ ၂ᚒᜪࠠᆶషӝᚒࠠȐх֖Βϡीϩ၂ᚒϷӭᗺीϩ၂ᚒȑǶԶෳᡍၗ਑ύޑ၂ ᚒёаӄ೽ࣁ࣬ϕᐱҥޑǴΨёаӄ೽ࣁᚒಔǴ܈ޣࢂٿޣషӝǶ ҁࣴزаᚒಔϸᔈ౛ፕύΟୖኧᚒಔኳԄࣁ୷ᘵǴ٬ҔSCORIGHT 3.0೬ᡏ ჹᚒಔԄෳᡍ຾Չୖኧ՗ीǶ

ୖǵSPSS 12.0ύЎຎืހ೬ᡏ

SPSSӄӜࣁStatistical Package for Social ScienceǴࢂ΋ᅿ಍ी঺း೬ᡏǴёז ೲӦ᠐ڗ٠ϩ݋εໆޑၗ਑ǶԜ೬ᡏڀԖᙦ൤Ъᝄᙣޑ಍ीБݤǴаϷ஑཰Ъᆒ ጏޑ಍ीკ߄Ǵගٮ٬Ҕޣӧ಍ीϩ݋ޑၸำύ࣬྽ֹ᏾ޑЍජǶ

ҁࣴز٬ҔSPSS 12.0ύЎຎืހ೬ᡏ຾ՉᐱҥኬҁTᔠۓǴஒ܌Ԗᡂ໨ϐ֡ Бਥᇤৡ຾ՉᐱҥኬҁTᔠۓǴҔаղձࢂցԖᡉ๱ৡ౦Ƕ

(43)

ಃѤകʳ ࣴز่݀

ҁࣴزаᚒಔϸᔈ౛ፕύΟୖኧᚒಔኳԄࣁ୷ᘵǴ٠аRMSEբࣁୖኧ՗ी ᇤৡǴ٩Ԝٰຑᘐӧόӕ฻ϯෳᡍ௃ნΠϩ݋ᚒಔԄෳᡍϐ฻ϯਏ݀ǶӢԜǴҁ കӅϩࣁΟ࿯Ǵಃ΋࿯ࣁBIB฻ϯ೛ीϐୖኧ՗ी่݀ǴಃΒ࿯ࣁNEAT฻ϯ೛ी ϐୖኧ՗ी่݀ǴಃΟ࿯ࣁBIBᆶNEAT฻ϯ೛ीϐୖኧ՗ी่݀КၨǶਥᏵኳᔕ ࣴزϐ่݀Ǵஒ՗ीᇤৡаკ߄և౜Ǵ၁ಒ่݀ஒӧߕᒵ΋ᆶߕᒵΒև౜Ƕ

ಃ΋࿯ʳ BIB฻ϯ೛ीϐୖኧ՗ी่݀

ଞჹ BIB ฻ϯ೛ीܭόӕኳᔕ௃ნ຾ՉКၨǴа௖૸ᚒಔԄෳᡍӧୖኧ՗ी ਔࢂց཮ڙډΓኧǵᚒಔኧǵᚒಔਏ݀ᡂ౦ኧޑόӕԶቹៜځୖኧ՗ीᆒྗࡋǶ

൘ǵόӕΓኧჹୖኧ՗ीϐቹៜ

ҁࣴزӧڙ၂ᕴΓኧޑ೽ϩǴϩࣁ 3570 Γǵ5460 Γǵ7560 ΓΟᅿ௃׎Ǵਥ Ᏽኳᔕࣴزϐ่݀Ǵځ՗ीᇤৡаკ߄և౜Ƕӧڰۓෳᡍߏࡋࣁ 60 ᚒǵۓᗕК ٯࣁ 1/3ǵᚒಔኧࣁ 12 ᆶ 6 ঁޑ௃ݩΠǴკ 4-1 Կკ 4-4 ϩձࣁόӕڙ၂Γኧჹ ܭ၂ᚒ᠘ձࡋǵᜤࡋǵ౒ෳࡋϷڙ၂ޣૈΚୖኧϐ՗ीᇤৡǶҗ߄ 4-1 аϷკ 4-1 Կკ 4-4 ёว౜Ǵ၂ᚒୖኧаϷᚒಔਏ݀ϐ՗ीᇤৡ཮ᒿ๱ڙ၂ΓኧቚуԶफ़ եǴа 3570 Γਔϐ՗ीᇤৡനεǴԶڙ၂ޣૈΚୖኧ՗ीᇤৡ߾ό཮ڙډڙ၂ ΓኧቹៜǶ

(44)

߄ 4-1 BIB ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}_T J 0.164 0.205 0.052 0.351 0.340 0 0.014 0.026 0.005 0.007 0.060 0.157 0.197 0.051 0.380 0.734 0.25 0.013 0.018 0.005 0.007 0.107 0.158 0.206 0.052 0.404 1.142 0.5 0.013 0.026 0.006 0.007 0.152 0.160 0.212 0.051 0.445 1.889 1 0.014 0.025 0.005 0.008 0.209 0.160 0.203 0.052 0.379 0.918 12 5 mix 0.012 0.024 0.005 0.007 0.122 0.159 0.197 0.051 0.349 0.280 0 0.016 0.020 0.005 0.007 0.037 0.152 0.199 0.052 0.397 0.807 0.25 0.013 0.025 0.006 0.006 0.096 0.147 0.196 0.049 0.437 1.316 0.5 0.014 0.020 0.004 0.007 0.136 0.152 0.201 0.048 0.498 2.156 1 0.011 0.016 0.004 0.006 0.174 0.154 0.197 0.050 0.396 1.011 3570 6 10 mix 0.014 0.021 0.005 0.006 0.098 0.122 0.182 0.048 0.348 0.286 0 0.010 0.015 0.003 0.006 0.046 0.129 0.177 0.048 0.378 0.689 0.25 0.010 0.015 0.003 0.007 0.085 0.133 0.181 0.048 0.405 1.094 0.5 0.009 0.015 0.003 0.007 0.126 0.135 0.187 0.047 0.449 1.817 1 0.008 0.015 0.003 0.007 0.164 0.125 0.182 0.048 0.379 0.861 5460 12 5 mix 0.011 0.024 0.005 0.006 0.093

(45)

߄ 4-1Ȑុȑ BIB ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}_T J 0.127 0.181 0.049 0.349 0.241 0 0.011 0.019 0.005 0.007 0.028 0.120 0.181 0.049 0.399 0.763 0.25 0.009 0.018 0.004 0.006 0.078 0.121 0.180 0.047 0.438 1.264 0.5 0.008 0.019 0.004 0.006 0.107 0.123 0.180 0.045 0.502 2.078 1 0.008 0.015 0.003 0.006 0.137 0.122 0.179 0.047 0.398 0.973 5460 6 10 mix 0.009 0.015 0.003 0.006 0.080 0.108 0.168 0.046 0.349 0.257 0 0.008 0.018 0.004 0.007 0.039 0.113 0.172 0.046 0.378 0.672 0.25 0.011 0.017 0.004 0.006 0.077 0.115 0.175 0.046 0.404 1.077 0.5 0.010 0.017 0.004 0.006 0.111 0.120 0.177 0.045 0.448 1.809 1 0.008 0.015 0.003 0.006 0.151 0.112 0.173 0.046 0.380 0.849 12 5 mix 0.008 0.021 0.004 0.006 0.084 0.109 0.166 0.046 0.346 0.216 0 0.008 0.017 0.004 0.010 0.006 0.108 0.166 0.045 0.398 0.754 0.25 0.009 0.017 0.004 0.006 0.068 0.110 0.169 0.045 0.439 1.261 0.5 0.008 0.015 0.003 0.006 0.095 0.112 0.170 0.043 0.502 2.036 1 0.010 0.013 0.003 0.006 0.231 0.111 0.167 0.045 0.396 0.939 7560 6 10 mix 0.009 0.015 0.003 0.012 0.128

(46)

კ4-1 BIB ฻ϯ೛ीΠǴόӕڙ၂Γኧჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ

კ4-2 BIB ฻ϯ೛ीΠǴόӕڙ၂Γኧჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ

(47)

კ4-4 BIB ฻ϯ೛ीΠǴόӕڙ၂ΓኧჹܭૈΚୖኧϐ՗ीᇤৡ

ມǵᚒಔኧȐᚒಔ၂ᚒኧȑ

ҁࣴزӧڰۓෳᡍߏࡋޑ௃ݩΠǴᏹ׋ᚒಔኧࣁ 12 ঁᚒಔ܈ 6 ঁᚒಔٿᅿ ௃׎ǴΨ൩ࢂ؂ঁᚒಔ၂ᚒኧࣁ 5 ᚒ܈ 10 ᚒٿᅿǴ௖૸όӕᚒಔኧჹୖኧ՗ी ϐቹៜǶਥᏵኳᔕࣴزϐ่݀Ǵځ՗ीᇤৡаკ߄և౜Ǵӧڰۓෳᡍߏࡋࣁ 60 ᚒǵۓᗕКٯࣁ 1/3ǵᕴڙ၂Γኧࣁ 3570 Γǵ5460 Γǵ7560 Γޑ௃ݩΠǴკ 4-5 Կკ 4-8 ϩձࣁόӕᚒಔኧܭ၂ᚒ᠘ձࡋǵᜤࡋǵ౒ෳࡋǵڙ၂ޣૈΚୖኧϐ՗ ीᇤৡǶҗ߄ 4-1 аϷკ 4-5 Կკ 4-8 ёޕǴ྽ෳᡍߏࡋόᡂǴЪӧόӕᚒಔਏ ݀ޑᡂ౦ำࡋΠǴᚒಔኧҗ 6 ঁᚒಔቚуࣁ 12 ঁᚒಔਔǴڙ၂ޣૈΚୖኧ՗ी ᇤৡ཮ᒿϐफ़եǴԶ၂ᚒୖኧ՗ीᇤৡ཮ᒿ๱ᚒಔኧޑቚуԶᡂεǴՠ၂ᚒ᠘ձ ࡋ ୖ ኧ ϐ ᇤ ৡ ᡂ ౦ ϟ ܭ 0.005~0.011 ϐ ໔ Ǵ ၂ ᚒ ᜤ ࡋ ୖ ኧ ϐ ᇤ ৡ ᡂ ౦ ϟ ܭ 0.002~0.011ϐ໔Ǵ၂ᚒ౒ෳࡋୖኧϐᇤৡᡂ౦ϟܭ 0.001~0.003 ϐ໔ǹќѦǴᚒ ಔਏ݀՗ीᇤৡҭ཮ᒿ๱ᚒಔኧቚуԶफ़եǴନΑӧᚒಔਏ݀ᡂ౦ኧࣁ 0 ਔǴځ ՗ीᇤৡӧ 6 ঁᚒಔਔၨλǶ࿶җ SPSS 12.0 ύЎຎืހ೬ᡏ຾Չᐱҥኬҁ T ᔠ ۓǴёޕᚒಔኧჹܭ၂ᚒୖኧ՗ीᇤৡ٠คᡉ๱ৡ౦Ƕ

(48)

კ4-5 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ

კ4-6 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ

(49)

კ4-8 BIB ฻ϯ೛ीΠǴόӕᚒಔኧჹܭૈΚୖኧϐ՗ीᇤৡ

ୖǵᚒಔਏ݀ᡂ౦ኧ

ҁࣴزӧᚒಔਏ݀ᡂ౦ኧޑ೽ϩǴᏹ׋ 0ǵ0.25ǵ0.5ǵ1ǵmixȐషӝȑϖᅿ ௃׎Ƕҗ߄ 4-1 аϷკ 4-1 Կკ 4-8 ёว౜Ǵᒿ๱ᚒಔਏ݀ᡂ౦ኧᡂεǴڙ၂ޣ ૈΚୖኧϷᚒಔਏ݀՗ीᇤৡ཮ᒿϐቚуǹԶӧషӝᚒಔਏ݀ᡂ౦ኧޑ೽ҽǴҗ ܭӧෳᡍᚒҁύޑᚒಔϩձԖόӕำࡋޑ၂ᚒ٩ᒘ௃׎Ǵ᏾ҽෳᡍޑѳ֡ᚒಔਏ ݀ᡂ౦ኧऊࣁ 0.44Ǵࡺڙ၂ޣૈΚୖኧϷᚒಔਏ݀՗ीᇤৡ཮ϟܭᚒಔਏ݀ᡂ౦ ኧࣁ 0 ᆶ 1 ϐ໔ǶฅԶǴᚒಔਏ݀ᡂ౦ኧჹܭ၂ᚒୖኧ՗ीᇤৡ٠ؒԖ΋ठޑ่ ݀Ƕ

(50)

ಃΒ࿯ʳ NEAT฻ϯ೛ीϐୖኧ՗ी่݀

ଞჹ NEAT ฻ϯ೛ीܭόӕኳᔕ௃ნ຾ՉКၨǴа௖૸ᚒಔԄෳᡍӧୖኧ՗ ीਔࢂց཮ڙډΓኧǵᚒಔኧǵᚒಔਏ݀ᡂ౦ኧޑόӕԶቹៜځୖኧ՗ीᆒྗ ࡋǶਥᏵߕᒵΒёޕǴӧόӕΓኧǵόӕᚒಔኧᆶόӕᚒಔਏ݀ᡂ౦ኧޑ௃ݩΠǴ ځ่݀ᆶ BIB ฻ϯ೛ी฻ϯࡕϐ՗ी่݀ࢂ΋ठޑǶ ӧόӕڙ၂Γኧޑ೽ҽǴ၂ᚒୖኧϷᚒಔਏ݀՗ीᇤৡ཮ᒿ๱ڙ၂Γኧቚу Զफ़եǹӧόӕᚒಔኧޑ೽ҽǴڙ၂ޣૈΚୖኧϷᚒಔਏ݀ϐ՗ीᇤৡ཮ᒿ๱ᚒ ಔኧቚуԶफ़եǹӧόӕᚒಔਏ݀ᡂ౦ኧޑ೽ϩǴڙ၂ޣૈΚୖኧϷᚒಔਏ݀ϐ ՗ीᇤৡ཮ᒿ๱ᚒಔਏ݀ᡂ౦ኧᡂεԶቚуǴԶӧషӝᚒಔਏ݀ᡂ౦ኧޑ೽ҽǴ җܭӧෳᡍᚒҁύޑᚒಔϩձԖόӕำࡋޑ၂ᚒ٩ᒘ௃׎Ǵ᏾ҽෳᡍޑѳ֡ᚒಔ ਏ݀ᡂ౦ኧऊࣁ 0.44Ǵࡺڙ၂ޣૈΚୖኧϷᚒಔਏ݀ϐ՗ीᇤৡ཮ϟܭᚒಔਏ݀ ᡂ౦ኧࣁ 0 ᆶ 1 ϐ໔Ƕ ӢԜǴҁ࿯໻ଞჹόӕۓᗕКٯܭ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀уаඔ ॊǶҁࣴزϩࣁۓᗕ၂ᚒ՞᏾ҽᚒҁޑ 1/3 ᆶ 1/6 ٿᅿ௃׎ǴਥᏵኳᔕࣴزϐ่ ݀Ǵځ՗ीᇤৡаკ߄և౜Ǵҗ߄ 4-2 аϷკ 4-9 Կკ 4-12 ёޕǴ྽ෳᡍߏࡋό ᡂǴЪӧόӕᚒಔਏ݀ޑᡂ౦ำࡋΠǴۓᗕКٯҗ 1/6 ቚуࣁ 1/3 ਔǴڙ၂ޣૈ ΚୖኧϷ၂ᚒୖኧ՗ीᇤৡ཮ᒿϐफ़եǴԶᚒಔਏ݀ϐ՗ीᇤৡ཮ᒿϐቚуǴନ Αӧᚒಔਏ݀ᡂ౦ኧࣁ 0 ਔǴځ՗ीᇤৡӧۓᗕКٯࣁ 1/3 ਔၨλǶฅԶǴ၂ᚒ ᠘ձࡋୖኧϐᇤৡᡂ౦ϟܭ 0.0004~0.008 ϐ໔Ǵ࿶җ SPSS 12.0 ύЎຎืހ೬ᡏ ຾Չᐱҥኬҁ T ᔠۓǴёޕόӕۓᗕКٯჹܭ၂ᚒ᠘ձࡋୖኧ՗ीᇤৡ٠คᡉ๱ ৡ౦Ƕ

(51)

߄ 4-2 NEAT ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ۓᗕ Кٯ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}T J 0.138 0.207 0.051 0.333 0.328 0 0.013 0.021 0.005 0.007 0.057 0.139 0.204 0.051 0.365 0.753 0.25 0.013 0.023 0.005 0.007 0.101 0.144 0.205 0.051 0.393 1.172 0.5 0.013 0.027 0.005 0.007 0.149 0.149 0.213 0.050 0.441 1.932 1 0.013 0.025 0.005 0.007 0.207 0.143 0.202 0.050 0.370 1.027 1/3 mix 0.011 0.021 0.004 0.007 0.125 0.145 0.231 0.056 0.352 0.331 0 0.014 0.036 0.008 0.008 0.060 0.145 0.220 0.054 0.380 0.710 0.25 0.013 0.021 0.006 0.008 0.101 0.146 0.218 0.053 0.407 1.088 0.5 0.011 0.018 0.005 0.006 0.149 0.150 0.226 0.052 0.451 1.790 1 0.008 0.019 0.005 0.008 0.212 0.145 0.226 0.054 0.383 0.988 3570 12 5 1/6 mix 0.011 0.024 0.006 0.007 0.140 0.137 0.203 0.051 0.332 0.275 0 0.012 0.023 0.005 0.007 0.038 0.135 0.199 0.050 0.387 0.836 0.25 0.010 0.019 0.004 0.007 0.093 0.135 0.206 0.050 0.431 1.369 0.5 0.010 0.029 0.007 0.007 0.126 0.135 0.207 0.048 0.497 2.210 1 0.009 0.020 0.004 0.007 0.182 0.135 0.202 0.050 0.378 1.017 3570 6 10 1/3 mix 0.010 0.021 0.005 0.006 0.098

(52)

߄ 4-2Ȑុȑ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ۓᗕ Кٯ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}T J 0.138 0.219 0.053 0.351 0.277 0 0.011 0.022 0.005 0.008 0.036 0.135 0.213 0.052 0.399 0.785 0.25 0.012 0.020 0.005 0.007 0.094 0.137 0.215 0.051 0.439 1.263 0.5 0.010 0.018 0.005 0.007 0.125 0.137 0.219 0.050 0.503 2.063 1 0.009 0.019 0.004 0.007 0.183 0.136 0.214 0.052 0.389 0.934 3570 6 10 1/6 mix 0.012 0.021 0.006 0.008 0.096 0.120 0.188 0.049 0.331 0.286 0 0.011 0.023 0.005 0.006 0.047 0.122 0.186 0.049 0.363 0.725 0.25 0.011 0.021 0.005 0.006 0.089 0.127 0.189 0.049 0.392 1.155 0.5 0.010 0.020 0.004 0.006 0.123 0.132 0.195 0.047 0.439 1.916 1 0.009 0.020 0.005 0.007 0.168 0.122 0.189 0.049 0.370 1.005 1/3 mix 0.010 0.023 0.005 0.006 0.104 0.123 0.203 0.052 0.350 0.285 0 0.010 0.026 0.007 0.007 0.048 0.124 0.204 0.051 0.367 0.569 0.25 0.010 0.016 0.005 0.017 0.147 0.128 0.202 0.051 0.407 1.065 0.5 0.011 0.022 0.005 0.007 0.125 0.135 0.213 0.050 0.450 1.776 1 0.011 0.018 0.004 0.006 0.173 0.126 0.203 0.051 0.383 0.961 5460 12 5 1/6 mix 0.011 0.020 0.005 0.007 0.118

(53)

߄ 4-2Ȑុȑ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ۓᗕ Кٯ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}T J 0.120 0.185 0.049 0.330 0.236 0 0.011 0.024 0.005 0.006 0.027 0.117 0.187 0.049 0.386 0.815 0.25 0.008 0.020 0.005 0.005 0.080 0.116 0.186 0.047 0.429 1.348 0.5 0.008 0.017 0.004 0.006 0.110 0.121 0.190 0.046 0.495 2.202 1 0.009 0.022 0.004 0.005 0.150 0.118 0.187 0.048 0.380 1.000 1/3 mix 0.010 0.021 0.004 0.006 0.079 0.122 0.199 0.052 0.349 0.228 0 0.010 0.023 0.007 0.006 0.030 0.119 0.197 0.051 0.398 0.764 0.25 0.007 0.023 0.005 0.007 0.078 0.122 0.195 0.049 0.439 1.249 0.5 0.008 0.016 0.004 0.005 0.108 0.121 0.199 0.048 0.502 2.060 1 0.008 0.016 0.004 0.006 0.151 0.119 0.197 0.050 0.391 0.918 5460 6 10 1/6 mix 0.007 0.018 0.004 0.007 0.080 0.106 0.177 0.047 0.329 0.253 0 0.009 0.017 0.004 0.006 0.040 0.109 0.178 0.047 0.363 0.695 0.25 0.008 0.014 0.003 0.007 0.017 0.115 0.182 0.047 0.392 1.145 0.5 0.009 0.027 0.006 0.005 0.113 0.120 0.184 0.046 0.438 1.913 1 0.007 0.017 0.003 0.005 0.153 0.111 0.178 0.047 0.369 0.983 7560 12 5 1/3 mix 0.010 0.024 0.005 0.006 0.024

(54)

߄ 4-2Ȑុȑ NEAT ฻ϯ೛ीϐୖኧ՗ी่݀ RMSE / STD Γኧ ᚒಔኧ ᚒಔ၂ ᚒኧ ۓᗕ Кٯ ᚒಔਏ݀ ᡂ౦ኧ _{a b c}_T _J 0.109 0.189 0.050 0.348 0.253 0 0.007 0.018 0.004 0.007 0.041 0.110 0.187 0.049 0.379 0.656 0.25 0.009 0.019 0.004 0.005 0.078 0.115 0.189 0.048 0.405 1.053 0.5 0.008 0.019 0.004 0.006 0.115 0.120 0.196 0.048 0.450 1.767 1 0.009 0.017 0.004 0.006 0.158 0.113 0.186 0.048 0.382 0.943 7560 12 5 1/6 mix 0.008 0.016 0.003 0.007 0.102 0.105 0.170 0.046 0.328 0.213 0 0.008 0.014 0.003 0.007 0.008 0.107 0.171 0.045 0.386 0.810 0.25 0.008 0.017 0.004 0.006 0.021 0.107 0.172 0.045 0.428 1.342 0.5 0.006 0.016 0.003 0.005 0.088 0.109 0.174 0.043 0.495 2.198 1 0.008 0.016 0.004 0.004 0.126 0.106 0.172 0.046 0.381 0.988 1/3 mix 0.009 0.018 0.003 0.007 0.023 0.107 0.184 0.049 0.348 0.214 0 0.007 0.017 0.004 0.006 0.026 0.109 0.179 0.048 0.397 0.676 0.25 0.009 0.015 0.004 0.006 0.059 0.110 0.186 0.048 0.438 1.248 0.5 0.008 0.015 0.004 0.006 0.099 0.110 0.184 0.045 0.502 2.050 1 0.006 0.014 0.003 0.006 0.130 0.107 0.185 0.048 0.390 0.905 7560 6 10 1/6 mix 0.008 0.021 0.005 0.007 0.075

(55)

კ4-9 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ

(56)

კ4-11 NEAT ฻ϯ೛ीΠǴόӕۓᗕКٯჹܭ၂ᚒ౒ෳࡋୖኧϐ՗ीᇤৡ

(57)

ಃΟ࿯ʳ BIBᆶNEAT฻ϯ೛ीϐୖኧ՗ी่݀Кၨ

ਥᏵኳᔕࣴزϐ่݀Ǵځ՗ीᇤৡаკ߄և౜Ƕҗ߄ 4-1ǵ߄ 4-2 аϷკ 4-13 Կ 4-16 ёޕǴӧڰۓෳᡍߏࡋࣁ 60 ᚒǴۓᗕКٯࣁ 1/3 ਔǴ၂ᚒ᠘ձࡋୖኧϷ ڙ၂ޣૈΚୖኧϐ՗ीᆒྗࡋࢂ NEAT ฻ϯ೛ीᓬܭ BIB ฻ϯ೛ीǴԶ၂ᚒᜤࡋ ୖኧǵ౒ෳࡋୖኧϷᚒಔਏ݀ϐ՗ीᆒྗࡋεठ΢ࢂ BIB ฻ϯ೛ीᓬܭ NEAT ฻ ϯ೛ीǴᚒಔਏ݀ϐ՗ीᆒྗࡋ໻ӧᚒಔਏ݀ᡂ౦ኧࣁ 0 ਔࣁ NEAT ฻ϯ೛ीᓬ ܭ BIB ฻ϯ೛ीǶฅԶǴ၂ᚒᜤࡋୖኧϐᇤৡᡂ౦ϟܭ 0.0005~0.009 ϐ໔Ǵ၂ᚒ ౒ෳࡋୖኧϐᇤৡᡂ౦ϟܭ 0.0001~0.002 ϐ໔Ǵ࿶җ SPSS 12.0 ύЎຎืހ೬ᡏ ຾Չᐱҥኬҁ T ᔠۓǴёޕόӕ฻ϯ೛ीჹܭ၂ᚒᜤࡋୖኧϷ၂ᚒ౒ෳࡋୖኧ՗ ीϐᇤৡ٠คᡉ๱ৡ౦Ƕ კ4-13 όӕ฻ϯ೛ीჹܭ၂ᚒ᠘ձࡋୖኧϐ՗ीᇤৡ

(58)

კ4-14 όӕ฻ϯ೛ीჹܭ၂ᚒᜤࡋୖኧϐ՗ीᇤৡ

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კ4-16 όӕ฻ϯ೛ीჹܭૈΚୖኧϐ՗ीᇤৡ ԜѦǴҁࣴزҭଞჹNEAT฻ϯ೛ीύۓᗕ၂ᚒᆶߚۓᗕ၂ᚒϐ՗ीਏ݀຾ Չ௖૸Ǵӵ߄4-4܌ҢǶځύǴࣴزᡂ໨аN_n_m_r߄ҢǴNж߄ᕴڙ၂ΓኧǴn ж߄ӚᚒҁෳᡍߏࡋǴmж߄Ӛᚒҁ܌х֖ϐᚒಔኧǴrж߄ᚒಔਏ݀ᡂ౦ኧǶ җ߄4-4ёޕǴ၂ᚒᜤࡋୖኧϷ၂ᚒ౒ෳࡋୖኧӧۓᗕᚒޑ೽ҽᇤৡၨλǴԶ ၂ ᚒ ᠘ ձ ࡋ ୖ ኧ ࣁ ߚ ۓ ᗕ ᚒ ޑ ೽ ҽ ᇤ ৡ ၨ λ Ǵ ନ Α ӧ 5460_60_6_mix ǵ 7560_60_6_0.5ǵ7560_60_6_1аϷ7560_60_6_mix೭Ѥᅿࣴزᡂ໨Πࣁۓᗕᚒޑ೽ ϩᇤৡၨλǴՠৡ౦όεǶ࿶җSPSS 12.0ύЎຎืހ೬ᡏ຾ՉᐱҥኬҁTᔠۓࡕǴ ว౜၂ᚒ᠘ձࡋୖኧϷ၂ᚒ౒ෳࡋୖኧӧۓᗕᚒᆶߚۓᗕᚒϐᇤৡ٠คᡉ๱ৡ ౦ǹΨ൩ࢂᇥǴ၂ᚒᜤࡋୖኧӧNEAT฻ϯ೛ीύۓᗕᚒޑ೽ϩ՗ीޑၨࣁᆒྗǴ Զ၂ᚒ᠘ձࡋୖኧϷ၂ᚒ౒ෳࡋୖኧӧۓᗕᚒᆶߚۓᗕᚒϐᇤৡ߾ؒԖܴᡉৡ ౦ǶќѦǴ၂ᚒ᠘ձࡋୖኧǵ၂ᚒᜤࡋୖኧϷ၂ᚒ౒ෳࡋୖኧӧۓᗕᚒᆶߚۓᗕ ᚒϐ՗ीᇤৡࣣ཮ᒿ๱ڙ၂ΓኧቚуԶᡂλǶ

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߄ 4-3 NEAT ฻ϯ೛ीܭۓᗕᚒᆶߚۓᗕᚒϐ၂ᚒୖኧ՗ी่݀ RMSE / STD ࣴزᡂ໨ a b c 0.162ʳ 0.121ʳ 0.043ʳ ۓᗕᚒ! 0.028ʳ 0.025ʳ 0.008ʳ 0.131ʳ 0.217ʳ 0.053ʳ ߚۓᗕᚒ! 0.014ʳ 0.023ʳ 0.005ʳ 0.138 0.207 0.051 3570_60_12_0 ѳ֡! 0.013 0.021 0.005 0.161ʳ 0.113ʳ 0.043ʳ ۓᗕᚒ! 0.029ʳ 0.022ʳ 0.008ʳ 0.135ʳ 0.216ʳ 0.052ʳ ߚۓᗕᚒ! 0.013ʳ 0.026ʳ 0.006ʳ 0.139 0.204 0.051 3570_60_12_0.25 ѳ֡! 0.013 0.023 0.005 0.165ʳ 0.116ʳ 0.042ʳ ۓᗕᚒ! 0.032ʳ 0.023ʳ 0.009ʳ 0.139ʳ 0.216ʳ 0.052ʳ ߚۓᗕᚒ! 0.014ʳ 0.029ʳ 0.006ʳ 0.144 0.205 0.051 3570_60_12_0.5 ѳ֡! 0.013 0.027 0.005 0.165ʳ 0.118ʳ 0.040ʳ ۓᗕᚒ! 0.026ʳ 0.022ʳ 0.006ʳ 0.146ʳ 0.224ʳ 0.051ʳ ߚۓᗕᚒ! 0.016ʳ 0.028ʳ 0.006ʳ 0.149 0.213 0.050 3570_60_12_1 ѳ֡! 0.013 0.025 0.005 0.164ʳ 0.116ʳ 0.045ʳ ۓᗕᚒ! 0.036ʳ 0.024ʳ 0.009ʳ 0.138ʳ 0.213ʳ 0.051ʳ ߚۓᗕᚒ! 0.012ʳ 0.023ʳ 0.004ʳ 0.143 0.202 0.050 3570_60_12_mix ѳ֡! 0.011 0.021 0.004