ҰൠԽઢܗࠞ߹ޮՌϞσϧ ೖ໳ͷೖ໳ 2014. 12. 6. Nagoya.R #12 ໊ݹ԰େֶେֶӃࠃࡍ։ൃݚڀՊɹD1ɹాଜ༞

಺༰ʹೖΔલʹ • ۙ೥ͷSLAݚڀ͸ྔతݚڀʹภΓ͕ͪ ʢMizumoto, Urano, & Maeda, 2014ʣ • ಛʹ෼ࢄ෼ੳʢANOVA)ͱt ݕఆ͕ଟ͍ʢ૲ಽɼ ਫຊˍ஛಺, 2014ʣ • ฏۉ஋ʹجͮ͘ύϥϝτϦοΫݕఆʹཔΓ͕ͪ ʢPlonsky, 2011; Plonsky & Gass, 2011)

σʔληοτͱRͷεΫϦϓτ ΛआΓΔ࿦จ Cunnings, I. (2012). An overview of mixed-effects statistical models for second language researchers. Second Language Research, 28, 369-382.

Ծ૝σʔλ • ඃݧऀ • 24ਓͷඇӳޠ฼ޠ࿩ऀʢେֶੜʣ˞L1͸ڞ༗ • ߲໨ • ӳޠʹ͓͚ΔओޠͱಈࢺͷҰகʢSubject-Verb Agreement) • ํ๏ • ༰ೝ౓λεΫ(Acceptability Judgment Task) • 1(unacceptable)-10(acceptable)ͰධՁ • 20ϖΞͷจ๏จɾඇจ๏จʢશ40จʣ • ϥϯμϚΠζͨ͠2छྨͷςετΛ࡞Γ20จʢG10ɾUG10ʣʹ෼͚Δ • RQɿจ๏จͱඇจ๏จͰ༰ೝ౓ʹҧ͍͕͋Δ͔

ҎԼͷ͜ͱΛߟ͑Δඞཁੑ • ࣮ݧͷ݁ՌʹӨڹΛ༩͑ΔཁҼΛߟྀͰ͖͍ͯ Δ͔ • ඃݧऀͷ͹Β͖ͭ • ߲໨ͷ͹Β͖ͭ • ܹࢗͷจ๏ੑ • ख़ୡ౓ • จ௕ʢޠ਺ʣ

͜ΕΒΛߟྀͨ͠෼ੳ ΛՄೳʹ͢Δͷ͕…

ઢܗࠞ߹Ϟσϧ (ࠞ߹ޮՌϞσϧ)

ઢܗࠞ߹Ϟσϧʁࠞ߹ ޮՌϞσϧʁ

ઢܗϞσϧͷൃలʢٱอ,2012) ҰൠԽઢܗࠞ߹Ϟσϧ ҰൠԽઢܗϞσϧ ઢܗϞσϧ ֊૚ϕΠζϞσϧ ࠷খೋ৐๏ ࠷໬ਪఆ๏ MCMCʹΑΔࣄޙ෼෍ͷਪఆ ਪఆͷܭࢉํ๏ ਖ਼ن෼෍Ҏ֎ͷ ֬཰෼෍Λѻ͍ͨ ͍ ݸମࠩɾ৔ॴࠩͱ ͍ͬͨϥϯμϜޮ ՌΛ͔͍͍͋ͭͨ ΋ͬͱࣗ༝ Ͱݱ࣮తͳ ౷ܭϞσϦ ϯάΛʂ

ઢܗϞσϧͷൃలʢٱอ,2012) ҰൠԽઢܗࠞ߹Ϟσϧ ҰൠԽઢܗϞσϧ ઢܗϞσϧ ֊૚ϕΠζϞσϧ ࠷খೋ৐๏ ࠷໬ਪఆ๏ MCMCʹΑΔࣄޙ෼෍ͷਪఆ ਪఆͷܭࢉํ๏ ਖ਼ن෼෍Ҏ֎ͷ ֬཰෼෍Λѻ͍ͨ ͍ ݸମࠩɾ৔ॴࠩͱ ͍ͬͨϥϯμϜޮ ՌΛ͔͍͍͋ͭͨ ΋ͬͱࣗ༝ Ͱݱ࣮తͳ ౷ܭϞσϦ ϯάΛʂ

ઢܗࠞ߹Ϟσϧ (Linear-Mixed Effect Model)

LME ͱݺ͹ΕΔ͜ͱ΋ଟ͍

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • L2ͷࢦಋ๏ޮՌݚڀΛߟ͑ͯΈΔ ࢦಋޮՌˠࠞ߹ޮՌϞσϧͰ͸ݻఆޮՌʢfixed effect) ࢀՃऀˠϥϯμϜޮՌʢࢀՃऀ͸L2ֶशऀͷத͔Βϥ ϯμϜʹαϯϓϦϯά͞ΕΔʣ • ΋͠௥ࢼΛߦ͏ͱͨ͠৔߹ɼࢦಋ๏͸ݻఆͰɼࢀՃ ऀ͸·ͨ৽͘͠ϥϯμϜʹαϯϓϦϯά͞ΕΔ

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ݻఆޮՌͱͯ͠ಠཱม਺Λෳ਺ઃఆՄೳ • ΧςΰϦΧϧσʔλʢe.g., NS vs NNS, ߴख़ୡ౓ vs ௿ख़ ୡ౓ʣ • ࿈ଓσʔλʢe.g., ೥ྸɼख़ୡ౓ͱͯ͠ͷςετείΞʣ • ͋Δ͍͸྆ํͱ΋ • ैଐม਺ • ࿈ଓσʔλʢe.g., ೥ྸɼςετείΞɼ൓Ԡ࣌ؒʣ • ΧςΰϦΧϧσʔλʢจ๏ੑ൑அ, ༰ೝੑ൑அ etc.ʣ

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ݱߦͷख๏ʢઢܗϞσϧʣͰલड़ͷσʔλΛѻ ͑ͳ͍Θ͚Ͱ͸ͳ͍͕ɼϑϨʔϜϫʔΫ͕ҧ͏ • ઢܗϞσϧͰ͸౰ͯ͸·Γͷѱ͍σʔλʢe.g., ֶशऀͷॎஅతൃୡσʔλʣΛѻ͏͜ͱ΋Մೳ • ͞ΒʹɼมྔޮՌͱ༷ͯ͠ʑͳม਺ΛϞσϧʹ ૊ΈࠐΊΔ

͖͞΄Ͳͷࢦಋ๏ޮՌݚڀ ͷྫΛ΋͏Ұ౓ߟ͑ͯΈΔ

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࢀՃऀͷֶੜ • ಉֶ͡ߍ಺Ͱ΋Ϋϥε͕ҧ͏ • ͦ΋ͦ΋ҧ͏ֶߍ ֶߍA ֶߍB ΫϥεA ΫϥεB ΫϥεC ΫϥεA ΫϥεB ΫϥεC

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࢀՃऀͷֶੜ • Ϋϥε಺ʢֶߍ಺ʣͰҰఆͷ܏޲ • ΫϥεؒʢֶߍؒʣͰ͸ͦͷ܏޲͕ͳ͘ͳΔ Մೳੑ ֶߍA ΫϥεA ΫϥεB ΫϥεC ΫϥεA ΫϥεB ΫϥεC ֶߍB

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࢀՃऀͷֶੜ • ಉ͡ूஂ͔ΒαϯϓϦϯά͞Εֶͨੜ͕ҧ͏ Ϋϥεʹ͍Δ ฼ूஂA ฼ूஂB ΫϥεA ΫϥεB ΫϥεC ΫϥεD ΫϥεE ΫϥεG ੜె2 ੜె1 ੜె3 ੜె4 ੜె5 ੜె6 ੜెa ੜెb ੜెc ੜెd ੜెe

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࠞ߹ޮՌϞσϧ͸ͲͪΒͷߏ଄ͷมྔޮՌ΋ѻ ͏͜ͱ͕Ͱ͖Δɻ

͞Βʹ

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ςετ߲໨ʢܹࢗʣͷόϥ෇͖ʹ΋దԠͰ͖Δɻ • ܹࢗจ͸ແݶʹੜ੒Մೳʢݪཧతʹ͸ʣ • ࣮ͨͩ͠ݧͰ༻͍ΒΕΔͷ͸ͦͷ͏ͪͷҰ෦ • ݴޠ΋࣮͸มྔޮՌ • “language-as-fixed-effect fallacy”(Clark, 1973)

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • “language-as-fixed-effect fallacy”(Clark, 1973) →߲໨෼ੳΛ΍Δཧ༝͸͜Ε ※ͨͩ͠ɼඃݧऀ෼ੳͱ߲໨෼ੳ͸1ͭͷϞσϧʹ ࠷ऴతʹ͸౷߹͞ΕΔ΂͖ • ଟ͘ͷݚڀऀ͸ɼ྆ํͷ෼ੳͰ༗ҙࠩͰͨΒΑ ͠ͱͯ͠͠·͍ͬͯΔ

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ผͷ໰୊఺ • ༗ҙ͕ࠩยํʹ͔͠ग़ͳ͔ͬͨ৔߹͸݁ՌΛ ͲͷΑ͏ʹղऍ͢Δ͔ʁ • ࿦จͳͲͰਖ਼نੑ͕ຬͨ͞Ε͍ͯΔ͔ͳͲ͕ ใࠂ͞ΕΔ͜ͱ͸·ΕʢPlonsky, 2011; Plosnky & Gass, 2011)

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࠞ߹ޮՌϞσϧͳΒ… • ඃݧऀɾ߲໨Λಉ࣌ʹมྔޮՌͱͯ͠ѻ͏෼ੳ ͕Մೳ • ਖ਼ن෼෍Ҏ֎ͷ֬཰෼෍Λ༻͍Δ͜ͱ΋Մೳ • ্ݶͷͳ͍Χ΢ϯτσʔλˠϙΞιϯ෼෍ • ্ݶͷ͋ΔΧ΢ϯτσʔλˠೋ߲෼෍

ͳͥࠞ߹ޮՌϞσϧͳͷ͔ʁ • ࠞ߹ޮՌϞσϧͳΒ… • ٿ໘ੑ΍౳෼ࢄੑͷҳ୤ʹରͯ͠΋ؤ݈ • ܽଛ஋ͷ͋Δσʔλʹ΋ରԠͰ͖Δʢܽଛ஋ ΋ϥϯμϜޮՌͱΈͳ͢ʣ

࣮ࡍʹLMEΛ΍ͬͯΈΔ

ύοέʔδΛDL 1. RΛىಈͯ͠ҎԼͷίϚϯυΛଧͪࠐΉ >install.packages(“lme4”) 2. ϛϥʔαΠτΛબ୒ʢJapanͷͲ͔͜ʣ

ࠓճ࢖͏ؔ਺ • lmer()ͱ͍͏ؔ਺Λ࢖͏ • ͜ΕΛ࢖ͬͯ෼ੳΛ͢Δ

USBʹ͋ΔϑΝΠϧΛ ࢖͍·͢

΍Γํ • USBʹ͋ΔdataϑΝΠϧΛRͷίϯιʔϧʹD&D >ratings ͱଧͬͯத਎Λ֬ೝ

͜Μͳײ͡ʹͳͬͯΔ͸ͣ

΍Γํ جຊతͳೖྗ๏͸ҎԼͷͱ͓Γʢx=ैଐม਺, y=ಠ ཱม਺ʢݻఆޮՌʣ, z=มྔޮՌ, dataʹ࢖͏σʔλ ηοτΛ͍ΕΔʣ >lmer(x ~ y + z, data=ratings) >model1 <- lmer(zrating ~ condition + (1|subject) + (1|item),data=ratings) ()಺ʹcrossed random effectsΛ͍ΕΔ conditionͰzratingʹҧ͍͕͋Δ͔ΛΈ͍ͨ ੾ย ઃఆ͢Δม਺

΍Γํ • summaryؔ਺Ͱ݁ՌΛΈΔ >summary(model1)

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΍Γํ • ϞσϧϑΟοςΟϯάͷ܎਺͕lmer()ؔ਺Ͱ͸ REMLʢrestricted maximum likelihoodʣ๏ʢ੍ ݶ෇͖࠷໬ਪఆ๏ʣͷ஋͔͠ग़ͯ͜ͳ͍ͷͰɼ ଞͷ܎਺Λ֬ೝ͍ͨ͠৔߹͸AIC()ؔ਺౳Λ࢖͏ • AIC(Akaike’s information criterion) ؔ਺Ͱ༧ଌͷ ྑ͞ΛΈΔ

΍Γํ • AIC(Akaike’s information criterion) • ༧ଌͷྑ͞Λද͢ฏۉର਺໬౓ʹ΋ͱͮ͘ • খ͍͞ํ͕ྑ͍

΍Γํ • جຊతʹ͸ɼ͜ͷΑ͏ʹͯ͠ϞσϧΛ૊Έɼߟ ͑ΒΕΔෳ਺ͷϞσϧΛൺֱͯ͠ɼanova()ؔ਺ Λ࢖ͬͯͲͷϞσϧ͕Ұ൪ద߹౓͕ߴ͍͔Λൺ ֱ͍ͯ͘͠ • ϞσϧΛෳࡶʹ͢Ε͹͢Δ΄Ͳઆ໌ྗ͕͕͋Δ Θ͚Ͱ͸ͳ͍ͱ͍͏͜ͱʹ஫ҙ

΍Γํ >model1 <- lmer(zrating ~ condition + (1|subject) + (1|item),data=ratings) • ্هͷϞσϧʹΑͬͯɼࢀՃऀͱ߲໨ΛϥϯμϜ ੾ยͱͯ͠૊ΈࠐΉ͜ͱ͕Ͱ͖ͨ →ࢀՃऀݸਓͷ܏޲ΛߟྀͰ͖Δ

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ϥϯμϜ੾ย ܏͖͸ಉ͡Ͱ੾ย͕ҧ͏

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ϥϯμϜ܏͖ ੾ย͸ಉ͡Ͱ܏͖͕ҧ͏

΍Γํ • ͔͠͠ࢀՃऀ΍߲໨ʹΑͬͯ൓Ԡ͕ҟͳΔ͔΋͠ Εͳ͍ʁ • ਖ਼จͱඇจʹର͢ΔରԠͷࠩ΍͹Β͖ͭͷఔ౓͕ ͋Δͱ૝ఆͰ͖Δ →ϥϯμϜ܏͖΋ߟྀ͢Δඞཁੑ >model2 <- lmer(zrating ~ condition + (1+condition| subject) + (1|item),data=ratings) ඃݧऀͷมಈΛ੾ยͱconditionͷ܏͖ʹ͍ΕΔ

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ϥϯμϜ܏͖&ϥϯμϜ੾ย ੾ย΋܏͖΋ҧ͏

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΍Γํ • ͜ͷ࣮ݧͰ͸ͻͱͭͷจ͕ਖ਼จͱඇจͷͦΕͧΕͰ࢖ ΘΕ͍ͯΔ • จ๏ੑʢconditionʣ͸܁Γฦͯ͠ଌఆ͞Ε͍ͯΔ • ߲໨ͷϥϯμϜ܏͖΋Ϟσϧʹ૊ΈࠐΉ >model3 <- lmer(zrating ~ condition + (1+condition| subject) + (1+condition|item),data=ratings)

΍Γํ • 3ͭͷϞσϧΛൺֱ͢ΔͨΊʹɼanova()ؔ਺Λ ࢖ͬͯൺֱɻద߹౓͕༗ҙʹߴ͍ϞσϧΛબͿ >anova(model1, model2, model3)

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͔͠͠

࣮͸·ͩ͜ΕͰऴΘΓ Ͱ͸ͳ͍

ֶशऀͷख़ୡ౓͸ʁ

ඃݧऀཁҼͷ߲໨΁ͷӨڹ • Ұൠతͳ౷ܭతԾઆݕఆͰ͸ɼ͜ΕΒͷཁҼΛ ڞมྔʹઃఆͯ͠ɼڞ෼ࢄ෼ੳʢANCOVA)Λ༻ ͍Δ͜ͱ͕͋Δ • ͔͠͠ɼ͜ΕͰ͸߲໨΁ͷӨڹͷҟͳΓ۩߹͕ ߟྀ͞Ε͍ͯͳ͍ʢ೥ྸ΍ख़ୡ౓ͷӨڹ͕͋Δ ߲໨ͱͳ͍߲໨͕͋ΔՄೳੑʣ

จͷ௕͞͸ʁ

߲໨ཁҼͷඃݧऀ΁ͷӨڹ • ߲໨ͷฏۉಘ఺ʹରͯ͠ɼจͷ௕͞Λڞมྔʹ ͯ͠ڞ෼ࢄ෼ੳΛ͢Δ͜ͱ͕͋Δ • ͜ͷ৔߹͸ඃݧऀཁҼ͕ߟྀ͞Ε͍ͯͳ͍ʢจ ௕ͷӨڹΛड͚Δඃݧऀͱड͚ͳ͍ඃݧऀ͕͍ ΔՄೳੑʣ

͖ͭͮ • ͜ΕΒͷ໰୊Λղܾ͢Δʹ͸ɼ೥ྸ΍จ௕ͷΑ ͏ͳ࿈ଓม਺Λ0/1ͷΧςΰϦΧϧσʔλʹͯ͠ ૊ΈࠐΉ͜ͱʹͳΔʢ೥ྸɿ௿ɾߴɼจ௕ɿ୹ɾ ௕ʣ →LMEͳΒ͜ΕΒͷσʔλ΋ʢ࿈ଓͰ͋ΕΧςΰ ϦΧϧͰ͋ΕʣϞσϧʹ૊ΈࠐΉ͜ͱ͕Մೳ

͖ͭͮ • ࿈ଓσʔλΛϞσϧʹ૊ΈࠐΉͱ͖͸ɼத৺Խ͓ͯ͠ ͘ͱΑ͍ →ڞઢੑʢ2ͭҎ্ͷม਺͕͓ޓ͍ڧ͘࿈ಈ͢Δͱ͖ʹ ൃੜ͢Δʣͷ໰୊ΛճආͰ͖Δ ratings$clength <- ratings$length - mean(ratings $length) ratings$cprof <- ratings$proficiency - mean(ratings $proficiency)

͖ͭͮ • ·ͣɼจ௕ʹΑͬͯ༰ೝ౓͕มΘΔ͔Λߟྀ • model4ʹɼจ௕ͷݻఆޮՌΛ͍ΕΔ >model4 <- lmer(zrating ~ condition + clength + (1+condition|subject) + (1+condition|item),data=ratings)

͖ͭͮ • ख़ୡ౓ʹΑͬͯ༰ೝ౓͕มΘΔ͔Λߟྀ • model5ʹɼख़ୡ౓ͷݻఆޮՌΛ͍ΕΔ >model5 <- lmer(zrating ~ condition + clength + cprof + (1+condition|subject) + (1+condition|item),data=ratings)

͖ͭͮ • จ௕ͷݻఆޮՌ͸จ๏ੑʢconditionʣͱަޓ࡞༻͕͋Δ͔ ΋ʁ • ྫɿਖ਼จͩͱจ௕ͷӨڹ͕͋ͬͯɼඇจͩͱจ௕ͷӨڹ͕ ͳ͍ >model6 <- lmer(zrating ~ condition + clength + cprof + condition:clength + (1+condition|subject) + (1+condition| item),data=ratings) ίϩϯ͸ަޓ࡞༻

͖ͭͮ • ख़ୡ౓ͷݻఆޮՌ͸จ๏ੑʢconditionʣͱަޓ࡞༻͕͋Δ ͔΋ʁ • ྫɿਖ਼จͩͱख़ୡ౓ͷӨڹ͕͋ͬͯɼඇจͩͱख़ୡ౓ͷӨ ڹ͕ͳ͍ >model7 <- lmer(zrating ~ condition + clength + condition:clength + condition:cprof + (1+condition|subject) + (1+condition| item),data=ratings) ίϩϯ͸ަޓ࡞༻

͖ͭͮ • ΋͔͢͠Δͱɼจ௕ͱख़ୡ౓΋ަޓ࡞༻͋Δ͔΋ʁ • ྫɿख़ୡ౓͕ߴ͍ͱจ௕ͷӨڹ͕ͳͯ͘ɼख़ୡ౓͕ ௿͍ͱจ௕ͷӨڹ͕͋Δ >model8 <- lmer(zrating ~ condition + clength + condition:clength + condition:cprof + clength:cprof + (1+condition|subject) + (1+condition|item),data=ratings) ίϩϯ͸ަޓ࡞༻

͖ͭͮ • ߟ͑ΒΕΔ3ͭͷཁҼͷ͢΂ͯͷݻఆޮՌͱަޓ ࡞༻Λ͍ΕΔͱ͖ʹ͸ΞελϦεΫ(*)Λ࢖͏ >model9 <- lmer(zrating ~ condition * clength * cprof + (1+condition|subject) + (1+condition|item),data=ratings) ΞελϦεΫ͸ߟ͑ΒΕΔ͢΂ͯͷཁҼͷݻఆޮՌͱަޓ࡞༻ condition*clength͸ɼcondition + clength +condition:clengthͱಉ͡

͖ͭͮ • ͜Ε·Ͱ࡞͖ͬͯͨmodel3͔Βmodel9·ͰͰɼ ͲΕ͕Ұ൪ϞσϧͷϑΟοςΟϯάΛ޲্ͤ͞ ͔ͨΛanova()ؔ਺Ͱݕূ >anova (model3, model4, model5, model6, model7, model8, model9)

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·ͩ·ͩऴΘΓ͡Όͳ͍

͖ͭͮ • จ௕ΛඃݧऀͷϥϯμϜ܏͖ʹ͍ΕΔ • ͋Δֶशऀ͚͕ͩจ௕ͷӨڹΛड͚͍ͯͯଞͷֶशऀ ͸ड͚͍ͯͳ͍ͱ͍͏ݸਓࠩΛߟྀ • ߲໨ͷϥϯμϜ܏͖ʹ͸͍Εͳ͍ • ಉ͡จͷจ௕͸߲໨͝ͱͰҟͳΔ͕ɼ߲໨಺Ͱ͸ಉҰ

͖ͭͮ • จ௕ΛඃݧऀͷϥϯμϜ܏͖ʹ͍ΕΔ • ͋Δֶशऀ͚͕ͩจ௕ͷӨڹΛड͚͍ͯͯଞͷֶशऀ͸ ड͚͍ͯͳ͍ͱ͍͏ݸਓࠩΛߟྀ • ߲໨ͷϥϯμϜ܏͖ʹ͸͍Εͳ͍ • ಉ͡จͷจ௕͸߲໨͝ͱͰҟͳΔ͕ɼ߲໨಺Ͱ͸ಉҰ >model10 <- lmer(zrating ~ condition + clength + (1+condition + clength|subject) + (1 + condition|item), data=ratings)

͖ͭͮ • model4ͱmodel10Λanova()ؔ਺Ͱൺֱ >anova(model4, model10)

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model4͕࠷ڧʂ

·ͩऴΘΓ͡Όͳ͍

͖ͭͮ • Α͏΍͘࠷దͳϞσϧ͕ܾఆͰ͖ͨ • lme4ύοέʔδͷlmer()ؔ਺Ͱ͸౷ܭྔ͸ܭࢉ͢Δ ͕ɼp஋Λࢉग़ͯ͘͠Εͳ͍ • lmerTestύοέʔδͷ࢖༻ʢ͓͢͢Ίʣ • t஋͔Βp஋Λܭࢉʢࢀߟ·Ͱʹʣ

ύοέʔδΛDL 1. RΛىಈͯ͠ҎԼͷίϚϯυΛଧͪࠐΉ >install.packages(“lmerTest”) 2. ϛϥʔαΠτΛબ୒ʢJapanͷͲ͔͜ʣ 3. lme4ύοέʔδͱಉ༷ʹlmer()ؔ਺Λ࢖͏ͱɼ Welch-SatterthwaiteͷࣜΛ༻͍ͯۙࣅࣗ༝౓ͱ p஋Λܭࢉͯ͘͠ΕΔ

࣮͸

࣮͸ • lmerTestύοέʔδͷstep()ؔ਺Λ࢖͑͹΋ͬͱָʂ • step()ؔ਺͸ϞσϧϑΟοςΟϯάΛ޲্ͤ͞ͳ͍ཁҼ Λഉআͯ͘͠ΕΔؔ਺ • ͭ·ΓɼҰ൪ෳࡶͳϞσϧΛ૊ΜͰstep(model)ͷΑ͏ ʹ͢Ε͹ɼ࠷దͳϞσϧΛग़ͯ͘͠ΕΔ

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͖ͭͮ • Α͏΍͘࠷దͳϞσϧ͕ܾఆͰ͖ͨ • ݁Ռͷղऍ • ඇจ͸ਖ਼จΑΓ΋༗ҙʹ༰ೝ౓͕ߴ͍ • ௕͍จ͸୹͍จΑΓ΋༰ೝ౓͕௿͍

͖ͭͮ • Α͏΍͘࠷దͳϞσϧ͕ܾఆͰ͖ͨ • lme4ύοέʔδͷlmer()ؔ਺Ͱ͸౷ܭྔ͸ܭࢉ͢Δ ͕ɼp஋Λࢉग़ͯ͘͠Εͳ͍ • lmerTestύοέʔδͷ࢖༻ʢ͓͢͢Ίʣ • t஋͔Βp஋Λܭࢉʢࢀߟ·Ͱʹʣ

t஋͔Βp஋Λܭࢉ • t෼෍ͷ෼෍ؔ਺Ͱ͋Δpt()ؔ਺Λ࢖͏ • 2 * (1 - pt(abs(t஋), σʔλ਺ - ݻఆޮՌͷ਺)) • จ๏ੑͷӨڹ > 2 * (1 - pt(abs(-4.980), 480 - 3)) • จ௕ͷӨڹ > 2 * (1 - pt(abs(-2.151), 480 - 3))

t஋͔Βp஋Λܭࢉ • t෼෍ͷ෼෍ؔ਺Ͱ͋Δpt()ؔ਺Λ࢖͏ • 2 * (1 - pt(abs(t஋), σʔλ਺ - ݻఆޮՌͷ਺)) • ͨͩ͜͠ͷํ๏ͩͱɼσʔλ਺͕গͳ͍ͱ༗ҙ͕ࠩͰ ΍͘͢ͳΔͷͰ஫ҙʢType Ⅰ errorͷةݥੑʣ

࠷ޙʹ • ࠓճͷํ๏͸͋͘·ͰҰྫ • ͞Βʹʮೖ໳ͷೖ໳ʯ • ຊ౰͸΋ͬͱԞ͕ਂ͍Ͱ͢ • ࠷໬๏ʹΑΔਪఆ͸ݶք͕͋Δ • ϕΠζਪఆʢMCMC)͕ඞཁʹͳͬͯ͘Δ

΋ͬͱৄ͘͠஌Γ͍ͨਓ͸

ँࣙ • Cunnings(2012)ͷαϯϓϧσʔλΛ୳ͤͲ୳ͤͲݟͭ ͔Βͣʹ్ํʹ͘Ε͍ͯͨͱ͜Ζɼؔ੢େֶͷਫຊಞ ઌੜ͕ʮࢲ΋ݟ͔ͭΒͣʹஶऀʹ໰͍߹Θͤͯૹͬͯ ΋Β͍·ͨ͠ʯͱ੠Λ͔͚ͯͩ͘͞ΓɼͳΜͱ͔σʔ λΛ࢖͏͜ͱ͕Ͱ͖·ͨ͠ɻ͜ͷ৔ΛआΓ͓ͯྱΛਃ ্͛͠·͢ɻ

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