2021-11-06 LMM and GLMM

2021年11月6日（土）名古屋大学大学院人文学研究科英語教育分野主催の連続公開講座『データサイエンス時代の英語教育』（2）における発表資料です。

Transcript

1. ҰൠԽઢܗࠞ߹Ϟσϧͷ
   ࣮ફ
   ؾΛ͚͍ͭͨ3ͭͷϙΠϯτ
   2021.11.06 ࿈ଓެ։ߨ࠲ʮσʔλαΠΤϯε࣌୅ͷݴޠڭҭʯୈ2ճݴޠڭҭݚڀͷ࣮ࡍ
   

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2. ͸͡Ίʹ
   2
   

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3. ͜Εͷʮվగ൛ʯͱ͍͏͔ʮൃల൛ʯͱ͍͏͔…
   

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4. • ҰൠԽઢܗࠞ߹ϞσϧΛ༻͍ͨ෼ੳ͸ීٴ͕ਐΜͩͱࢥΘΕ
   ΔҰํͰɼϋʔυϧ͸Ή͠Ζ͕͍͋ͬͯΔ͔΋
   
   
   • ϨϏϡʔ࿦จ͕ग़͖͍ͯͯΔ͚ΕͲ΋ɼ࣮ࡍͷ෼ੳͷաఔʹ
   ͸͍͔ͭ͘൑அ͕෼͔ΕΔ෦෼΋
   
   
   • ࠓճ͸ɼͦ͏ͨ͠෦෼Ͱ͜͜͸͓͓͖͍͑ͯͨ͞ͱ͍͏ϙ
   ΠϯτʹϑΥʔΧε
   
   
   • શฤʹΘͨͬͯlme4ύοέʔδʢBates et al, 2019ʣ࢖͏લ
   ఏͰ͢
   ͸͡Ίʹ
   4
   

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5. “[T]here is no single correct way to
   implement an LMM, and…the choices
   they [researchers] make during analysis
   will comprise one path, however
   justi
   f
   ied, amongst multiple alternatives. ”
   Meteyard & Davies (2020, pp.1–2)
   

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6. • ͸͡Ίʹ
   
   
   • ҰൠԽઢܗࠞ߹ޮՌϞσϧͱ͸
   
   
   • ݚڀऀͨͪͷײ͡Δෆ҆
   
   
   • ෼ੳͷํ๏
   
   
   • ෼ੳͷʢ݁Ռʣͷใࠂ
   
   
   • ࠶ݱੑͷ֬อ
   ͸͡Ίʹ
   3ͭͷϙΠϯτ
   6
   

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7. • ాଜ༞ʢͨΉΒΏ͏ʣ
   
   
   • ؔ੢େֶ֎ࠃޠֶ෦ʢ4೥໨ʣ
   
   
   • ઐ໳
   
   
   • ୈೋݴޠशಘʢओʹจ๏ʣ
   
   
   • ୈೋݴޠจॲཧ
   
   
   • झຯɿαοΧʔ؍ઓ
   
   
   • Rͷ͜ͱɿ݁ߏ޷͖ʢҰॹʹ͍Δͱ࣌ؒΛ๨Εͤͯ͘͞ΕΔʣ
   ࣗݾ঺հ
   7
   https://tam07pb915.wordpress.com/
   https://tamurayu.wordpress.com/
   

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8. ҰൠԽઢܗࠞ߹ޮՌ
   Ϟσϧͱ͸
   8
   

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9. • tݕఆɼ෼ࢄ෼ੳɼ୯ճؼɾॏճؼ -> ʢҰൠʣઢܗϞσϧ
   
   
   • ਖ਼ن෼෍Ҏ֎ͷ෼෍΁ͷ֦ு -> ҰൠԽઢܗϞσϧ
   
   
   • ݸਓࠩ౳Λߟྀ͍ͨ͠ ->ࠞ߹ޮՌϞσϧ
   
   
   • ܏͖and/or੾ยΛࢀՃऀ͝ͱɾ߲໨͝ͱʹਪఆ
   
   
   • ࢀՃऀ෼ੳͱ߲໨෼ੳΛ଍͠߹ΘͤͨΑ͏ͳ΋ͷ
   ҰൠԽઢܗࠞ߹ޮՌϞσϧͱ͸
   ઢܗʁҰൠԽʁࠞ߹ޮՌʁ
   9
   

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10. • LME (Linear Mixed-Effect)
    
    
    • ઢܗࠞ߹ޮՌϞσϧͱݺ͹ΕΔ΋ͷ
    
    
    • ਖ਼ن෼෍
    
    
    • GLMM (Generalized Linear Mixed-Effect Model)
    
    
    • ҰൠԽઢܗࠞ߹Ϟσϧͱݺ͹ΕΔ΋ͷ
    
    
    • ਖ਼ن෼෍Ҏ֎ʢϙΞιϯ෼෍ɼೋ߲෼෍ɼΨϯϚ෼෍,
    etc.ʣ
    ҰൠԽઢܗࠞ߹ޮՌϞσϧͱ͸
    LMEʁGLMMʁ
    10
    

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11. ࠞ߹ޮՌϞσϧͷಋೖ͸
    Gries (2021)ͷΠϯτϩ෦
    ෼͕؆ܿͰΘ͔Γ΍͍͢
    Gries, S. T. (2021). (Generalized Linear) Mixed-E
    ff
    ects
    Modeling: A Learner Corpus Example. Language Learning, 71,
    757
    –
    798. https://doi.org/10.1111/lang.12448
    
    
    11
    

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12. ݚڀऀͨͪͷײ͡Δෆ҆
    12
    

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13. • खॱ΁ͷίϯηϯαε͕͚͍ܽͯΔ͜ͱ
    
    
    • ෼ੳͷͨΊͷτϨʔχϯά΍෼ੳɾ݁Ռͷղऍ΍ใࠂʹ͍ͭ
    ͯͷ໌֬ͳΨΠυϥΠϯͷෆ଍
    ݚڀऀͨͪͷײ͡Δෆ҆
    Meteyard & Davies (2020)
    13
    Best practice guidance for reporting LMMs
    

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15. ͜ͷ࿦จʹԊͬͯ࿩͠Α͏ͱࢥͬͯ
    ·͕ͨ͠ઌʹ΋ͬͱ༗ӹͳ·ͱΊΛ
    ͞Εͨํ͕…
    

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16. ໊ാ໨ઌੜͷnoteͷهࣄΈͳ͞ΜಡΜͰ͍ͩ͘͞…
    

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17. ෼ੳͷख๏
    17
    

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18. • ࢀՃऀ਺ɾ߲໨਺ͱݕఆྗ෼ੳ
    
    
    • Ԡ౴ม਺͸ͳʹʁ
    
    
    • આ໌ม਺͸ͳʹʁ
    
    
    • ݻఆޮՌ͸ʁ
    
    
    • มྔޮՌ͸ʁ
    
    
    • Ϟσϧͷ਍அ
    ෼ੳͷख๏
    ϙΠϯτ
    18
    

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19. • ʮαϯϓϦϯάɾϢχοτʯΛ૿΍͢ʢMeteyard & Ravies,
    2020)
    
    
    • “As a general rule of thumb, increasing the sample size at
    the highest level (i.e., sampling more groups) will do
    more to increase power than increasing the number of
    individuals in the groups. “ (Scherbaum & Ferreter, 2009,
    p.352)
    ෼ੳͷख๏
    ࢀՃऀ਺ɾ߲໨਺ͱݕఆྗ෼ੳ
    19
    

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20. ֶߍB
    Ϋϥε2 Ϋϥε3 Ϋϥε1 Ϋϥε2 Ϋϥε3
    ֶߍA
    Ϋϥε1
    ࢀՃऀ͕ωετ͍ͯ͠Δ৔߹͸্ͷϨϕϧΛͰ͖Δ
    ͚ͩ૿΍͠·͠ΐ͏
    

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21. • ࣮ݧܥͰ͋Ε͹ɼࢀՃऀ਺ͱ߲໨਺ͷֻ͚ࢉΛҙࣝ
    
    
    • ࢀՃऀؒͷ͹Β͖͕ͭେ͖͍->ࢀՃऀΛ૿΍͢
    
    
    • ߲໨ؒͷ͹Β͖͕ͭେ͖͍->߲໨਺Λ૿΍͢
    
    
    • มྔޮՌͷ෼ࢄΛใࠂ͢Δ͜ͱ͕େࣄͳཧ༝͸͜͜
    ෼ੳͷख๏
    ࢀՃऀ਺ɾ߲໨਺ͱݕఆྗ෼ੳ
    21
    

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22. •
    
    
    • Ԡ౴ม਺ = ੾ย + ݻఆޮՌ + ݸਓࠩ + ߲໨ࠩ
    
    
    • ඞͣʮԠ౴ม਺͸XXXͰ͢ʯͱॻ͘
    
    
    • ͱ͘ʹ஫ҙ͍ͨ͠ͷ͸ϩδεςΟοΫճؼͷͱ͖
    
    
    • ਖ਼౴ɾޡ౴͸ਖ਼౴1ɼޡ౴0ͰΘ͔Γ΍͍͕͢…
    
    
    • preference taskͷΑ͏ͳͱ͖͸Ͳ͕ͬͪ0ͰͲ͕ͬͪ1͔໌ࣔత
    ʹهड़
    yi
    = β1
    + β2
    xi
    + ri
    + rj
    ෼ੳͷख๏
    Ԡ౴ม਺ʢresponse variableʣ͸ͳʹʁ
    22
    

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23. •
    
    
    • Ԡ౴ม਺ = ੾ย + ݻఆޮՌ + ݸਓࠩ + ߲໨ࠩ
    
    
    • ඞͣʮઆ໌ม਺ʢݻఆޮՌʣ͸XXXͰ͢ʯͱॻ͘
    
    
    • ΧςΰϦม਺ͷίʔσΟϯάͷઆ໌͸ஸೡʹʢޙड़ʣ
    
    
    • Ͳͷํ๏ͰίʔσΟϯά͔ͨ͠
    
    
    • ਫ४ͷઃఆΛͲ͏ͨ͠ͷ͔
    
    
    • ݚڀ՝୊ʹج͍͍ͮͯΔ͔Ͳ͏͔
    yi
    = β1
    +β2
    xi
    +ri
    + rj
    ෼ੳͷख๏
    આ໌ม਺ʢexplanatory variableʣ͸ͳʹʁ
    23
    

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24. Hou (2021, Language and Cognition)
    Ԡ౴ม਺ͳʹ…
    p.481
    

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25. Hou (2021, Language and Cognition)
    ਫ४Ͳ͏ͳͬͯΔͷ…
    p.480
    

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26. Ϟσϧͷ਍அ
    DHARMaύοέʔδʢHartig, 2021ʣ
    26
    simulateResiduals(model,plot=T) %>% testResiduals()
    ৄ͘͠͸͜ͷϖʔδɿhttps://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html
    

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27. ͲͷΑ͏ʹใࠂ͢΂͖͔
    27
    

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28. • ෼ੳʹ༻͍ͨ΋ͷ
    
    
    • ม਺ͷίʔσΟϯά΍த৺Խ
    
    
    • ϞσϧΛཱͯͨํ๏
    
    
    • දͱͯ͠ͷใࠂ
    ࿦จͰͷใࠂͷ࢓ํ
    ϙΠϯτ
    28
    

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29. • ιϑτ΢ΣΞʢRͷόʔδϣϯ΋ؚΊͯʣ
    
    
    • ύοέʔδ
    
    
    • όʔδϣϯΛඞؚͣΊΔ
    
    
    • ԿΛ͢ΔͨΊʹͲͷύοέʔδΛ༻͍ͨͷ͔
    ෼ੳʹ༻͍ͨ΋ͷ
    29
    

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30. ෼ੳʹ༻͍ͨ΋ͷ
    RͳΒsessionInfo()ؔ਺͕ศར
    30
    

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31. • ྫ1ɿcontrasts(dat$freq) <- contr.sum(2)
    
    
    • ྫ2ɿifelse(dat$freq == “low”, -0.5, 0.5) -> dat$freq_c
    
    
    • RͰ͸σϑΥϧτͩͱΞϧϑΝϕοτॱͰਫ४͕ܾ·ΔͷͰɼඞཁͰ͋Ε
    ͹factor()ؔ਺Ͱࢦఆ
    ม਺ͷίʔσΟϯά΍த৺Խ
    ίʔσΟϯάʹ͍ͭͯ
    31
    dat$freq<-factor(dat$condition, levels = c(“low","high"))
    Schad et al. (2020)
    

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32. ίʔσΟϯάํ๏ͷൺֱ
    Schad et al. (2020, p.15)
    32
    ੺࿮Ͱғͬͨ෦෼͕RͰcontr.treament(4)ͷΑ͏ʹೖྗͨ͠ͱ͖ʹग़ͯ͘Δ෦෼
    

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33. ίʔσΟϯάํ๏ͷൺֱ
    Schad et al. (2020, p.15)
    33
    

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34. • ݸͷਫ४͕͋Δͱͨ͠Βɼ ݸͷൺֱ͔͠Ͱ͖ͳ͍͜ͱʹ஫ҙʢ1͕ͭ
    ੾ยʹͳΔͷͰʣ
    
    
    • ԾઆͱηοτͰߟ͑Δͷ͕ॏཁʢSchad et al. 2020ʣ
    
    
    • ͱ͘ʹ3ਫ४Ҏ্ͷ৔߹͸ݚڀ՝୊ʹরΒ͠߹ΘͤͯɼͲͷਫ४ͱͲͷਫ४
    Λൺֱ͢Δ͔Λߟ͑Δ
    
    
    • ౷੍܈ʢϕʔεϥΠϯ৚݅ʣͱ2ͭҎ্ͷ࣮ݧ܈ʢ࣮ݧ৚݅ʣΛൺ΂͍ͨ -
    > dummy coding
    
    
    • 3ͭ͋Δதͷ͋Δ܈ʢ৚݅ʣͱଞͷ2ͭͷ܈ʢ৚݅ʣͷฏۉΛൺ΂͍ͨ ->
    sum coding
    k k − 1
    ม਺ͷίʔσΟϯά΍த৺Խ
    ίʔσΟϯάʹ͍ͭͯ
    34
    

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35. • ަޓ࡞༻ͷ͋ΔϞσϧͷέʔε
    
    
    • 2*2ͷ৔߹ͷओޮՌ͕Έ͍ͨ -> sum contrasts͕Ϛετ
    
    
    • μϛʔίʔσΟϯά͸ยํͷཁҼͷθϩʹͳͬͯΔਫ४ͷ
    ͱ͖ͷsimple effectʹͳͬͯ͠·͏
    ม਺ͷίʔσΟϯά΍த৺Խ
    ίʔσΟϯάʹ͍ͭͯ
    35
    sum contrast treatment contrast
    

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36. • 2ཁҼҎ্Ͱަޓ࡞༻ʹڵຯ͕͋Γɼ͋ΔཁҼͷ୯७ओޮՌ͕ݟ
    ͍ͨ
    
    
    1. sum contrastsͰަޓ࡞༻Λ֬ೝ
    
    
    2. A: dummy codingʹ੾Γସ͑ͯ୯७ޮՌͷ֬ೝʢ3ཁҼҎ্
    Ͱྡ઀ͯ͠Δਫ४ͷൺֱͳΒrepeated coding΋ʣ
    
    
    2. B: emmeansύοέʔδΛ࢖ͬͯԼҐݕఆ
    
    
    ม਺ͷίʔσΟϯά΍த৺Խ
    ίʔσΟϯάʹ͍ͭͯ
    36
    emmeans(model, pairwise~ཁҼA|ཁҼB)$contrastsʢཁҼBͷͦΕͧΕͷਫ४ͰͷཁҼAͷਫ४ؒൺֱʣ
    emmeans(model, pairwise~ཁҼB|ཁҼA)$contrastsʢཁҼAͷͦΕͧΕͷਫ४ͰͷཁҼBͷਫ४ؒൺֱʣ
    

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37. • ίʔσΟϯάʹؔͯ͠ࢀߟʹͳΔ΋ͷ
    
    
    • Shravan Vasishthͷಈըɿhttps://youtu.be/hD2XjoP5WBI
    
    
    • ΢Σϒϖʔδ
    
    
    • Coding categorical predictor variables in factorial designs
    
    
    • CODING SYSTEMS FOR CATEGORICAL VARIABLES IN REGRESSION
    ANALYSIS
    
    
    • ࿦จɿSchad, D. J., Vasishth, S., Hohenstein, S., & Kliegl, R. (2020). How
    to capitalize on a priori contrasts in linear (mixed) models: A tutorial.
    Journal of Memory and Language, 110, 104038. https://doi.org/10.1016/
    j.jml.2019.104038
    ม਺ͷίʔσΟϯά΍த৺Խ
    ίʔσΟϯάʹ͍ͭͯ
    37
    

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38. • ࿈ଓม਺Ͱ͋Ε͹த৺Խ౳Λͨ͠ͷ͔
    
    
    • த৺ԽͷࡍʹͳʹΛج४ʹͨ͠ͷ͔ʁʢBrauer & Curtin, 2018)
    
    
    • શମฏۉʢࢀՃऀؒʣʁूஂฏۉʢࢀՃऀ಺ʣʁ
    
    
    • Longܕͷσʔλͷࡍʹ͸த৺Խʹ஫ҙ
    
    
    • ख़ୡ౓ͷείΞͳͲɼ1ਓʹ͖ͭ1ͭͷ஋͔͠ͳ͍৔߹ɼ෼ࢄ͕
    ຊདྷͷ஋ΑΓখ͘͞ͳͬͯ͠·͏
    
    
    •
    ม਺ͷίʔσΟϯά΍த৺Խ
    த৺Խʹ͍ͭͯ
    38
    

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39. • maximal model͔Βελʔτͯ͠backward stepwiseͰ΍Γ
    ·ͨ͠
    
    
    • null model͔Βελʔτͯ͠forward stepwiseͰ΍Γ·ͨ͠
    ϞσϧΛཱͯͨํ๏
    39
    ͜Ε͚ͩͰ͸ෆे෼
    

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40. • ʮBarr et al. (2013)ʹैͬͯ࠷େϞσϧΛཱ͕ͯͨऩଋ͠ͳ
    ͔ͬͨͷͰɼ୯७Խͯ͠ऩଋͨ͠ϞσϧΛ࠾༻ͨ͠ɻʯ
    ϞσϧΛཱͯͨํ๏
    Α͋͘Δ΍ͭ
    40
    Ұ൪஌Γ͍ͨͷ͸Ͳ͏΍ͬͯϞσϧΛ
    ൺֱͨ͠ͷ͔ͳͷʹɼͦͷաఔ͸ҋͷ
    தͰ͜͏͍͏ਓ͍͍ͨͯσʔλ΋ίʔ
    υ΋ग़͞ͳ͍
    

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41. • ྫͱͯ͠ཁҼAͱཁҼBͷओޮՌͱަޓ࡞༻ͷσβΠϯΛߟ͑Δ
    
    
    • (1 + A*B | subject) + (1 + A*B | item)
    
    
    • ͔͜͜ΒͲ͏΍ͬͯ….ʁ
    
    
    • Մೳੑ1: (1 + A + B | subject) + (1 + A*B | item)
    
    
    • Մೳੑ2: (1 + A*B | subject) + (1 + A + B | item)
    
    
    • Մೳੑ3: (1 + A | subject) + (1 + A*B | item)
    
    
    • Մೳੑ4: (1 + B | subject) + (1 + A*B | item)
    
    
    • Մೳੑ5: (1 + A*B | subject) + (1 + A | item)
    
    
    • Մೳੑ6: (1 + A*B | subject) + (1 + B | item)
    ϞσϧΛཱͯͨํ๏
    ҋͷதͰى͜Δ͜ͱͷ૝૾
    41
    ΋͠ԾʹՄೳੑ1ͱՄ
    ೳੑ2ͷ྆ํ͕ऩଋ
    ͨ͠ͱͨ͠ΒɼͲ͏
    ΍ͬͯબΜͰΔͷʁ
    

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42. ʮBarr et al. (2013)ʹैͬͯ࠷େϞσϧΛཱ͕ͯͨ
    ऩଋ͠ͳ͔ͬͨͷͰɼ୯७Խͯ͠ऩଋͨ͠Ϟσϧ
    Λ࠾༻ͨ͠ɻৄ͍͠Ϟσϧબ୒ͷखॱʹ͍ͭͯ
    ͸ɼSupplementary MaterialΛࢀরͷ͜ͱɻʯ
    ͜ΕͰΑ͘ͳ͍Ͱ͔͢ʁ
    

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43. “[W]hile the maximal model indeed
    performs well as far as Type I error rates
    were concerned, power decreases
    substantially with model complexity.
    
    
    Matuschek et al. (2017, pp.310
    –
    311)
    

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44. LMEͷ৔߹͸lmerTestύοέʔδͷstepؔ
    ਺ͰϞσϧΛ୯७Խͯ͘͠Ε·͕͢ɼͦΕ
    ͳΒstepؔ਺࢖͍·ͨ͠ͱॻ͖·͠ΐ͏ɻ
    ͦͷ৔߹Ͱ΋ࣗ෼ͷखͰ୯७Խͨ͠৔߹ͱҰக͢Δ͔νΣοΫ͢Δͷ͕๬·͍͠ʢݸਓతҙݟʣ
    

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45. 1. ࠷େϞσϧΛߏஙʢऩଋ͠ͳͯ͘΋OKʣ
    
    
    2. ͦͷϞσϧͷมྔޮՌʹ͍ͭͯओ੒෼෼ੳ
    
    
    1. lme4::rePCA(maxmodel)%>%summary
    
    
    2. “Proportion of Variance”͕θϩʢ·ͨ͸ݶΓͳ͘θϩʹ͍ۙ஋ʣͷྻ͕͋Δ͔νΣοΫ
    
    
    3. มྔޮՌʹ͓͚Δ੾ยͱ܏͖ͷ૬ؔύϥϝʔλΛআ֎ͯ͠࠶౓ओ੒෼෼ੳ
    
    
    • (1+A | subject)ɿ૬ؔύϥϝʔλ͋Γ
    
    
    • (1+A || subject)ɿ૬ؔύϥϝʔλͳ͠
    
    
    4. มྔޮՌͷ෼ࢄΛνΣοΫͯ͠ɼ஋ͷ௿͍ཁҼΛݮΒͯ͠ϞσϧΛߏங
    
    
    5. anovaؔ਺Ͱ໬౓ൺݕఆʢMatuschek et al., 2017Ͱ͸ ͰγϛϡϨʔγϣϯʣ
    
    
    1. or Ͱ༗ҙ -> ΑΓෳࡶͳϞσϧʢཁҼͷଟ͍ํʣΛબ୒
    
    
    2. or Ͱ༗ҙͰ͸ͳ͍ ->෼ࢄͷ௿͍ཁҼΛݮΒͯ͠Ϟσϧߏஙˍ໬౓ൺݕఆ
    
    
    6. બ͹ΕͨϞσϧʹ૬ؔύϥϝʔλ௥Ճͨ͠΄͏͕͍͍͔໬౓ൺݕఆ
    αLRT
    = .20
    αLRT
    = .10 αLRT
    = .20
    αLRT
    = .10 αLRT
    = .20
    ϞσϧΛཱͯͨํ๏
    มྔޮՌͷܾఆखॱʢBates et al., 2015)
    45
    ೔ຊޠͰ͸৽ҪɾRoland (2016)ͷ4.2અʹղઆ͕͋Γ·͢
    lmer()ͷ৔߹͸໬౓ൺݕఆ͢ΔͷͰREFL=FͰ࠷໬ਪఆ -> ࠷ޙʹREML=Tʹ໭͢
    

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46. 1. ϥϯμϜ੾ยͷΈͷϞσϧΛߏங
    
    
    2. ϥϯμϜ܏͖Λ1ͭͣͭೖΕͯAICΛ࠷΋Լ͛Δ΋ͷΛ࢒͢
    
    
    3. ͞ΒʹϥϯμϜ܏͖Λ௥Ճͯ͠AICΛ࠷΋΋ͷΛ࢒͢
    
    
    4. AIC͕ͦΕҎ্Լ͕Βͳ͘ͳΔ·Ͱ௥Ճͯ͠ετοϓ
    
    
    • AICʹΑΔϞσϧબ୒͸ωετͯ͠ͳ͍Ϟσϧಉ࢜ͷൺֱ΋ෳ਺Ϟσϧͷ
    ൺֱ΋Մೳͱ͍͏ϝϦοτ
    
    
    • ͨͩ͠αϯϓϧαΠζ͕খ͍͞ͱAIC͸”too anti-conservative”ʹͳΔة
    ݥੑ΋͋ΔʢMatuschek et al., 2017, p.313ʣ
    ϞσϧΛཱͯͨํ๏
    มྔޮՌͷܾఆखॱʢforward approachʣ
    46
    ୳ࡧతͳΞϓϩʔνͳͲɼݻఆޮՌͷ਺͕ଟ͍৔߹ʹ͸Ϟσϧ
    ϑΟοτ͕޲্͢Δ΋ͷΛೖΕΔͱ͍͏ํ๏΋͋Δ
    ۩ମతͳํ๏͸Murakami (2016)ͷSupplementary Materials͕ࢀߟʹͳΓ·͢
    

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47. • “Model failed to converge…”ܥ΋”boundary (singular)
    f
    it:
    see ?isSingular”΋͖͞΄ͲͷཁྖͰมྔޮՌΛ୯७Խ͢Ε
    ͹ղܾՄೳ
    ϞσϧΛཱͯͨํ๏
    ϞσϧͷऩଋΤϥʔ໰୊
    47
    

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48. ϞσϧΛཱͯͨํ๏
    Ϟσϧબ୒ͷϓϩηεͷใࠂʢMeteyard & Davies, 2020ʣ
    48
    

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49. • ਪఆ஋ʢEstimateʣ
    
    
    • ඪ४ޡࠩʢSEʣ
    
    
    • ౷ܭྔʢz஋·ͨ͸t஋ʣ
    
    
    • p஋
    
    
    • มྔޮՌͷඪ४ภࠩ
    
    
    • σʔλϙΠϯτ਺
    
    
    • Ϟσϧࣜ
    ใࠂ͞ΕΔ΂͖͜ͱ
    49
    

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50. දͱͯ͠ใࠂ͞ΕΔ΂͖͜ͱ
    50
    มྔޮՌͷඪ४ภࠩ
    σʔλϙΠϯτ਺
    ਪఆ஋
    ਪఆ஋ͷඪ४ภࠩ
    ౷ܭྔ
    p஋
    Ϟσϧࣜ
    

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51. ࢲ͕͍ͭ΋ਅࣅ͢Δ΍ͭ
    Linck & Cunnings (2015)
    

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52. ࢲ͕աڈʹ࡞ͬͨ΋ͷ
    Tamura et al. (2019)
    

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53. Meteyard & Davies
    (2020) Supplementary
    Material
    ΋͏Ұͭͷྫ
    

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54. • ࠷΋؆୯ͳํ๏͸performanceύοέʔδʢLüdecke et al.,
    2021ʣͷར༻
    
    
    • r2(model)
    
    
    • conditional R2: ݻఆޮՌʴมྔޮՌ
    
    
    • marginal R2: ݻఆޮՌ෦෼ͷΈ
    
    
    • piecewiseSEM::rsquared()Ͱ΋ܭࢉՄʢ˞R 4.0.0Ҏ্ͷΈ
    ରԠʣ
    ใࠂ͞ΕΔ΂͖͜ͱ
    R2ͷࢉग़ํ๏
    54
    performanceύοέʔδʹ͸ଞʹ΋৭ʑؔ਺͋ΔͷͰ৮ͬͯΈ͍ͯͩ͘͞
    

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55. • con
    f
    int.merMod()ؔ਺Λར༻ʢlme4ύοέʔδ͕ϩʔυ͞
    ΕͯͨΒcon
    f
    int()Ͱಉ͡Ͱ͕͢statsύοέʔδͷ΋ͷͰ͸
    ͳ͍͜ͱΛ໌ࣔͯ͠·͢ʣ
    
    
    • ݻఆޮՌͷ৴པ۠ؒͷΈ -> ”parm = “beta_”Ͱࢦఆ
    ใࠂ͞ΕΔ΂͖͜ͱ
    ਪఆ஋ͷ৴པ۠ؒ
    55
    ਪఆ஋ͱ95%৴པ۠ؒΛ·ͱΊͯදʹ͢Δίʔυ͸͜ͷεϨου͕ࢀߟʹͳΓ·͢
    

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56. ใࠂ͞ΕΔ΂
    ͖͜ͱ
    • sjPlot::tab_model()
    
    
    • tab_model(model,
    show.stat = T, show.est =
    T, dv.labels = “Accuracy”)
    
    
    • ৴པ۠ؒͷਪఆํ๏͕
    con
    f
    int()ؔ਺ͷσϑΥϧ
    τʢpro
    f
    ileʣͱҧ͏
    ʢͬͪ͜͸Waldʣ
    ศརͳؔ਺
    By-subject slope
    By-item slope
    Φοζൺ͸
    f
    ixef(model)%>%exp()Ͱ΋ग़ͤ·͢
    By-subject intercept
    Within-group variance
    By-item intercept
    ࢀߟɿhttps://strengejacke.github.io/sjPlot/articles/tab_model_estimates.html
    ࢀՃऀͷ੾ยͱ܏͖ͷ૬ؔ
    ߲໨ͷ੾ยͱ܏͖ͷ૬ؔ
    ڃ಺૬ؔ܎਺
    

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57. • sjPlot::plot_model()
    sjPlotύοέʔδ͸ඳը΋͍͚Δ
    57
    ࢀߟɿhttps://strengejacke.wordpress.com/2017/10/23/one-function-to-rule-them-all-visualization-of-regression-models-in-rstats-w-sjplot/
    ࢀߟɿhttps://cran.r-project.org/web/packages/sjPlot/vignettes/plot_interactions.html
    

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58. ࠶ݱੑͷ֬อ
    58
    

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59. σʔλɼίʔυɼग़ྗ
    ݁Ռͷఏग़Λڧ͘ਪ঑
    59
    

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60. • ʢҰൠԽʣઢܗࠞ߹ޮՌϞσϧʹΑΔ෼ੳ͸෼ੳͷϓϩηε
    ͕ඇৗʹෳࡶ
    
    
    • ͜ͱ͹Ͱઆ໌͞ΕΔΑΓίʔυͱग़ྗݟͤͯ΋Β͏΄͏͕ཧ
    ղ͕༰қ
    
    
    • ίʔυ͚ͩ͡Όͳ͘ग़ྗ΋ݟͤͯ΄͍͠ʢίʔυ͚ͩͩͱ࣮
    ࡍͷ෼ੳͰͲ͏ͳͬͨͷ͔ҋͷதͳͷͰʣ
    
    
    • ʮ͑ɼ͡Ό͋εΫϦϓτͱRͷίϯιʔϧը໘Λίϐϖͯ͠
    ςΩετϑΝΠϧͱ͔Ͱ…?ʯ->͍΍͋͋͋͋͋͋͋͋͋͋͋
    ෼ੳͷʮཪଆʯΛݟͤͯ
    60
    

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61. R markdown
    
    
    ࢖͍·͠ΐ͏
    ೔ຊޠͰॻ͔Εͨ৘ใ΋΢Σϒʹΰϩΰϩస͕ͬͯ·͢ʂ
    61
    

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62. 5೥લͷࣗ෼φΠεʂ
    

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63. ւ֎ͷֶज़ࢽͰ͸…
    

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64. ౤ߘنఆΛΈΔͱ…
    64
    

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65. ౤ߘنఆΛΈΔͱ…
    65
    

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66. ࠃ಺Ͱ͸…
    

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67. • ओཁࠃ಺ࢽͷ౤ߘنఆʹ͸σʔλͷެ։౳ʹؔ͢Δهड़ͳ͠
    
    
    !Language Education and Technology
    
    
    !Annual Review of English Language Education in Japan
    
    
    !JACET Journal
    
    
    !Studies in Language Sciences
    
    
    !Second Language
    ࠃ಺ࢽͰ΋౤ߘنఆͷ੔උΛ
    67
    

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68. • ʮࢴ෯ͷ౎߹ʯ͸΋͏௨༻͠ͳ͍
    
    
    • શ෦ग़͢
    
    
    • ʮಗ໊Խʯͱ͍͏໰୊͸͋Δ͕…
    ࠃ಺ࢽͰ΋౤ߘنఆͷ੔උΛ
    68
    

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69. Open Science
    FrameworkʢOSFʣ
    
    
    ͕ศར
    69
    

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70. • https://osf.io/
    
    
    • ݚڀϓϩδΣΫτͷϚωʔδϝϯτʹศརͳػೳ͕࣮૷͞Ε
    ͨ΢ΣϒαΠτ
    
    
    • σʔλɾϚςϦΞϧͷެ։
    
    
    • ݚڀͷࣄલొ࿥
    
    
    • ϓϨϓϦϯτͷެ։
    
    
    • ݚڀऀಉ࢜ͷίϥϘʹ΋˕
    OSFͱ͸
    70
    

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71. OSFͰσʔλɾϚςϦΞϧͷެ։
    ಗ໊ͷURLΛ࡞੒͢Δ͜ͱ͕Մೳ
    71
    ๭ࢽ
    

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72. OSFͰσʔλɾϚςϦΞϧͷެ։
    ಗ໊ͷURLΛ࡞੒͢Δ͜ͱ͕Մೳ
    72
    ͜͜ʹνΣο
    ΫΛೖΕΔ
    

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73. OSFͰσʔλɾϚςϦΞϧͷެ։
    ಗ໊ͷURLΛ࡞੒͢Δ͜ͱ͕Մೳ
    73
    

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74. σʔλɼίʔυɼग़ྗ
    ݁ՌΛग़ͤ͹৭ʑղܾ
    74
    

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75. ·ͱΊ
    75
    

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76. • ʮϞσϦϯάʯͰ͋ΔҎ্“single correct way”͸ͳ͍
    
    
    • ݚڀ՝୊ʹ͋ͬͨํ๏Λબ୒͢Δ͜ͱ
    
    
    • બ୒ͨ͠ํ๏΍෼ੳͷաఔΛ໌Β͔ʹ͢Δ͜ͱ
    
    
    • σʔλɾίʔυɾग़ྗ݁Ռͷڞ༗Λ͢Δ͜ͱ
    ·ͱΊ
    76
    

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77. • Barr, D. J., Levy, R., Scheepers, C., and Tily, H. J. (2013). Random effects structure for con
    f
    irmatory hypothesis testing: Keep it maximal.
    Journal of memory and language, 68(3), 255
    –
    278.
    
    
    • Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015). Parsimonious Mixed Models. https://arxiv.org/abs/1506.04967v2
    
    
    • Brauer, M., & Curtin, J. J. (2018). Linear mixed-effects models and the analysis of nonindependent data: A uni
    f
    ied framework to analyze
    categorical and continuous independent variables that vary within-subjects and/or within-items. Psychological Methods, 23(3), 389
    –
    411.
    https://doi.org/10.1037/met0000159
    
    
    • Brysbaert, M., & Stevens, M. (2018). Power Analysis and Effect Size in Mixed Effects Models: A Tutorial. Journal of Cognition, 1(1), 9. https://
    doi.org/10.5334/joc.10
    
    
    • Burnham, K. P., & Anderson, D. R. (2004). Multimodel Inference: Understanding AIC and BIC in Model Selection. Sociological Methods &
    Research, 33(2), 261
    –
    304. https://doi.org/10.1177/0049124104268644
    
    
    • Frossard, J., & Renaud, O. (2019). Choosing the correlation structure of mixed effect models for experiments with stimuli. https://arxiv.org/
    abs/1903.10766v3
    
    
    • Gries, S. T. (2021). (Generalized Linear) Mixed-Effects Modeling: A Learner Corpus Example. Language Learning, 71(3), 757
    –
    798. https://
    doi.org/10.1111/lang.12448
    
    
    • Hou, X. (2021). Learning two syntactic constructions simultaneously: A case of overshadowing. Language and Cognition, 13(3), 467
    –
    493.
    https://doi.org/10.1017/langcog.2021.10
    
    
    • Matuschek, H., Kliegl, R., Vasishth, S., Baayen, H., & Bates, D. (2017). Balancing Type I error and power in linear mixed models. Journal of
    Memory and Language, 94, 305
    –
    315. https://doi.org/10.1016/j.jml.2017.01.001
    
    
    • Meteyard, L., & Davies, R. A. I. (2020). Best practice guidance for linear mixed-effects models in psychological science. Journal of Memory
    and Language, 112, 104092. https://doi.org/10.1016/j.jml.2020.104092
    
    
    • Murakami, A. (2016). Modeling Systematicity and Individuality in Nonlinear Second Language Development: The Case of English
    Grammatical Morphemes: Modeling Individual Nonlinear Development. Language Learning, 66(4), 834
    –
    871. https://doi.org/10.1111/lang.12166
    
    
    • RPubs—Reduction of Complexity of Linear Mixed Models with Double-Bar Syntax. (n.d.). Retrieved November 3, 2021, from https://
    rpubs.com/Reinhold/22193
    
    
    • RPubs—The Correlation Parameter in the Random Effects of Mixed Effects Models. (n.d.). Retrieved November 3, 2021, from https://
    rpubs.com/yjunechoe/correlationsLMEM
    
    
    • Schad, D. J., Vasishth, S., Hohenstein, S., & Kliegl, R. (2020). How to capitalize on a priori contrasts in linear (mixed) models: A tutorial.
    Journal of Memory and Language, 110, 104038. https://doi.org/10.1016/j.jml.2019.104038
    
    
    • Scherbaum, C. A., & Ferreter, J. M. (2009). Estimating Statistical Power and Required Sample Sizes for Organizational Research Using
    Multilevel Modeling. Organizational Research Methods, 12(2), 347
    –
    367. https://doi.org/10.1177/1094428107308906
    
    
    • Should we
    f
    it maximal linear mixed models? | R-bloggers. (2014, November 25). https://www.r-bloggers.com/2014/11/should-we-
    f
    it-maximal-
    linear-mixed-models/
    
    
    • ৽Ҫֶ, & Roland D. (2016). ݴޠཧղݚڀʹ͓͚Δ؟ٿӡಈσʔλٴͼಡΈ࣌ؒσʔλͷ౷ܭ෼ੳ. ౷ܭ਺ཧ, 64(2), 201
    –
    231.
    ࢀߟจݙ
    77
    

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