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Abstract

Over the last 30 years statistical algorithms have been developed to analyse datasets that have a hierarchical/multilevel structure. Particularly within developmental and educational psychology these techniques have become common where the sample has an obvious hierarchical structure, like pupils nested within a classroom. We describe two areas beyond the basic applications of multilevel modelling that are important to psychology: modelling the covariance structure in longitudinal designs and using generalized linear multilevel modelling as an alternative to methods from signal detection theory (SDT). Detailed code for all analyses is described using packages for the freeware R.
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A\b!A b_\[_AA_ bg:A_u A \__ A d_bA r\dYA\g $ !A8  \dYA\g8
!A8 A)g8 $ !^!8 Bs !d: _bAO r!A8 su YAA g p!2^!QA Y!A
\b\_! d! !d: 2!d :g \b\_! Y\dQu d_bA Y! \d[)\_ 2gA_!\gd
2A Y\2Y b!^A \ )AA \A: Jg g K A!bp_A !d: _bAO !__g
QAdA!_\A: _\dA! bg:A_ rs Y\2Y b!^A \ )AA \A: Jg g A2gd:
A!bp_Au
OO !d\A_ u \QY !d: !b!_! gd:gd
Y\ \ ! pA:!QgQ\2!_ p\A2Au Y\ \ Y  2g:A !d: gp !A \d2_:A: \d YA Au
g dA !\\2!_ pg2A:A !A :A2\)A:u A _gg^ ! g \!\gd8 2gbbgd \d
p2Yg_gQ8 !d: Yg Yg AAd\gd gJ YA !d:!: b_\[_AA_ bg:A_ pAAdA:
!)gA 2!d )A A: g !d!_A YA :!!u YAA !A _gdQ\:\d!_ :A\Qd !d: \dQ b_\[
_AA_ _gQ\\2 AQA\gd ! !d !_Ad!\A g bAYg: Jgb u
ju !bp_A fj E gdQ\:\d!_ :A\Qd7 Y\_: )\Y
A rjeees _gdQ\:\d!_ : gJ gbAd bAd!_ YA!_Y :\dQ !d: !JA
pAQd!d2 \ A: g \__!A A!b\d\dQ pg\)_A !\!d2AE2g!\!d2A 2Au
YAA AA Jg \bA pg\d r:\dQ pAQd!d28 j AA^8  AA^8 !d:  bgdY !JA
)\Ys !d: B gbAd \d g!_u A \__ _gg^ ! YA\ !d\A 2gA8 Y\2Y !dQA Jgb 
g j8 ! YAA Jg \bA pg\d7 !dj !d !d !d: !dOu AA !A YA !_A Jg
YA K JA 2!A rYA :Ap r:ApA\gds !\!)_A !A dg 2gd\:AA: YAAs7
gbA gJ YA !_A !A b\\dQ !d: !A _!)A__A:  \d YA :!! K_A rAuQu p!\2\p!d
f Jg YA : !d: OY A\gdsu YAA !A ! !\A gJ :\JJAAd bAYg: Jg :A!_\dQ
\Y b\\dQ !_A r\_A $ )\d8 s8 gJAd A\b!\dQ gbA !_A Jg A!2Y b\\dQ
!_Au YAA 2!d )A 2gbp!\gd!__ 2b)AgbA \Y !:\\gd!_ \Y\d[)]A2
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ru g Y\QYAsu g :gd_g!:  Qg g Yp72!du[pg]A2ugQ !d: Jg__g\dQ YA \d2\gdu d_bA
!d: _bAO 2!d )A \d!__A: !d: _g!:A: Jgb \Y\d  )7
\d!__up!2^!QAr2r_bAO8d_bAss8_\)!r_bAOs8 !d: _\)!rd_bAsu
gbA ^dg_A:QA gJ  \ !bA: rAd!)_A A !_u8 Bsu __ gJ YA 2g:A Jg dd\dQ YA !d!_A
\ gd Y\ p!pA A)\A rYp7uAu!2u^A:!duYbsu YA A!bp_A
:!! !A p! gJ YA :!_ p!2^!QA r\QY8 g8 $ ^!QA)AQ8 \d pAs Y\2Y 2!d )A
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p!dg :Apj :Ap :Ap :ApO !dj !d !d !dO
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O      L  
_\_AA_ bg:A__\dQ OOj
!ppg!2YA g :!! !d!_\u A2!A gJ Y\8 \d YA p! AA!2YA g_: Qg g QA!
_AdQY g \d2_:A !__ p!\2\p!d ! A!2Y A\dQ pY!A8 b!^A A Y! YA A\dQ
pY!A AA !__ ! YA !bA \bA8 !d: gJAd g_: Yg g p!\2\p!d \Y
\d2gbp_AA :!!u YA b_\[_AA_ !ppg!2Y g_A gbA gJ YAA 2gbp!\gd!_
:\JK2_\A )A2!A YA \d:\\:!_ bA!AbAd !A A!A: ! !d:gb_ !bp_A:
A_AbAd dAA: \Y\d YA \d:\\:!_ !d: ! !\!)_A Jg \bA 2!d )A A: \d YA bg:A_u
gd2Ap!_ :\JK2_\A \__ Ab!\d \Y YA b_\[_AA_ !ppg!2Y \J YA b\\dQ !_A
!A dg b\\dQ ! !d:gb8 ) YA 2gbp!\gd!_ bA!d Jg \d2_:\dQ \d2gbp_AA 2!A
!A !::AA:u
YA :!! AA pg\\A_ ^AA: Jg A!2Y !d\A !\!)_A ru8 ue8 juj8 !d: uej8
Jg !dj g !dOsu YA bg:A_ \d Y\ A!bp_A !bA Y! YA A\:!_ !A dgb!__
:\\)A:u Y\_A Y!\dQ dgb!__ :\\)A: ApgdA !\!)_A :gA dg \bp_ Y!
YA A\:!_ \__ )A dgb!__ :\\)A: rdg \2A A!s8 \ ! YA 2!A YAA !d:
YAAJgA A !dJgbA: YA !\!)_Au AA!_ !dJgb!\gd AA \A: !d: YA
z!A gg gJ YA !\!)_A p_ uL ! A:u A !dj hbbbbbbbbbbbbbbbbbbbb
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!d 9[ zr!d |uLs !dO 9[ zr!dO |uLs
YA dA ^AdA !_A !A7 ruj8 uj8 u8 !d: uju
YA db)A gJ gbAd 2gbp_A\dQ A!2Y !A AA Lj8 OO8 je8 !d: j8 !d:
YA bA!d ! YAA \bA AA7 uLe uje ue !d: ujO8 ApA2\A_u gbp_AA :!!
!A !!\_!)_A Jg gd_ j gJ YA B gbAdu  bAd\gdA: !)gA8 \Y YA
!:\\gd!_ !ppg!2Y b\\dQ !_A b )A :A!_ \Yu YA g \bp_A !ppg!2YA
Jg :A!_\dQ \Y b\\dQ :!! !A7 A2_:A \d2gbp_AA 2!A !d: 2!_2_!A bA!A
Jg !__ p!\ \Y :!!u YA dA Ap \d !d!_\dQ YAA :!! Yg_: )A g _gg^ ! YA
A_!\gdY\p )AAAd p!\ gJ YAA !\!)_A8 )gY Q!pY\2!__ !d: dbA\2!__u
\QA j Yg YA 2!Ap_g8 YA Y\gQ!b8 !d: \d YA ppA \!dQ_A YA
2gA_!\gd !d: YA\ eLt 2gdK:Ad2A \dA!_u YA 2g:A Jg \QA j Jg__g YA
A!bp_A Jg p!\ gd YA  YA_p J!2\_\u gb \QA j8 \ \ 2_A! Y! YA !d\A
2gA !A !__ pg\\A_ A_!A:u
!)_A j Yg YA 2gA_!\gd )AAAd :!! ! YA Jg \bA pg\d \d YA _gA
\!dQ_A8 YA 2g!\!d2A \d YA ppA \!dQ_A8 !d: YA !\!d2A !_gdQ YA :\!Qgd!_u YA
_AJ \:A gJ YA !)_A Yg YA !_A gd_ Jg p!\2\p!d \Y 2gbp_AA :!! !d: YA
\QY \:A Jg !__ p!\\A 2gbp_AAu YA A_!\gdY\p )AAAd 2g!\!d2A8 2gA_!\gd8
!d: !\!d2A \ \bp_A !d: \ \bpg!d Jg d:A!d:\dQ  gpu YA 2g!\!d2A
)AAAd !\!)_A !d: \7 2g h::2g u d  YA 2gA_!\gd !d: 2g!\!d2A
!)_A 2!d )A 2gb)\dA: \dg ! \dQ_A !)_A8 _\^A !)_A j8 \Y7
!d! 9[ 2)\d:r!dj8!d8!d8!dOs
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2g!d 9[ 2gr!d!8A h}2gbp_AAug)}s
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r2g!ds'2g!d
2g!d 9[ 2gr!d!8A h}p!\\Au2gbp_AAug)}s
2g!d 9[ 2gr!d!8A h}p!\\Au2gbp_AAug)}s
2b! 9[ ppAu\r2g!d8:\!Q hs'2g!d |_gAu\
r2g!ds'2g!d
p\dr2)\d:r2b!j82b!s8:\Q\ hs
OO !d\A_ u \QY !d: !b!_! gd:gd
YAA !A ! JA Y\dQ g dgA Jgb !)_A ju \8 YA 2gA_!\gd !A !__ )!d\!_ !d:
pg\\Au A2gd:8 YA 2gA_!\gd Ad: g )A _\QY_ Y\QYA YAd YA !\!)_A !A
dA!A \d \bA rJg YA p!\\A 2gbp_AA :!!7 uO uLO uj8 Jg gdA Ap !! 2gbp!A:
\Y uOL uOe8 Jg g Ap !! !d: uO Jg YAA Ap !!su d b!d 2gA_!\gd
b!\2A YAA :\JJAAd2A !A bgA pgdgd2A:8 ) \ \ \__ gY A!b\d\dQ \J Y\
p!Ad Yg_: )A !^Ad \dg !22gd YAAu
\QA ju 2!Ap_g r_gA \!dQ_As8 Y\gQ!b r:\!Qgd!_s8 !d: 2gA_!\gd rppA \!dQ_As Jg
A rjeees :!!u __ p!\\A 2gbp_AA :!! !A \d2_:A:u
!)_A ju YA 2gA_!\gd r_gA \!dQ_As8 !\!d2A r:\!Qgd!_s8 !d: 2g!\!d2A rppA \!dQ_As Jg YA
Jg !A gJ :!! Jg !d\A Jgb A rjeees
2_:A \d2gbp_AA __ p!\\A :!! \d2_:A:
!dj !d !d !dO !dj !d !d !dO
!dj uB uOj uL u uB uO uB u
!d uO uej uOB uOj uO ueO uOe uO
!d uO uL u uO uOL uLO uB uL
!dO uOO uOB u uB uO uOe uj uB
_\_AA_ bg:A__\dQ OO
_YgQY Y\ \ dg ! b_\[_AA_ :!!A pA A8 AA!2YA dg gJAd 2gd2Ap!_\A
ApA!A: bA!A :!! ! b_\[_AA_8 !d: A b_\[_AA_ !_Qg\Yb g 2\2bAd gbA
gJ YA pg)_Ab gJ YA !d:!: ApA!A: bA!A  r\dQA $ \__A8 su YA
K Ap \ A2\dQ YA :!!A g Y! YAA \ ! \dQ_A ApgdA !\!)_A8 !d8 !
A\gd !\!)_A 2!__A: A\gd8 !d: ! p!\2\p!d db)A r2!__A: p!dgsu
!d 9[ 2r!dj8!d8!d8!dOs
A\gd 9[ Aprj7O8A!2Y h_AdQYr!djss
p!dg 9[ Aprp!dg8Os
YA b\\dQ !_A AA !_g AbgA:u d  Y\ \ :gdA )7
:A!2Yr!As
!A 9[ d!ugb\r:!!uJ!bArp!dg8A\gd8!dss
brp!dgs brA\gds br!ds
!!2Yr!As
AA !A YA K JA _\dA Jg YAA :!!7
YAA !A gYA ! g A2A YA :!!u d gbA p!2^!QA YAd 2A!\dQ !
dA b_\[_AA_ 2A YA g\Q\d!_ !\!)_A g_: dg _gdQA )A !2\Au AA YA
!A8 g !dj \__ A\u Y\ \ Y p!dg ! A: !YA Y!d p!dg8 !d: Y
YA AbgA Jd2\gd rbs ! A: g 2_A!d[p YA g^\dQ Ad\gdbAd rgYA
!\!)_A 2g_: !_g )A AbgA:su g  !\\2 Jd2\gd !__g Jg YA \d2_\gd g
A2_\gd gJ b\\dQ !_A8 ) YAA !__  AA AbgA: \Y YA d!ugb\ Jd2\gdu
YA dA :!! K_A !A Y! ejL _\dA Jg YA ejL !d\A bA!AbAd
r\uAu Lj |OO |je |jsu
YA b!\d )!d\A zA\gd \d A rjeees ! !)g :\JJAAd2A \d !d\A !
YA :\JJAAd pg\d \d \bA !d: Yg YAA A_!A g gYA J!2gu AA A 2gd2Ad!A
gd Kd:\dQ ! Qgg: 2gA_!\gd 2Au gbA\bA AA!2YA !A pA2\K2!__
\dAAA: \d YA 2gA_!\gd !bgdQ !\!)_A8 ) !d g)\g zA\gd \ YAYA
2Ygg\dQ ! Qgg: 2gA_!\gd 2A b!^A ! :\JJAAd2A Jg A\b!\dQ YA KA: AJJA2u
YA Yg !dA \ Y! \ !__ :gA dg QA!_ !JJA2 YA A\b!A gJ YA KA:
AJJA28 ) \ gJAd !JJA2 YA pA2\\gd gJ YAA A\b!Au YAAJgA8 \ \ \bpg!d g
Ap_gA \J 2gdK:Ad2A \dA!_ g p!_A !A g )A ApgA:u
!A.j78/
p!dg A\gd !d
j  j juBBe
  j juLBjje
 O j uLOeLj
Q_ E QAdA!_\A: _A! z!A Jgb d_bA _\)! r\dYA\g $ !A8 s
Q_rAp! 82g!\!A8 A\QY h!\!d2A Jd2\gd8
2gA_!\gd h2gA_!\gd 2As
!bp_A !\!d2A !d: 2gA_!\gd Jd2\gd r!_g !!\_!)_A Jg _bAs7
!:AdrJgb h8j]ApA!A: bA!As
2gjrJgb h8j]_AA_s
OOO !d\A_ u \QY !d: !b!_! gd:gd
 \ dA2A! g A!b\dA )gY YA !\!d2A gJ YA \d:\\:!_ bA!A !d: YA
2gA_!\gd !bgdQ YA bA!Au A \__ A YA Q_ Jd2\gd Jgb d_bA r\dYA\g $
!A8  \dYA\g A !_u8 Bs8 !d: YAd \dQ Y\ Jd2\gd YAA g J!2A
r!\!d2A !d: 2gA_!\gds !A 2gd\:AA: Ap!!A_ \dQ YA A\QY !d: YA
2gA_!\gd gp\gdu YA d_bA p!2^!QA Y! AA!_ )\_[\d !\!d2A !d: 2gA_!\gd
2Au g YA !\!d2A Ab8 YA 2!d !__ )A Az!_ r!bA YgbgQAdA\s8 !__ )A
:\JJAAd \Y dg p!\2_! A_!\gdY\p !bgdQ YAb rd2A: YAAgQAdA\s8 )A
! Jd2\gd gJ YA \bA A\A rAuQu !\!d2A 2_gA \d \bA bgA \b\_!s8 g )A ! Jd2\gd
gJ gYA !\!)_A rAuQu !\!d2A ! Jd2\gd gJ pA:\2A: !_Asu
\b\_!_8 YA !\!)_A 2!d )A !bA: g )A d2gA_!A: ! \d ! )AAAd[)]A2
:A\Qd8 Y!A Az!_ 2gA_!\gd8 !__ Y!A :\JJAAd 2gA_!\gd \Yg !d p!\2_!
p!Ad8 g ! !\A gJ 2gA_!\gd 2Au g gJ YA 2A \d Y\2Y
p2Yg_gQ\ g_: )A \dAAA: 2gbA \Y d_bA8 ) YA A 2!d 2gd2
YA\ gd r\dYA\g A !_u8 Bsu YA bg 2gbbgd p!Ad Jg _gdQ\:\d!_ :\A \
K g:A !gAQA\A rjs YAA YA 2gA_!\gd A!:\_ :A2A!A \Y :\!d2A
Jgb YA b!\d :\!Qgd!_u !)_A  Yg YA p!Ad gJ !d:!: :A\!\gd !d:
2gA_!\gd Jg gbA gJ YAA bg:A_ r!bA: 2g!\!d2A 2!d )A 2!_2_!A: \dQ
2g h::2gsu
YA :AJ!_ 2gd! Jg !d g:AA: !\!)_A rA\gds !A pg_dgb\!_ r_\dA!8
z!:!\28 A2us !d: YAA \__ )A A: Jg YA KA: p! gJ YA bg:A_u YA :AJ!_
A\b!\gd pg2A:A Jg YAA bg:A_ \ A\2A: b!\bb _\^A_\Ygg: rs !d:
Y\ \__ )A A: Jg Y\ A!bp_Au YA b!\d !_Ad!\A \ b!\bb _\^A_\Ygg: rA
bAYg: hsu AA \ YA 2g:A Jg YAA j bg:A_u YA bg:A_8 b\]8 2gApgd:
g YA \Y g !d: ]Y 2g_bd gJ !)_A u YA gd_ :\JJAAd2A )AAAd YA K KA !d:
YA _! KA bg:A_ \ YA !d:!: :A\!\gd !A !__gA: g :\JJA \d YA _!A bg:A_u
bjj 9[ Q_r!d 8!ug:AA:rA\gdss
bj 9[ Q_r!d 8!ug:AA:rA\gds8
2gA_!\gd h2ggbpbbrJgb h8j]p!dgss
bj 9[ Q_r!d 8!ug:AA:rA\gds8
2gA_!\gd h2gjrJgb h8j]p!dgss
bjO 9[ Q_r!d 8!ug:AA:rA\gds8
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gY :jrL88O8Ls !d: :rL88O8Ls pg:2A :hjBL !d:
hLu \2g\!__8 \QA  Yg YAA !_Au
YAA g bAYg: !A Az\!_Ad Jg 2!_2_!\dQ :!d: 8 g \J YAA !\\2 !A !__
Y! \ dAA:A: YAd A\YA 2!d )A A:u \dQ : !__g !22A g gYA \dJgb!\gd8 g
\J bb!rbg:A_s ! Ab)A::A: \d : YAd \ g_: Yg Y!8 Jg A!bp_A8 YA
!d:!: Ag gJ :Jg YAA :!! \ uOu YA MA\)\_\ gJ \dQ YA Q_b Jd2\gd bA!d
Y! gYA bAYg: 2!d !_g )A A:u d bA:\2\dA8 YA _gQ\\2 bg:A_ \ bgA 2gbbgd Y!
Y!d YA !\!ddgb!_ bg:A_ r Yg8 )2Yg^\8 $ 2_\Y8 su Y\ 2!d )A
Jgd: ) 2Y!dQ\dQ : g Y! \ A YA :AJ!_ J!b\_ h)\dgb\!_ _\d^ Jd2\gd8
YA _gQ\u YA 2gAJK2\Ad gJ \dAA Jg YA _gQ\\2 bg:A_ \ YA _gQ gJ YA g::
!\g8 _drsu gd2Ap!__8 _drs 2!d )A YgQY gJ \d ! A \b\_! ! g :u Y\_A
:hSY\ !A7rSJ!_A !_!b !A78 _drs h_drg:: gJ ! Y\s r_drg:: gJ ! J!_A
!_!bsu d !ppg\b!A A_!\gdY\p )AAAd YAb \ _dS7Oj:8 !d: Y\ Yg_:
A2Ap YAd :\ A\YA A _!QA g A b!__ r\uAu ]:]`Osu g YA A!bp_A !)gA8
_dS7 h j Y\2Y \ !)g ju \bA YA g)AA: :u A \__ A YA _gQ\\2 bg:A_
)A2!A Y! \ YA d!!_ _\d^ Jd2\gd Jg YA )\dgb\!_ :\\)\gd rgJJb!dd8 Osu
dgYA ! \d Y\2Y YA  !ppg!2Y \ MA\)_A \ Y! pA:\2g !\!)_A Y\2Y
! \!_[)[\!_8 _\^A 2gdK:Ad2A g ApgdA \bA8 2!d )A \d2_:A: \Y\d YA bg:A_u
\QA u  p\2g\!_ ApAAd!\gd gJ :hjBL !d: hL Jg YA Az!_ !\!d2A dgb!_ \Qd!_
:AA2\gd YAg bg:A_u
OOB !d\A_ u \QY !d: !b!_! gd:gd
Y\ \ :\JK2_ g :g \Y YA !d:!: !ppg!2Y g u YA dgb \Y\d bg bAbg
A2gQd\\gd AA!2Y \ g 2!_2_!A :rg gYA bA!As Jg A!2Y p!\2\p!d8
gbA\bA Ap!!A_ Jg :\JJAAd \Y\d[)]A2 2gd:\\gd8 !d: 2gbp!A YAA
!QQAQ!A bA!Au dA gJ YA b!\d !QbAd Jg b_\[_AA_ bg:A__\dQ \ g bgA
!! Jgb !d!_\dQ !QQAQ!A _AA_ :!! _\^A YAAu
d Y\ A!bp_A YA Jd2\gd _bA \ A: !YA Y!d _bA g Q_ )A2!A _bA
!__g QAdA!_\A: _\dA! b_\[_AA_ bg:A__\dQu _bA ! dg A: \d YA _! A!bp_A
)A2!A \ :gA dg Y!A )\_[\d 2g!\!d2A 2Au g _bA YA !d:gb AJJA2 !A
p_!2A: \Y\d YA bg:A_u Y8 bj Jgb YA K A!bp_A 2g_: )A \Ad !7
_bAr!d 8!ug:AA:rA\gds |rj]p!dgss
YA gp \ _\QY_ :\JJAAd )A2!A :\JJAAd A\b!\gd pg2A:A !A A:8 )
YA )!\2 bg:A_ !A Az\!_Adu
\Y _bA Jg 8 b!\bb[_\^A_\Ygg: A\b!A gJ YA p!!bAA !A Jgd:
\Y !d \A!\A pg2A:Au YA _bAO b!d!_ _\ YAA !ppg\b!\gd bAYg:
r!A8 su d g:A gJ YA\ _AA_ gJ !22!2 !d: YA\ 2gbp!\gd \bA8 YAA !A7
pAd!_\A: z!\[_\^A_\Ygg: rs !p_!2\!d !ppg\b!\gd r!p_!2As !d: !:!p\A
!\!d z!:!A !ppg\b!\gd rsu !A A2gbbAd: \dQ !p_!2A8 g \ \
A: YAAu A!\_ gJ _bAO !A \d !A r8 Yp72!du[pg]A2ugQA)p!2^!QA
_bAO\QdAAbp_AbAd!\gdup:Jsu
A )AQ\d \Y ! \bp_A A!bp_A YAA !:\\gd!_  2g_: !_g )A A:7 Yg\dQ
Y! Y\A pAgp_A Y!A )AA A2gQd\\gd bAbg Jg Y\A J!2A Y!d Jg )_!2^ J!2Au
A YAd !:: \d ! 2gd\dg pA:\2g !\!)_A Y! !\A ) \!_8 YA _gQ gJ YA
ApgdA \bAu YA :!! !A Jgb YA Y\A dQ_\Y p!\2\p!d gJ \QY8 g:8 !d:
A:g rsu
_bA E rQAdA!_\A:s _\dA! b\A: AJJA2 AQA\gd Jgb _bAO _\)! r!A8 s
_bArAp! 82g!\!A |r!d:gb !\!)_A ]_AA_s8
J!b\_ h)\dgb\!_r_\d^ h}_gQ\}ss
YA :AJ!_ J!b\_ \ !\!d \Y \:Ad\ _\d^ Jd2\gdu A J!b\_ h)\dgb\!_ Jg
_gQ\\2 AQA\gdu
g :gd_g!: :!!7
bAbA2 9[ A!:u!)_Ar
}Yp7uAu!2u^A:!dbAbA2u:!}8YA!:Ahs
g
_\)!r:!_s
YAd
!!2YrbAbA2s
_\_AA_ bg:A__\dQ OOe
YA :!! !A \d bAbA2u YA !\!)_A !A7 J!2A !g_: J!2Ag_:
J!2AY\A _d\bA !d: p!dgu \QA  Yg YA JAzAd2 gJ g_: ApgdA \d
YA :\JJAAd 2gd:\\gdu YA pgpg\gd gJ Y\ \ !)g YA !bA Jg Y\A !d: )_!2^
J!2A8 ) YA db)A gJ J!_A !_!b \ b2Y QA!A Jg )_!2^ J!2Au Y\ \ 2gd\Ad
\Y YA bAbg _\A!A rg $ \QY8 Bsu
YA bg:A_ g A Jg Y! \ 2!__A: YA gd !2A )\! 2gbp!A bg:A_j !d:
bg:A_ )A_gu bg:A_j \d2_:A YA b!\d AJJA2 Jg YAYA YA J!2A ! pA\g
Ygd rJ!2Ag_:8 Y\2Y bA!A !22!2s8 Yg b!d gJ YAA AA Y\A J!2A
rJ!2AY\As8 !d: \ !__g YA \dA2Ap g ! Jg pAgp_Au d  Ab\dg_gQ
Y\ 2gApgd: g pAgp_A Y!\dQ :\JJAAd ApgdA 2\A\!u d !\\2!_ dg!\gd \ \7
_gQ\Spg!g_:\] 7 h |j J!2AY\A\] | J!2Ag_:\] |]|A\]
YAA YA A
\]
!A !bA: g )A )\dgb\!__ :\\)A: !d: YA
]
!A !bA: g )A
dgb!__ :\\)A:u d  Y\ \7
bg:A_j 9[ _bAr!g_: 8J!2AY\A |J!2Ag_: |rj]p!dgs8
J!b\_ h)\dgb\!_8 bAYg: h}!p_!2A}s
\\dQ bb!rbg:A_js pg:2A !\\2 Jg YA gA!__ K gJ Y\ bg:A_
!d: YA \d:\\:!_ 2gAJK2\Ad A\b!A7 hree jhrLj h !d:
!S]7 h ju A 2!d 2gd2_:A Y! pAgp_A ! g_: bgA g )_!2^ J!2A !d: g \Ab
Y! !A g_:u gY gJ YAA AJJA2 !A A\:Ad Jgb \QA u
bg:A_ !:: YA \dA!2\gd )AAAd YA g pA:\2g !\!)_A g \ A YAYA
!22!2 :ApAd: gd YAYA YA J!2A ! Y\A g )_!2^u YA p:!A Jd2\gd \
2gdAd\Ad Jg \d2AbAd!__ )\_:\dQ bg:A_u
\QA u YA pg)!)\_\ gJ !d g_: ApgdA Jg YA :!! Jgb Y\A dQ_\Y p!\2\p!d \d \QY
A !_u rsu
bg:A_ 9[ p:!Arbg:A_j8u 8u|J!2AY\A7J!2Ag_:s
!dg!rbg:A_j8bg:A_s
J   _gQ\^ Y\z Y\ :J r`Y\zs
bg:A_j O OLLuO OeuL rju
bg:A_ L Ou OLu rjuj LuL j ueA re'''
OL !d\A_ u \QY !d: !b!_! gd:gd
YA gd !2A )\! \ g)AA:8 MSj7 h L8 p9ju !\2\p!d AA bgA
!22!A Apgd:\dQ g Y\A J!2Au YA 2gAJK2\Ad Jg YAYA gbAY\dQ !
pA\g_ Ygd rYAA J!2Ag_:s bA!A :\2\b\d!)\_\ r! bA!A gJ bAbgs
!d: \dA!2\gd )AAAd Y\ !d: gYA !\!)_A Yg YAYA YAA gYA !\!)_A
bg:A!A !22!2u YA KA: AJJA2 Jg bg:A_ 2!d )A Jgd: A\YA ) p\dQ bg:A_
rY\2Y pg:2A YA KA: AJJA2 !d: ! _g gJ gYA gps g ) KAJrbg:A_su
YA A\b!A: p!!bAA Jg J!2Ag_: \ juLu Y\ A\b!A _drs
)_!2^
u YA
\dA!2\gd ! ju8 g YA A\b!A gJ _drs
Y\A
\ jL |j hLeu YA pg)\
bg:A_ 2!d !_g )A A: !d: YA b_\[_AA_ A\b!A Jg :
)_!2^ !d: :
Y\A ) \dQ YA
pg)\ _\d^u
YA A\b!A: !_A Jg :
)_!2^ \ ue !d: Jg :
Y\A \ e |Le hjLu g\2A Y!
YA _dS7Oj:!ppg\b!\gd Yg_:u
J A Y!: 2!_2_!A: _drs !d: :Ap!!A_ Jg A!2Y \d:\\:!_ Jg A!2Y !2A8 YA
bA!d gJ YAA g_: )A _dS7)_!2^ hje8 _dS7Y\A hLO8 :
)_!2^ hj8 !d:
:
Y\A hu g\2A Y! YAA !_A !A A :\JJAAd Jgb YgA Jgd: \Y YA
b_\[_AA_ bg:A_ Jg Y\A J!2A !d: Y! YA _dS7Oj:!ppg\b!\gd :gA dg
Yg_: Jg YA Y\A J!2A rLOj hsu Y\ \ )A2!A gbA \d:\\:!_ Y!:
AAbA_ Y\QY !_A Jg YAA rb!d :`Os !d: Y! YA bA!d \ dg ! g) !\\2u
YA t \b bA!d !A7 _dS7)_!2^ hjO _dS7Y\A h :
)_!2^ hj !d:
:
Y\A hju YA !ppg\b!\gd dg Yg_: !d: YAA !_A !A 2_gA g YgA Jgd:
\Y YA b_\[_AA_ !ppg!2Yu
 \ gY Ap_g\dQ \J p!\2\p!d !22!2 !\Au Y\ 2!d )A :gdA ) 2Y!dQ\dQ
YA !d:gb p! gJ YA bg:A_ g rJ!2Ag_:]p!dgsu Y\ !:: )gY ! Ab Jg YA
!\!d2A gJ !22!2 !d: YA 2g!\!d2A )AAAd !22!2 !d: Apgd:\dQ g_:8 !d:
YAAJgA YAA \ !d \d2A!A gJ g :AQAA gJ JAA:gb \d YA bg:A_u d2_:\dQ Y\
Ab \d2A!A YA K gJ YA bg:A_8 MS7 h jLe8 phu  2!d )A \Ad \Y YA
Jg__g\dQ !d: 2gbp!A: \Y bg:A_u YA :\JJAAd2A \ !\\2!__ \Qd\K2!d8
MS7 h jLe8 ph8 !_YgQY YA  !_A \ \d2A!A:u
p g Y\ pg\d !:\\gd!_  2g_: Y!A )AAd A: g A!2Y YA !bA )!\2
2gd2_\gd8 pg\:\dQ 2!A ! !^Ad g A g) A\b!gu YA dA Ap \dg_A
!::\dQ ! 2gd\dg !\!)_A Y\2Y !\A ) \!_7 YA _gQ gJ YA ApgdA \bA
KAJrbg:A_s
rdA2Aps J!2AY\A J!2Ag_: J!2AY\A7J!2Ag_:
ru rjuBB juLLe jujB
bg:A_! 9[ p:!Arbg:A_8 J!b\_ h)\dgb\!_r_\d^ hpg)\ss
KAJrbg:A_!s
rdA2Aps J!2AY\A J!2Ag_: J!2AY\A7J!2Ag_:
ruOjejL ruLje ueLB uLeBBL
bg:A_) 9[ _bAr!g_: 8J!2Ag_:'J!2AY\A |rJ!2Ag_:]p!dgs8
J!b\_ h)\dgb\!_8bAYg: h}!p_!2A}s
!dg!rbg:A_8bg:A_)s
:J   _gQ\^ Y\z Y\ :J r`Y\zs
bg:A_ L Ou OLu rjuj
bg:A_)  Oju OLLu rjeeuB juLe ujBOO''
_\_AA_ bg:A__\dQ OLj
r_d\bAsu YA YAgA\2!_ zA\gd \ !)g YA A_!\gdY\p )AAAd ApgdA \bA
!d: !22!2 Jg YA :\JJAAd J!2Au 2Y AA!2Y Yg z\2^A ApgdA Ad: g )A
bgA !22!A8 ) YA A!2 A_!\gdY\p \ d2_A! rA)A8 AA8 A__8 Abb_A8 $
A!8 Osu  zA\gd \ YAYA YA A_!\gdY\p \ \b\_! Jg g_: !d: dA J!2A8
!d: Y\A !d: )_!2^ J!2Au
YA b!\d AJJA2 gJ \bA ! dgd[\Qd\K2!d8 MSj7 h B8 ph8 ) \ A!\dA: !
\dA!2\gd \d2_:\dQ Y\ Ab !A !::A: g YA bg:A_u YA )A bg:A_ \d Ab gJ 8
8 !d: \Qd\K2!d2A A8 \d2_:A gd_ !::\dQ YA \dA!2\gd )AAAd _d\bA !d:
J!2Ag_:7 \bpgAbAd MSj7 h LO8 p9ju
YA 2gAJK2\Ad Jg Y\ bg:A_ !A7
YA 2gAJK2\Ad !g2\!A: \Y YA J!2Ag_:7_d\bA \dA!2\gd \ dAQ!\A !d:
YAAJgA !22!2 :A2A!A \Y \d2A!A: ApgdA \bAu YA _!2^ gJ gYA \dA[
!2\gd \bpg\dQ YA bg:A_ Yg Y! YA A_!\gdY\p )AAAd \bA !d: !22!2 \
\b\_! Jg Y\A !d: )_!2^ J!2Au
d \QA O YA pg)!)\_\ gJ ! 2gA2 ApgdA ) YAYA YA J!2A ! dA
rYAA \ \ ! pg)!)\_\ gJ! 2gA2 A]A2\gds g g_: rYAA\ \ ! pg)!)\_\ gJ ! Y\s !d:
YA !2A gJ YA J!2A \ p_gA: \Y ApgdA \bAu A 2!_2_!A: YA pA:\2A: pg)!)\_\\A
\dQ YA A\b!A !)gA !d: !dJgbA: YA pA:\2A: !_A \Y ASj|A78
YA \dAA gJ YA _gQ\ !dJgb!\gdu A YAd 2Y!dQA: YAA pA:\2A: !_A g j b\d
YAbA_A Jg dA J!2A8 g Y! YA pg)!)\_\\A AA Jg 2gA2 ApgdAu
bg:O 9[ruLj |J!2Ag_:'juj |J!2AY\A'rju |_d\bA
'uB |J!2Ag_:'J!2AY\A'uee |J!2Ag_:'_d\bA'rjuL
pA:pg) 9[ Aprbg:Osrj |Aprbg:Oss
\QYpg) 9[ pA:pg)'J!2Ag_: |rj rJ!2Ag_:s'rj rpA:pg)s
Y\ Yg Y! !JA 2gdg__\dQ Jg ApgdA \bA YA pg)!)\_\ gJ 2gA2 ApgdA \
Y\QYA Jg dA Y\A J!2Au
bg:A_ 9[ p:!Arbg:A_)8u 8u|_d\bAs
!dg!rbg:A_)8bg:A_s
:J   _gQ\^ Y\z Y\ :J r`Y\zs
bg:A_) Oju OLLu rjeeuB
bg:A_ B OjLuO OuO rjeeu uBj j uLee
bg:A_O 9[ p:!Arbg:A_8u 8u|_d\bA7J!2Ag_:s
!dg!rbg:A_8bg:A_Os
:J   _gQ\^ Y\z Y\ :J r`Y\zs
bg:A_ B OjLuO OuO rjeeu
bg:A_O e Oue Ojeu rjuL LuOe j OuOjA rj'''
KAJrbg:A_Os
rdA2Aps J!2Ag_: J!2AY\A
ruLjOjj juL rjuLOO
_d\bA J!2Ag_:7J!2AY\A J!2Ag_:7_d\bA
uBLBLO ueeOejeO rjuLjj
OL !d\A_ u \QY !d: !b!_! gd:gd
YAA !A AA!_ gYA AAd\gd g YA b_\[_AA_  Y! 2!d )A Ap_gA:8
\d2_:\dQ A gJ YA !\!d2A2g!\!d2A b!\ ! A!2Y _AA_ gJ YA bg:A_8 ! :\2A:
\Y YA K A!bp_Au  \ !_g gJAd gY A!b\d\dQ YA \A gJ !rA
\]
s g AA \J YAA
\ bgA g _A !\!\gd Y!d pA:\2A: Jgb YA )\dgb\!_ :\\)\gd rgdA8
)!b!d\!d8 gdA8 $ g_:A\d8 L \QY8 jeesu Y\ \ ApgA: \Y YA
bb! \dJgb!\gd !d: Jg YAA :!! \ \ A \b\_! g Y! pA: \2A: ) YA )\dgb\!_
:\\)\gdu dgYA AAd\gd \ g bg:A_ bgA MA\)_A A_!\gdY\p \dQ b_\[_AA_
QAdA!_\A: !::\\A bg:A_ rAA gg:8 8 Jg :A!\_8 !d: !_g Q8 !pAdA8
g_:A\d8 $ !)!Y8 su gg: rs Y! \Ad ! pA2\!_\ p!2^!QA \Y\d  g
d YAA8 ) \ 2!d !_g )A :gdA \Y YA ) Jd2\gd Jgb YA p_\dA _\)!u ) \ !
[p_\dA Y\2Y \ ! A gJ pg_dgb\!_ _\d^A: gQAYA bggY_ ! ^dg rAA gg:8 8
Jg bgA :A!\_su YA Jg__g\dQ bg:A_ !__g YA A_!\gdY\p )AAAd ApgdA \bA
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gJ :AA2\dQ gYA AJJA2u Y\ \ ! b_\[_AA_ Q!b2g! r\QY $ gd:gd8 esu
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_\_AA_ bg:A__\dQ OL
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g_: ApgdA Jg gbA J!2A Y!d Jg gYAu
uju bb! E Abg A2gQd\\gd
Y\_A !:\\gd!_ bAYg: Jgb  !A gJAd A: Jg bAbg A2gQd\ \gd :\A8 YA
pAAd g :\JK2_\Au \8 YA !A !__ :gdA ) 2!_2_!\dQ bA!A r_\^A :s Jg
A!2Y \d:\\:!_ !d: YAd \dQ YAA !QQAQ!A bA!A \d !d!_\u _\A8
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A!gd Jg b_\[_AA_ bg:A__\dQu A2gd:8 \J \dAAA: \d ! 2g!\!A Y\2Y 2!d !^A
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A!2Y pAgd Jg A!2Y )\du Y\ 2!d 2A!A _g gJ pg)_Ab p!\2_!_ YAd YAA !A
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YA \d:\\:!_ )\d 2!d )A d!)_Au
YA b_\[_AA_ bg:A__\dQ !ppg!2Y \ A__ \A: g gA2gbA YAA pg)_Abu
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 r\d p!\2_! _gQ\\2 AQA\gd8 !_YgQY _\d^ hpg)\ 2g_: )A A:
YgQYg Y\ A2\gds Jg !d!_A8 A!\dQ \!_ ! dAA: \Y\d p!\2\p!du
_YgQY b_\[_AA_  Y!A )AAd A: \Y bAbg A2gQd\\gd :!! Jg b!d
A! rAuQu \QY $ 2!\:8 jees8 YA !A \__ dg A 2gbbgdu Y\_A  Y! !
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\ _\^A_ Y! YA MA\)\_\ gJ YA !ppg!2Y A: YAA \__ bA!d b_\[_AA_ bg:A_
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!:!d!QA Y! AA!2YA 2!d A bgA !\!)_A Y! :\JJA ) \!_ \Y\d YA\
:A\Qdu d Y\ A!bp_A ApgdA \bA ! \d2_:A: Y\2Y Q\Ad YA db)A gJ :\A
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u bb!
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\d2_:\dQ p2Yg_gQu Y\_A YA !:\\gd!_ A!bp_A Y! )AAd \Y pAgp_A dAA:
\Y\d _!QA 2_A rAuQu pp\_ dAA: \Y\d 2_!ggbs8 )A2!A gJ YA QA!
!bgd gJ bA:\2!_ AA!2Y \Y b_\p_A bA!AbAd pA pAgd8 b_\[_AA_ bg:A_
\Y YA pAgd ! YA Y\QYA g:A _AA_ !A dg 2gbbgd rpAY!p bgA 2gbbgdsu
!A g_:A\d8 gdA gJ YA p\gdAA gJ Y\ !ppg!2Y8 !_^ !)g Yg YAA !A
Y\A!2Y\A AAYAAu _\_AA_ bg:A__\dQ \ dg gdA gJ YA gg_ ApA2A: Jg g2\!_
!d: p2Yg_gQ\2!_ 2\Ad\u
A Ad: \Y ! 2!A!u Y\_A b_\[_AA_ bg:A_ !A dg ApA2A: g )A A: \d !A!
YAA YA Y\A!2Y\2!_ 2A \ g)\g8 bgA AA!2Y \ dA2A! g AA Yg
AJ_ YA !A YAd YA _AA_ !A dg 2Y 2_A!d 2A !d: YAA YA 2gbpgdAd
! :\JJAAd _AA_ 2!ddg )A \AA: ! gbA !d:gb !bp_A gJ YgA ! Y! _AA_u Y\
! gYAd rjes b!\d 2\\2\b gJ _!^ rjes _!dQ!QA ! ! KA: AJJA2 J!__!2u
bg:A_e 9[ _bAr!g_: 8J!2Ag_:'J!2AY\A |_d\bA'J!2Ag_: |rj]J!2As
|rJ!2Ag_:]p!dgs8 J!b\_ h)\dgb\!_8 bAYg: h!p_!2As
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2!AJ__ !d: 2gd\:A YA !_Ad!\A )AJgA dd\dQ !d !\\2!_ Au g !bgd gJ
!\\2!_ gpY\\2!\gd 2!d K ! )!: :A\Qdu
AJAAd2A
A8 u u rjeeesu g[!b!\2 A :\g:A Jg__g\dQ 2Y\_:)\Yu Y :\A!\gdu d\A\
gJ gd:gdu
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AJJA2 Jg )]A2 !d: \Abu gd!_ gJ Abg !d: !dQ!QAu
!d^8 u u rjesu \Qd!_ :AA2\gd YAg !d: Yb!d bAbgu 2Yg_gQ\2!_ __A\d8O8
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gdA8 u8 )!b!d\!d8 u8 gdA8 u8 $ g_:A\d8 u rLsu !\!d2A p!\\gd\dQ \d b_\_AA_
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!d!_\ bAYg: rd: A:usu Yg!d: !^8 7 !QAu
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bg:A_ A_A2\gdu g2\g_gQ\2!_ AYg: !d: AA!2Y88 jEOu
Y!b)A8 u u rBsu gJ!A Jg :!! !d!_\7 gQ!bb\dQ \Y u gd:gd7 p\dQAu
_!^8 u u rjesu YA _!dQ!QA[![KA:[AJJA2 J!__!27  2\\zA gJ _!dQ!QA !\\2 \d
p2Yg_gQ\2!_ AA!2Yu gd!_ gJ A)!_ A!d\dQ !d: A)!_ AY!\g8j8 LELeu
gYAd8 u rjesu !d:gb bA!d !d:gbu gd!_ gJ A)!_ A!d\dQ !d: A)!_ AY!\g8jL8
jEu
!_A8 u u rLsu !\\27 d \dg:2\gd \dQ u Y\2YAA8 7 \_Au
!_A8 u u rsu YA  )gg^u Y\2AA8 7 \_Au
A!_g8 u u rjeeBsu \Qd!_ :AA2\gd YAg !d: QAdA!_\A: _\dA! bg:A_u 2Yg_gQ\2!_
AYg:88 jBELu
!!!8 u u rOsu \dA! bg:A_ \Y u g2! !gd8 7 Y!pb!d !d: !__u
!!!8 u u rsu Ad:\dQ YA _\dA! bg:A_ \Y 7 AdA!_\A: _\dA!8 b\A: AJJA2 !d:
dgdp!!bAA\2 AQA\gd bg:A_u g2! !gd8 7 Y!pb!d !d: !__u
g8 u rsu d  !d: [_ 2gbp!d\gd g !pp_\A: AQA\gdu Yg!d: !^8 7 !QA
)_\2!\gdu
g_:A\d8 u rsu _\_AA_ !\\2!_ bAYg: r: A:usu gd:gd7 :!: dg_:u
gJJb!dd8 u u rOsu AdA!_\A: _\dA! bg:A_7 d !pp_\A: !ppg!2Yu ggd8 7 A!gd
:2!\gdu
gJJb!d8 u8 $ g\dA8 u u rsu _\_AA_ bg:A_ Jg YA ApA\bAd!_ p2Yg_gQ\7
gd:!\gd !d: \__!\A A!bp_Au AY!\g AA!2Y AYg:8e8 jjEjju
g8 u8 $ \QY8 u u rBsu  ^dg g J!2A ) dg YAA  ! g7 gdA bAbg \
\bp!\A: Jg gYA !2A J!2Au 2Ygdgb\2 __A\d !d: A\A8jLrs8 OEeu
g8 u rsu _\_AA_ !d!_\7 A2Yd\zA !d: !pp_\2!\gdu gd:gd7 _)!bu
AJ8 u u8 $ :A AA8 u rjeeBsu dg:2\dQ b_\_AA_ bg:A_\dQu gd:gd7 !QA )_\2!\gdu
\_A8 u u u8 $ )\d8 u u rsu !\\2!_ !d!_\ \Y b\\dQ :!! rd: A:usu A g^7
\_Au
g2^Y!8 u u8 $ :g2^8 u u rjesu Abg !d: YA YAg gJ \Qd!_ :AA2\gdu
2Yg_gQ\2!_ __A\d8O8 jEjeu
!2\__!d8 u u8 $ AA_b!d8 u u rLsu AA2\gd YAg7  A Q\:Au !Y!8 7
_)!bu
Q8 u u u8 !pAdA8 u u8 g_:A\d8 u8 $ !)!Y8 u rsu \b!\gd \d QAdA!_\A: _\dA!
b\A: bg:A_ \Y )\d! g2gbA ) \b_!A: b!\bb _\^A_\Ygg:u !\\2!_ g:A__\dQ8
8 EOu
_\_AA_ bg:A__\dQ OLL
\dYA\g8 u u8 $ !A8 u u rsu \A:[AJJA2 bg:A_ \d  !d: [_u A g^7 p\dQAu
\dYA\g8 u u8 !A8 u u8 A)g8 u8 $ !^!8 u rBsu d_bA7 \dA! !d: dgd_\dA! b\A:
AJJA2 bg:A_u  p!2^!QA A\gd uj[Bu
 AA_gpbAd gA A!b rBsu 7  _!dQ!QA !d: Ad\gdbAd Jg !\\2!_ 2gbp\dQu
\Add!8 \!7  gd:!\gd Jg !\\2!_ gbp\dQ8 Yp7u[pg]A2ugQu
!)!Y8 u8 AA_A8 u8 gdA8 u8 $ gA8 u rLsu  A Q\:A g \u Yp7u
2bbu)\g_u!2u^\:gd_g!:Ab!dLup:J
\dQA8 u u8 $ \__A8 u u rsu pp_\A: _gdQ\:\d!_ :!! !d!_\7 g:A_\dQ 2Y!dQA !d:
AAd g22Ad2Au Jg:7 Jg: d\A\ Au
\dQA8 u u8 $ \__A8 u u resu pp_\A: b_\_AA_ :!! !d!_\u !d2\p \d pAp!!\gdu
!d\_!8 u8 $ g:gg8 u rjeeesu !_2_!\gd gJ \Qd!_ :AA2\gd YAg bA!Au AY!\g
AA!2Y AYg:8 dbAd8 !d: gbpA8j8 jEjOeu
Ad!)_A8 u u8 b\Y8 u u8 $ YA  AA_gpbAd gA A!b rBsu d \dg:2\gd g u 
[eLj[j[u Yp72!du[pg]A2ugQ:g2b!d!_[\dgup:J
A)A8 u8 AA8 u8 A__8 u u8 Abb_A8 u8 $ A!8 u rOsu A\dA \:Ad\K2!\gd
!22!2 !d: ApgdA _!Ad27 YA d_ jEj A2gd: _Au gd!_ gJ pA\bAd!_
2Yg_gQ7 pp_\A:8j8 jeEjOu
gg:8 u u rsu AdA!_\A: !::\\A bg:A_7 d \dg:2\gd \Y u g2! !gd8 7
Y!pb!d !d: !__u
\QY8 u u rjeesu ![)\dgb\!_ !\!\gd \d b_\_AA_ _gQ\\2 bg:A_ \Y p!A 2Au
\\Y gd!_ gJ !YAb!\2!_ !d: !\\2!_ 2Yg_gQ8L8 jEeu
\QY8 u u rjeeBsu g:A__\dQ 2_AA: :!! \d !g)\gQ!pY\2!_ bAbg AA!2Y7 YA
b_\_AA_ !ppg!2Yu pp_\A: gQd\\A 2Yg_gQ8j8 eELu
\QY8 u u8 g:8 u u8 $ A:g8 u u rsu dA[!2\!_ 2gd!2 !d: YA gd !2A )\! Jg
J!2A A2gQd\\gd \d gY J\2! !d: dQ_!d:u pp_\A: gQd\\A 2Yg_gQ8j8 LEu
\QY8 u u8 g8 u8 $ ^!QA)AQ8 u u r\d pAsu d2\gd Jg !:\\gd!_ !d: b_\_AA_
!ppg!2YA g \Qd!_ :AA2\gd YAgu AY!\g AA!2Y AYg:u
\QY8 u u8 $ gd:gd8 u resu g:Ad AQA\gd A2Yd\zA \dQ 7  p!2\2!_ Q\:A Jg
:Ad !d: AA!2YAu gd:gd7 !QA )_\2!\gdu
\QY8 u u8 $ 2!\:8 u u rjeesu gbp!\dQ Ab !d: A\b!g !\!)_A \dQ :!! Jgb
A!_ _\dA[pu pp_\A: gQd\\A 2Yg_gQ8j8 LEBOu
Yg8 u[u8 )2Yg^\8 u u8 $ 2_\Y8 u u rsu !\\2!_ bAYg: \d :\!Qdg\2
bA:\2\dAu A g^7 \_Au
A2A\A: B !2Y B A\A: A\gd A2A\A: B ! B
ppAd:\
 ! A: Jg YAA !d!_Au g :gd_g!:  Qg g Yp72!du[pg]A2ugQ !d:
Jg__g\dQ \d2\gd Jg \d8 !2 8 g \d:gu
YA :!! !d: :A!\_A: 2g:A Jg  u !A !!\_!)_A gd Yp7uAu!2u^
A:!duYbu YA gp \ !ddg!A:u YA 2g:A !d: p!QA \__ )A p:!A: !
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... For SDT analyses, a multilevel probit regression was run to determine bias (c) and sensitivity DeCarlo, 1998;Wright & London, 2009). This model predicted participants' binary perception of sexual interest for each vignette they saw using the binary categorization for that vignette (i.e., interest/disinterest), participant sex, mate value, short-term mating orientation, long-term mating orientation, and life history strategy as predictors. ...
... Study 2 manipulated the stimuli to address this difference, but issues with interpretation due to negative misperception scores persisted. Additionally, EMT analyses typically aggregate across trials and within sex, losing valuable information and statistical power, whereas SDT analyses can use a within-subjects multilevel approach that can account for individual and stimuli variation through inclusion of individuals and stimuli in the random effects structure (Wright & London, 2009). ...
... Example vignettes for both sexes communicating interest and disinterest.1 Allowing the intercept to vary for each vignette accounts for participants seeing different stimuli based on their sex, sexual orientation, and randomization of stimuli presentation(Wright & London, 2009).2 Because multilevel probit regression outputs -c (DeCarlo, 1998), the estimates for each effect on bias must be inverted. ...
Article
Although Error Management Theory (EMT) can explain male sexual overperception, more advanced Signal Detection Theory (SDT) analyses can identify sensitivity and bias separately. An SDT analysis of perceptions of relatively clear interest/disinterest signals (Study 1) found that sensitivity to sexual interest/disinterest signals drove participants' perceptions, rather than an overall bias to perceive sexual interest. Cues of interest were generally underperceived, while sensitivity and accuracy were uniformly high. EMT analysis also found overall sexual interest underperception, but with men slightly overperceiving interest relative to women. These discrepant results were due to EMT using difference scores, which obscure baseline perceptions for men and women. Individual differences in life history strategy, mating strategy, and mate value did not affect sensitivity or bias. Study 2 largely replicated these results using more ambivalent scenarios, except EMT analyses found men's misperception to be significantly larger than women's, despite being closer to pre-rated communication levels. These results show that sexual communication may be more nuanced than previously thought, and that an SDT analysis is more appropriate for such data.
... The first step of episodic memory, which corresponds here to recognition responses, has been analyzed by adapting the signal detection theory framework to GLMM analysis (Fawcett and Ozubko, 2016;Wright and London, 2009;, using sum contrast coding so that the intercept represents reference modalities. A probit mixed model (estimated using maximum likehood or ML, and the base optimizer) was fitted to predict the probability to answering "Yes" with a 3 Sensory Modality (odor, music, face) x 2 Item Type (target, distractor) ...
... The first step of episodic memory, which is defined here as recognition responses, has been analyzed by adapting the signal detection theory framework to GLMM analysis (Fawcett and Ozubko, 2016;Wright and London, 2009;, using sum contrast coding so that the intercept represents reference modalities. A probit mixed model (estimated using maximum likehood or ML, and base optimizer) was fitted to predict the probability to answering "Yes" with a 3 Sensory Modality (odor, music, face) x 2 Item Type (target, distractor) mixed design. ...
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Thesis
Episodic memory concerns the re-experience of past personal events anchored in their encoding context. These episodic memories are not fixed: their content is influenced by the sensory modality of the recall cue. For example, memories evoked by smells are known to be less frequent, more surprising, vivid, emotional, and older than memories evoked by images or words. These phenomena are commonly explained by the close and direct anatomical links that exist between the primary olfactory, memory, and emotional brain structures. However, odors have rarely been compared to cues that also possess privileged links to memory, such as music and faces, both behaviorally and functionally. This thesis has two main objectives: 1) To identify and characterize the particularities of episodic memory attributable to the sensory modality of the recall cue (Studies 1 and 2); 2) To study the dynamics of the neural networks underlying episodic recall and more specifically the interactions that are modulated differently according to the sensory modality of the recall cue (Study 3). To test the hypothesis that emotion would be an essential factor in the particularity of olfactory cues to recall a memory, the secondary aim of this thesis is to evaluate the differential effect of emotion of the episodic recall cue as a function of its sensory modality. To meet our objectives and to allow for the study of episodic memory in the most ecological conditions possible, we have developed a non-immersive virtual reality protocol that can be declined in several versions allowing the encoding and recall of complex and multisensory episodes experienced in the laboratory. By using neutral stimuli, the first study showed that the sensory modality of the recall cue influenced recognition and episodic memory performance. Faces were very well recognized and very good cues for episodic memory; smells were less well recognized, but were good cues for episodic memory; musical excerpts, although very well recognized were not good cues for episodic memory. By using emotional stimuli, the second study confirmed the previous results, and clarified the effects of emotion on episodic memory performance by showing that the emotional valence of the recall cue favors globally all memory stages. The most pleasant and unpleasant stimuli, compared to the most neutral ones, were associated with better memory performance. In addition, the pronounced effectiveness of odors in evoking episodic recall was associated with participants’ individual motivation to resample the stimulus. This study also highlighted the importance of the ecological relevance of the stimuli, with the virtualization of faces leading to the suppression of their superiority as a memory cue in comparison to odors and music. The third study, still in progress, confirms the memory strength of odors, when they are pleasant, to recall the different dimensions of an episode. Preliminary data suggest that musical and olfactory cues in episodic memory activate autobiographical memory networks. In conclusion, our studies reveal an effect of the sensory modality of the recall cue on episodic recall and suggest that this effect is associated with the emotion carried by these cues. Odors appear to be singular recall cues, associated with average recognition performance, but favoring accurate recollection of episodic memories. This recollection is driven by the motivation the odors have generated. Music, although very well recognized, leads to less correct recall of associated episodic dimensions. Finally, visual stimuli seem to differ according to their ecological relevance, with more efficient cueing and more complete memory being associated with more ecologically relevant stimuli.
... Second, we constructed two multilevel probit generalized regression models (one for witnesses who received the ACI and one for witnesses who did not receive the ACI), predicting the likelihood of a suspect identification from lineup type (target-present vs. targetabsent), target appearance change score, the Lineup Type 3 Appearance Change interaction, and a nested participant variable to account for variance at the level of each participant. If, as predicted, discriminability decreases as target appearance change increases, that would be reflected as a significantly negative Lineup Type 3 Appearance Change interaction (see Wright & London, 2009). Model parameters are displayed in Table 7. ...
... Therefore, we analyzed not only mean individuals' values (e.g., mean of 20 post-tests trials) but also their evolution across time. In addition, linear mixed models are a flexible method appropriate to deal with intra-individuals' variability within each group (Wright and London, 2009). We could thus assess intersubject differences considering the intra-individual changes over time (through trial-by-trial repetition; Fleury et al., 2021). ...
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Article
Prism Adaptation (PA) is a useful method to study the mechanisms of sensorimotor adaptation. After-effects following adaptation to the prismatic deviation constitute the probe that adaptive mechanisms occurred, and current evidence suggests an involvement of the cerebellum at this level. Whether after-effects are transferable to another task is of great interest both for understanding the nature of sensorimotor transformations and for clinical purposes. However, the processes of transfer and their underlying neural substrates remain poorly understood. Transfer from throwing to pointing is known to occur only in individuals who had previously reached a good level of expertise in throwing (e.g., dart players), not in novices. The aim of this study was to ascertain whether anodal stimulation of the cerebellum could boost after-effects transfer from throwing to pointing in novice participants. Healthy participants received anodal or sham transcranial direction current stimulation (tDCS) of the right cerebellum during a PA procedure involving a throwing task and were tested for transfer on a pointing task. Terminal errors and kinematic parameters were in the dependent variables for statistical analyses. Results showed that active stimulation had no significant beneficial effects on error reduction or throwing after-effects. Moreover, the overall magnitude of transfer to pointing did not change. Interestingly, we found a significant effect of the stimulation on the longitudinal evolution of pointing errors and on pointing kinematic parameters during transfer assessment. These results provide new insights on the implication of the cerebellum in transfer and on the possibility to use anodal tDCS to enhance cerebellar contribution during PA in further investigations. From a network approach, we suggest that cerebellum is part of a more complex circuitry responsible for the development of transfer which is likely embracing the primary motor cortex due to its role in motor memories consolidation. This paves the way for further work entailing multiple-sites stimulation to explore the role of M1-cerebellum dynamic interplay in transfer.
... Responses were removed if a participant's response time on a given recognition trial was less than 150 msec or greater than 10 seconds, which resulted in the removal of 21 recognition trials from the recognition task analyses (0.93% overall data). The signal detection analysis was performed with a mixed effects probit model (Wright & London, 2009). The observed responses "old" or "new" were the DV and the fixed effects were the 2 (Item Type; old vs. new) x 5 (Commercial Condition: Boundary-Emotional, Boundary-Neutral, Non-Boundary-Emotional, Non-Boundary-Neutral, and No Commercial) with Participant and Recognition Item included as random intercepts and Item Type by-Participant included as a random slope. ...
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Article
Event boundaries are important moments throughout an ongoing activity that influence perception and memory. They allow people to parse continuous activities into meaningful events, encode the temporal sequence of events and bind event information together in episodic memory (DuBrow & Davachi, 2013). Thus, drawing attention to event boundaries may facilitate these important perceptual and encoding processes. In the current study, we used emotionally arousing stimuli to guide attention to event boundaries because this type of stimulus has been shown to influence perception and attention. We evaluated whether accentuating event boundaries with commercials improves memory and whether emotional stimuli further enhance this effect. A total of 97 participants watched a television episode in which we manipulated commercial break locations (boundary, non-boundary, no commercial) and the type of commercial (emotional, neutral) and then completed memory tasks. Overall, placing emotionally arousing commercials at event boundaries increased memory for the temporal order of events, but no other effects of accentuating event boundaries were observed. Thus, drawing attention to event boundaries—via emotionally charged commercials—increases the likelihood that people will perceive the change in events, update their mental model accordingly and better integrate temporal information from the just-encoded event.
... d' is a parametric estimate of the ROC curve under the assumption that both the match and non-match distributions are normally distributed and have equal variances. Moreover, there are also regression-based approaches that will lead to the same conclusions as a d' analysis [41,42]. For example, when one regresses the examiner's binary decision on ground truth with a probit regression analysis, the slope is equal to d' and if a researcher wishes to compare the discriminability of two different conditions or procedures, this can be done by incorporating an interaction term between condition and ground truth. ...
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Article
Forensic science plays an increasingly important role in the criminal justice system; yet, many forensic procedures have not been subject to the empirical scrutiny that is expected in other scientific disciplines. Over the past two decades, the scientific community has done well to bridge the gap, but have likely only scratched the tip of the iceberg. We offer the discriminability-reliability distinction as a critical framework to guide future research on diagnostic-testing procedures in the forensic science domain. We argue that the primary concern of the scientist ought to be maximizing discriminability and that the primary concern of the criminal justice system ought to be assessing the reliability of evidence. We argue that Receiver Operating Characteristic (ROC) analysis is uniquely equipped for determining which of two procedures or conditions has better discriminability and we also demonstrate how estimates of reliability can be extracted from this Signal Detection framework.
... d' is a parametric estimate of the ROC curve under the assumption that both the match and non-match distributions are normally distributed and have equal variances. Moreover, there are also regression-based approaches that will lead to the same conclusions as a d' analysis [37,38]. For example, when one regresses the examiner's binary decision on ground truth with a probit regression analysis, the slope is equal to d' and if a researcher wishes to compare the discriminability of two different conditions or procedures, this can be done by incorporating an interaction term between condition and ground truth. ...
Full-text available
Preprint
Forensic science plays an increasingly important role in the criminal justice system; yet, many forensic procedures have not been subject to the empirical scrutiny that is expected in other scientific disciplines. Over the past two decades, the scientific community has done well to bridge the gap, but have likely only scratched the tip of the iceberg. We offer the discriminability-reliability distinction as a critical framework to guide future research on diagnostic-testing procedures in the forensic science domain. We argue that the primary concern of the scientist ought to be maximizing discriminability and that the primary concern of the criminal justice system ought to be assessing the reliability of evidence. We argue that Receiver Operating Characteristic (ROC) analysis is uniquely equipped for determining which of two procedures or conditions has better discriminability and we also demonstrate how estimates of reliability can be extracted from this Signal Detection framework.
... Slow response times will be based on the residuals, the e ijk , of variance component model that includes random variables for the student (u1 j ) and item (u2 k ). This is often called a multilevel or cross-classified model (Goldstein, 2011;Wright & London, 2009). ...
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Article
When students respond rapidly to an item during an assessment, it suggests that they may have guessed. Guessing adds error to ability estimates. Treating rapid responses as incorrect answers increases the accuracy of ability estimates for timed high-stakes summative tests like the ACT. There are fewer reasons to guess rapidly in non-timed formative tests, like those used as part of many personalized learning systems. Data from approximately 75 thousand formative assessments, from 777 students at two northern California charter high schools, were analyzed. The accuracy of ability estimates is only slightly improved by treating responses made in less than five seconds as incorrect responses. Simulations show that the advantage is related to: whether guesses are made rapidly, the amount of time required for thoughtful responses, the number of response alternatives, and the preponderance of guessing. An R function is presented to implement this procedure. Consequences of using this procedure are discussed.
Article
The potential influence of eyewitnesses’ metacognitions on identification decisions when confronted with a police lineup is largely unexplored. In two experiments, we investigated whether eyewitnesses’ pre-lineup memory strength inferences influenced the likelihood of their choosing from a lineup. In experiment 1, manipulating witnesses’ memory strength inferences, while holding memory encoding and retention conditions constant, increased positive identifications from culprit-absent lineups when witnesses inferred they had a poor memory for the culprit. In experiment 2, witnesses who had been interviewed and experienced difficult rather than easy recall of the culprit that was likely suggestive of a poor memory made more positive identifications from both culprit-absent and culprit-present lineups than those who experienced easy recall. Signal detection analyses supported a criterion shift account that proposes that witnesses who infer they have a relatively poor memory may demand less evidence for a positive identification than if they inferred a good memory. Thus, witnesses’ memory strength inferences may influence identification decisions independent of encoding conditions and lineup characteristics.
Article
Whether sensorimotor adaptation can be generalized from one context to other represents a crucial interest in the field of neurological rehabilitation. Nonetheless, the mechanisms underlying transfer to another task rema in un clear. Prism Ad aptation (PA) is a useful method employed both to study short-term plasticity and for rehabilitation. Neuro-imaging and neuro-stimulation studies show that the cerebellum plays a substantial role in online control, strategic control (rapid error reduction), and realignment (after-effects) in PA. However, the contribution of the cerebellum to transfer is still unknown. The aim of this stud y was to test whether interfering with the activity of the cerebellum affected transfer of prism after-effects from a pointing to a throwing task. For this purpose, we delivered cathodal cerebellar transcranial Direct Current Stimulation (tDCS) to healthy participants during PA while a control group received cerebellar Sham Stimulation. We assessed longitudinal evolutions of pointing and throwing errors and pointing trajectories orientations du ring pre-tests, exposure and post-tests. Results revealed that participants wh o received active cerebe llar stimulation showed (1) altered error reduction and pointing trajectories during the first trials of exposure; (2) increased magnitude but reduced robustness of pointing after-effects; and, crucially, (3) slightly altered transfer of after-effects to the throwing task. Therefore, the present study confirmed that cathodal cerebellar tDCS interferes with processes at work during PA and provides evidence for a possible contribution of the cerebellum in after-effects transfer.
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Article
Much memory research involves recording several autobiographical memories for each of several people. These memories are not independent of each other, an assumption of the statistical procedures used in many cognitive psychology papers. In recent years there have been both statistical and computational advances for modelling these hierarchical data structures. This is often called multilevel modelling. Using data from recent memory research (Burt et al., 1995), I describe this approach and show how it compares favourably with traditional approaches. © 1998 John Wiley & Sons, Ltd.
Book
The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models. The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study.