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Random-effect models for ordinal responses: application to self-reported disability among older persons.

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(1)Random-effect models for ordinal responses: application to self-reported disability among older persons. Isabelle Carrière, Jean Bouyer. To cite this version: Isabelle Carrière, Jean Bouyer. Random-effect models for ordinal responses: application to selfreported disability among older persons.. Epidemiology and Public Health / Revue d’Epidémiologie et de Santé Publique, Elsevier Masson, 2006, 54, pp.61-72. �inserm-00077615�. HAL Id: inserm-00077615 https://www.hal.inserm.fr/inserm-00077615 Submitted on 31 Aug 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Hal author manuscript Rev Epidemiol Sante Publique 54 (2006) 61-72. Random-effect models for ordinal responses: Application to self-reported disability among older persons. Hal author manuscript.  

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(588) 47G r > ) \  ‚@Ms*")G TWD

(589) Fw n

(590) reL47 [  r%b VW1y1 VvA4. 4D'# 

(591) d47BH4D'  ru o. .  µ  =  

(592)    . +"$;+H0aHpHX&MuP47 9qr€G

(593)

(594) ns'

(595) #a4 r Y4D'Ce @GA47aH0#

(596). D

(597)    WfH0CFGw U f&YeA4G r s' ' ruz#FGFw(cr+HX4‚q&

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(601)

(602) u. #  #eA4H.

(603) fH4|‚q;&

(604) 4G

(605) Y;TWD

(606) 9FGY#FGGD

(607)  >z f&YeA4G rUD

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(610) 4 rU#

(611) "@MG '&H 'H4GuA4G  n

(612) t >e#a&aH0D

(613) L@MCq##zn

(614) 

(615) n jHt#94  @e#

(616) uz%4D

(617) +Hdr X eL&MFN4(

(618) TWD

(619)  uz HX4 L4f4]#e 4‚@ > 4D''Ht Hal author manuscript. n

(620) t >e#a&aH ‚t#eL47F ( u~uBH # n

(621) n

(622)  ~GuUL47 FG M#FGwD' >  'q;47G

(623) #3q

(624) ( a&MuUe#aF GB47

(625) L47G

(626)  #

(627) +H ucnF#u#B47#  rUwHX47#

(628) e#<€G 4D' ,

(629) Zz,y*"V\1 €.0l n

(630)  e##a&B T D' FsFGD

(631)  >"+HJ4D

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(633) tsF <> @4D

(634) S&' 'qMH@ ts'>

(635) u # X 7#eL4Ht<>

(636) Y4D

(637)  

(638) wB4rfH4 q;&

(639) 4G

(640) z > 4D'

(641) L47 

(642) 4D

(643)  '

(644) >u. #  #eA4HA. N47D ' r'tFGGM#yuz 

(645) #FfH< e#

(646) u"n&

(647) 47L4 r'sF Ga47#>H‚@j . inserm-00077615, version 1. GB47

(648) L47G

(649) uUL4D

(650) >H<HX&Me#D aHW4D'"b9A&JHpH  uzN47  &M#L4+& ?<YCa& #c47 L@rsF5&ML47 4D

(651) HzFf#FfGD

(652)  >Y  L@G n

(653) n

(654)  ~GuA47# 4D

(655)  FGsFGD

(656) Y < HX47

(657)

(658) yuz~fuz;L47G ryuUL4D' >>Ht< H&Me#DzaHJ4D'E*  4

(659) 

(660) +/Cn

(661) DYH

(662) cu L4D

(663) 

(664) <>S&H#C4 " aq;47sG94D'CaHX4GuUL47aH ,L@r#FWuz 

(665) #F H[D

(666) @r qs n

(667) t rn' jHt# 

(668) E4D

(669) z'sFG(YH+H[ > v rtw'#FJaH7n rHpaH[w4D'ze#Hz > ' r e rtsF L47#

(670) L47 taHn

(671) >HtaHA z . :

(672) <c

(673)  ETWD

(674) aHt uz 

(675) #F+H e##yqh~;47

(676)

(677)  47 4D

(678)  e#aHp

(679) "nL47#. A@<Y4D

(680) ze#D

(681) > e#z > 4D'cuz 

(682) #FWGucnM YHaH[e#

(683) >H4Ga4H[

(684) 4D

(685) "

(686)

(687) >u #  7#eL4. H4X&Me 4+&a>IM&X4D

(688) uz

(689) #<JG n

(690) #eL47Ge#< N4[+H

(691) G  eL&MFN4E47 Ga4 a&Me#cu r"4D

(692)    #  eL4H . 54Dc4D

(693) +H[aHX47GuUL4 rUn

(694)  >e#a&. #'

(695) >u . 9n

(696) H#a40D'H@r#FY4X(;nH

(697) E

(698) G

(699) #FKuz >

(700) #FH . N4Dz

(701) 

(702) F (c 

(703)

(704) u Ga47e#n4p . The proportional odds mixed models.   

(705) . VvA4.

(706) ' a47Cz G#F &

(707) 47e

(708) uz. TWD

(709)  eL&Yu"&MFL4‚@r F rN4Puz >

(710) #F .

(711) G

(712) #F[

(713) L4+& r 4D'-aH7n rHp n

(714) t 'qrLqfFGN47'H  . . &   ≥ . . N4D"g e#L47 r aHA . aH 4D

(715)  XG H4"uz 

(716) #F n

(717) 

(718) n

(719) YH  rz

(720) G

(721) #F aH7n rYHtaHA0T\D' .    ≥ " t<J

(722) 

(723) Lt#-BH. H 47yGa47 #e#e# &a4Cq

(724) (Re#

(725) >H

(726) G

(727)  4D

(728)  eL&Mu"&YFL47‚@M  >FGFG . Hz.  &    ≥ . . . ≥. . &   ≥ . . . ≥ . . &   ≥ "  . A. TWD

(729) Cuz 

(730) #Fe## qr n

(731) BH#a47#zaH  >FGFG . Ho C"

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(733)      ≥ . <.         

(734)           = α +   +.  . . D

(735)  +H\4D'9#

(736)

(737) >u s  7#eL4 HnesG e€47 HX&

(738) qtaeA4  

(739) . α.  fH\4D'"wB47e#n40  r eL47

(740)

(741) X(. ". Hal author manuscript. TWD

(742) -@raeA47 z r C4D

(743)  ‚~M#Rn#uA47 H znaHta4H"4D' FG r7 >

(744) >Hz 4G YHU r C4D

(745)  

(746) 7 '&n β. eL47

(747)

(748) GHUHX&nG

(749) 94 4D' eL&;47X

(750) X  " ze#

(751) u"nM# 4 4D

(752)  e#A47

(753)

(754) GaHzG

(755) 7G

(756) 94 " J 4D

(757) +H. . u >

(758) #FG<r4D' #

(759)

(760)

(761) u #  eL4  0'94D€ ‚~M##  #eA4H  0 G

(762)

(763) n#

(764)

(765) #B4W

(766) Y4D

(767)  eL&

(768) 47 r   " A TWD

(769)  H H&Yuzn47G r 4D'L4. β. β. fH"Gn#

(770)

(771) #a4€ r 4D

(772) -BHn rH-F@#F GuznFfH€4D'L4 4D'-FG

(773)  

(774) >H. inserm-00077615, version 1. tL4G 

(775)    @r# e# @qFf +H 4D

(776)  Ht#u 

(777)  sFF F@#F+H > 4D

(778)  BHn

(779) >H;TWD

(780) +H F# 1Re#\&YFF>D 4 " J47 C4D

(781) fH0uz >

(782) #FHJ4D'  n

(783)  rn' r+4G 'sFM 

(784) >HWuz 

(785) sF  A   TWD

(786)  e# rH

(787) L47G

(788)  > eL&Mu"&YFL47‚@ n

(789) t rn+4GH e r

(790) 7 HhHp@r#F9&KH# +&YFzn

(791) 

(792) n+4GH-4 4D'. . u >

(793) #F7o  dT D'9n

(794) 

(795) n

(796)

(797)  4G

(798) 

(799) #F 

(800) >H uz 

(801) #F+H G@M#a4vw J4D'"e# 

(802) aH 

(803) \4D

(804) 9taHn

(805) >Ht. . tL@pH#

(806) <EaH&YF54G

(807) 

(808) 

(809) Fw( G  e#D

(810) # G 4D

(811)  HG r 4D'-

(812) BH HG >hn#uUL47 Ht< X €4D' n

(813) t rn'  4G

(814) 

(815) #F 

(816) >Hyuz 

(817) #F  H w@rsB4 G 4D

(818)  eL47

(819) GaH > -4D'

(820) ‚#FBHn

(821) YH  e rFGFnH#. :  

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(823) Cn#uzL47 @r#eL47

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(825) 

(826) F‚(94D'€GB47e#n4Ht<. α. " LC X 7#eL47#Y. β. ! uz#GYHW&Y'e#D

(827) #M#G 0e#L47

(828) GHv. e# >u"qG#

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(830)  n

(831) t rn' r+4G

(832) 

(833) #F >

(834) >H uz 

(835) #F-+H  f47 n

(836) aHt#a47# aH

(837) BHw

(838)  

(839)  G

(840) #F-taHn

(841) YHp eL47

(842)

(843) GH uz

(844) 

(845) 4

(846) 

(847) GeB#FwFG( #FL47# 4  &'

(848) Fw(G> e#

(849) a4GB&M '&H FGL47a4z@qF. #. tsF L4 rHD

(850) wnzqL4  ## m#

(851) e rB4wB&

(852) &Yu. η. η. " . η.  dFfBH. &4Mq

(853) (91 e#\&MFfFD = <a4D'CL~+HX47'e#C

(854)   L@r<Y4D

(855) 9&Hz > vc#'

(856) >u. η. qL4  #. [T D'.  tS4D

(857)  eL&

(858) 47X

(859)  Jn >Ga4H r94D' '   L@r<WaH[n

(860) wB47# α α%$'&. +HEH&e#D94D'L44D

(861)  n#uUL47pH. ) Ea&M#F+H. ' 4D

(862) A4. η. α. . +HJ&HX&M#FfFG(9&M@MG qFfCG"n

(863) #eA4Ge. . s  7aeA47< <G

(864)

(865) nM#

(866) a4d r 0Hn

(867) >Hte#A47 r(  H[qaHt#

(868) . 4D' 

(869) 4G

(870)  4D'L4 i&

(871)  a&Mi&M  

(872) .  e# rB4GB&M '&H n

(873) D

(874) #

(875) >u s' r &Y'

(876) FfaH 4D

(877) 

(878) 

(879) w'aF. . taHn

(880) >HtX4fH0n jHpH qMF%4 e

(881) >H

(882) v9uz 

(883) #FYGe#F &M

(884) f;

(885) G  #a47G#FY#

(886)

(887)

(888) u #  7#eL4Ht< <

(889) q>(. (. eL47

(890)

(891) X( r } z . L@t<

(892) 'H4GuA4G

(893) z+H\u r[e# >u"nFfe#A47#"w 4D

(894)  H ~;47

(895)

(896) cuz 

(897) #FrqM#eL&Hp 9`

(898)  .

(899) e rHX4GB4Hzu9&JH4Cq 

(900)

(901) # 47 >HX&t 4D

(902) L4[4D

(903)  Ga47te#n4 t

(904) G +Hz

(905) 4C@G >FGL47YI rz ‚@#"BHn

(906) >HpCe#L47 X('< " <4D

(907)  GB47e#n4KfHK4D

(908) #o. &"  & ≥α#$  # ≥. α. %&  % . α. !   

(909) 94D

(910) #  rCN4KfH0

(911) eaBH Hp(. 4D

(912) L4o. ≥α . Hal author manuscript. TWD

(913) zn

(914) 

(915) n  4G

(916) 

(917) #F0 

(918) >HCHpHX&Mucn47G

(919)  . β. G

(920)

(921) n#

(922)

(923) #B4[ r 04D

(924) aH7n rHpF@r#F " CuU( qr 47

(925) . H4GeL4S

(926) HD

(927) &MFG

(928) < G #( e#H#<qM"47aHX47Y>IK E4D

(929)  H%n&n jHt94D

(930) cn

(931) t rn' r+4G

(932) 

(933) #F0 >

(934) >H%uz >

(935) BF uU(yqM e# u"n# 47 yuz rt-#F[

(936) GsF[uz 

(937) sF+H"4D'L4 nuzN4C4D

(938)  # X 7BeL4H<. inserm-00077615, version 1. e#e#

(939) Gy47 R4D

(940)  e#L47 GHU >. . < 4 @r|(. vT\D

(941)  uz HX4PtsF[uz 

(942) sF% > 94D

(943) +H"4(n +H}e##FfF# 4D. 

(944) #F s#z r

(945) #"FG

(946) >N4Kuz 

(947) #F#

(948) ze##9qC~'n

(949) aHAHcBH\  FwF .      ≥ . <. β.         

(950)           = α +   +. . Ho. X . 7R4D' n

(951) 

(952) n

(953)

(954)  4 r'sF 

(955) >H uz 

(956) #F  t<d4D

(957) h rt

(958) #y

(959) L4+&t

(960) 94D

(961)  aHn

(962) >Ht +H ~

(963) n

(964) t'HpHB A~e#F‚&JH‚@M#Fw( q

(965) (y4D

(966)  us  €4D'

(967) 

(968) t# Ga47te#n4H< e '@rGL47aH0€G@r rF‚@M#zw 4D

(969)  H r

(970) G. α. AO .  W. e rB4aHX4 <SG uz >

(971) #F X <d4D'. . TWD

(972) CD

(973) tesD(c r eL&Yu"&MFL4‚@r n

(974)  'qrqfFGN47fH0fuznFfaHJ4D' Ht#uC

(975) 

(976) GU  rJ4D'€F rN4HoFG

(977) N4  .  . ≥ . . ≥. &  . F rN4    . ≥. ". ≥ . &  . FG

(978) >54   . ≥ .   JTWDa&Ht< 4D

(979) -FGG# n

(980) #

(981) eL47  H . u"&H4 #F+H q G>#B4fesFGFG(y

(982) 

(983) t#YIK

(984) " HG;>F e# '@rqF#<vs' aHC4D' #'

(985) ru #  eL4 +H 4D' '&

(986) DB4C4 Rqr G

(987)

(988) ns'

(989) #a4 r C4D

(990)  Hn

(991) >Ht F@M#FG<S4D

(992) fHz#FL47G rYHD

(993)  n qM#e# >u aHo ≥α. #( β# ' ≥. . %&) &* β&% ) & ' 

(994) TWD

(995) H. ≥α. α. & β& '. gP t

(996) aHpHG >FGGHvC

(997) 4W

(998) e#aH HtfFG(n#FwF#F#. '. 4D'( uU( e YH H 

(999) cHt ruz @#F‚&M'HP

(1000) <0aHX&MFN47GyG @G FfA4G rh > 4D

(1001)  n

(1002) L@G &H"D

(1003) te#D(< #FN4D' '&

(1004) D 4D

(1005)  Hvet jHpHw

(1006) U > 

(1007) aHAHG >zFwBH\#'#FfFG( e#eL&pH0 '&;4HG

(1008) S4D

(1009) C;YC  J qHX@M#

(1010) A47

(1011)  40uz( ' r'L4D

(1012) #FH H q9n

(1013)  qF#uA4Ge" E~4tn FL4 r} > J4D

(1014) "uz 

(1015) #FqM(' >

(1016) c4D'9#M

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