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O  Z>?@CDFGH 6The prevailing practice of adjusting for all covariates, especially those that are good predictors of X (the  treatment assignment, Rubin, 2009) is totally misguided. The  outcome mechanism is as important, and much safer As X-rays are to the surgeon, graphs are for causation " " 8" " 7" " f@ 8 7/   0` MMM̙` fy3` f.f̙` jg3mof` e MMMfff` Po` yyOOw]]f` MMMr~` NfD+f3>?" dd@,?dd@   @ ` p?" dd@   @@``PR    @ ` ` p>> f^ d(  d d 6 " # T Click to edit Master title style! !$ d 0  "   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S d 6S #" `^`  F*  d 6X #" `^   H*  d 6) #" `  H* V d s *h޽h ?#" @@ MMM̙80___PPT10.ݿ 8,  Clouds  0 1)0h(  h h BX! ?#" `  T Click to edit Master title style! ! h 0\# " `    W#Click to edit Master subtitle style$ $ h 6/ #" `^`  F*  h 6$ #" `^   H*  h 6\ #" `^   H* V h s *h޽h ?#" @@ MMM̙80___PPT10.ݿ 8, 0 TLD(   D D Nruru &  # x*   V,,VV D Nԯruru  z&  *   V,,VVd D c $ ?p   D NDruru  KW  8________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________   D Truru    x*   V,,VV D Truru  z  z*   V,,VVH D 0xlZ ? ̙3380___PPT10.bUp,Q  ,( t; 4  C x {ruru Ԕ?&  # t*    V,,VV>  C x 9ruru Ԕ? z&  ~*   V,,VV4  C xD,ruru Ԕ?   t*    V,,VV6  C xruru Ԕ? z  v*    V,,VVH  0xlZ ? ̙3380___PPT10.bUQk  0 z(    0u@A OON BIAS AMPLIFIERS 6#  0 u KJudea Pearl University of California Los Angeles (www.cs.ucla.edu/~judea/).L8nKZL$&3      H  0޽h ? f̙f___PPT10i.:U+D=' = @B +  0 `"D@(  Dk D s *6of THE PROBLEM: We wish to estimate the causal effect P(y|do(x)) by adjusting for a set Z of variables. Given a graph, G, find Z so as to minimize the bias: , &           &3    a   D c $A '??"` x 'd D N ?"  'aON BIAS AMPLIFIERS Judea Pearl University of California Los Angeles (www.cs.ucla.edu/~judea/) l L8nKZ (L63      H D 0޽h ? MMM̙___PPT10i._LM+D=' = @B +  0 0("(AH (  H  H s *lr2 THE SOLUTION: Z must be admissible, i.e., satisfy the back-door criterion But what if some confounders remain unmeasured (e.g., U)? Would it help if we adjust for Z10? Z3? Perhaps Z5? Or would it increase bias?  (<            B  H Z DԔ?":D| :B  H@ Z DԔ?"R| B  H Z DԔ?" B H Z DԔ?"  H H|s ?"  HZ6*   H Hr ?"Kj HZ3*   H H~ ?", L HZ2*   H Hj ?"}  HZ5*   H Hpi ?",2L HZ1*   H H4 ?"  7X  H H|! ?"&) F  7Y 2 H N ?" >  H H?"Z  MZ10.0 2  H H?"  x  LZ7.0 2  !H H?"   LZ8.0 2  $H Hx?" V  LZ9.0 2 B *H@ Z DԔ?":l :B +H Z DԔ?": Z fB -H@ Z DԔ?":DfB .H@ Z DԔ?"B /H Z DԔ?"b  B 0H Z DԔ?"X  H H ?"F f HZ4*  B 1H Z DԔ?"  B 2H@ Z DԔ?" n8 "  5H B 3H T DԔ?" 2 4H N ?"d " |F "  6H  t  B 7H T DԔ?" 2 8H N ?"d " |F "  9H ,  B :H T DԔ?" 2 ;H N ?"d " B =H Z DԔ?"J2 >H T ?"2t @H H$ ?"5 4  7U W AH T?" h e.g., Z = {U, Z4, Z5}0     H H 0޽h ? MMM̙___PPT10i.` 8'+D=' = @B +  0 "L 4(  L L H4?"  =U 0 22 L T ?"t  2 L T ?" B 2 L@ T ?"6B   L ZP?"p  Jc1,0 B  L@ Z DԔ?" B L Z DԔ?"* *  L Z?"  ;X0 L Z?"$  ;Y0B L Z DԔ?" B L T DԔ?" 2 L N ?"tz L Tm?" ;Z0 L Th?"p  Jc2,0  L T#h?"p  Jc3,0  L Th?"x  Jc0,0 ~ L T,qh?"az9 |SURPRISING RESULT: Instrumental variables are Bias-Amplifiers in linear models (Bhattarcharya & Vogt 2007; Wooldridge 2009)2}0jQ * L T h?"z1  < Naive bias Adjusted bias@0 L c $A '??"` NSx 'd L c $A '??"`| VW x 'dH L 0޽h ? MMM̙___PPT10i.dOu+D=' = @B +3  0 22"+1Pw2(  Px P T(6$?"jr XINTUTION: When Z is allowed to vary, it absorbs (or explains) some of the changes in X.rY0  F  P Tԋ$?"j  _When Z is fixed the burden falls on U alone, and transmitted to Y (resulting in a higher bias)`0   |8   1P^  P Hd$?"   =U 0 22 P N ?" t 2 P N ?"  B 2 PB N ?"6B  P T,$?" p  Jc1,0 B  PB T DԔ?"  B  P T DԔ?" * *   P T8$?"   ;X0  P T$?"$  ;Y0B  P T DԔ?" B P T DԔ?" 2 P N ?"zt P Tt1$?" ;Z0 P T s$?" p Jc2,0  P T $?"p  Jc3,0  P T\?$?"x   Jc0,0 N P  70e0e    BCDE(F0A Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  T P  0e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  V T P  70e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  T T P  70e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  ,  P N"$?"  =U 0 22 P T ?"L 2 P T ?" 2 P@ T ?"!  P Z$?"H h Jc1,0 B !P@ Z DԔ?"j B "P Z DԔ?"  #P Z$?"  ;X0 $P Z<$?" ;Y0B %P Z DԔ?"j B &P Z DԔ?"j  2 'P T ?"L e  (P Zxu$?" t  ;Z0 )P Z$?"H h Jc2,0  *P ZX<?"H  h Jc3,0  +P Z@?"c l  Jc0,0 L ,P  70e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  L -P  0e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  AL .P  70e0e    BCDE(F0 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| <rDzff@"<  ? H P 0޽h ? MMM̙___PPT10i.fp!+D=' = @B +  0 "0T Q(  TB T  ` DԔ?"  B T@  ` DԔ?" B T  ` DԔ?"DX B  T@ Z DԔ?"  x B  T  ` DԔ?"D`  T@ NTH ?"  Hc0*   T@ N,M ?"8X Hc2*   T@ NHR ?"$D GZ*   T@ NdW ?"8X Hc3*   T@ N\ ?" 0 GU*   T@ Na ?"d  7Y  T@ Ne ?" 0 $  7X 2 T@ T ?" 8  T@ Nj?" " Lc4.0 2  "T@ Nn?"  LT1.0 2 2 $T@ T ?"j8 2 'T@ T ?"B )T@ H t ?"h q " Hc1*   *T Tx?"q WHAT S BETWEEN AN INSTRUMENT AND A CONFOUNDER? Should we adjust for Z?RH00  +T@ H$?"  LT2.0 2 2 ,T@ N ?" Bj -T Z<?" ~ RANSWER: CONCLUSION: dS0!  .T s *A '??"`,  x 'd /T Z?"  SYes, if No, otherwise Adjusting for a parent of Y is safer than a parent of X T0  H T 0޽h ? MMM̙___PPT10i.h?+D=' = @B +  0 #XA(  X  X H@?"*h* PH@___PPT9" +WHAT ABOUT NON-LINEAR MODELS? Conditioning on IVs may reduce or amplify bias; mostly amplify Conditioning on IVs may introduce its own bias where none existed.X01 @`H X 0޽h ? MMM̙___PPT10i.jP+D=' = @B +%  0 $$ #3Y\@v$(  \ \ TT?"; _!CAN AN IV AMPLIFY SELECTION BIAS?""0"  \ T?"mj/  wUANSWER: No Exercise: which selection bias will be amplified by Z? S1? S2? or S3?V0 ,2 \ T ?" @  \ Z$?"V ( v Lb1,0 B  \ Z DԔ?"v (B  \ Z DԔ?"\ \ \ Z_?"  ;X0 \ Zζ?" & ;Y0B \ Z DԔ?"j 4 \ Z9?"( ;Z0 \ Zն?"  Jc3,0  \ Z\ڶ?"8O X X Jc0,0 B /\ T DԔ?" F2 0\ N ?"J 2 2\ N ?"> v2 3\ N ?"  4\ T0?"  Lb2,0  5\ Tٶ?"M& s IS,0 B 6\ T DԔ?"b mR2 7\ N ?"HS 8\ T@?"i LUY.0  :\ Zp?"PF Ap gS= s0F0  ;\ HT?" b  \U1>0 2  2 <\ N ?" 8 j 2 =\ N ?" a  ?\ T1?"FZ JS1,0  B\ T)?"x"  ;X0 C\ T(+?"\; ;Y0B @\@ Z DԔ?"> < d B D\ Z DԔ?"> T HB E\ T DԔ?"> 2 2 F\ N ?" 3j  G\ T Ķ?"   ;Z0 H\ Tȶ?"n  JS2,0  I\ T|"?"  JS3,0  J\ T4,?" P0  LUY.0  K\ H ?" 8  \U2>0 2  2 N\@ T ?"5B O\@ Z DԔ?"> X @B P\ Z DԔ?"V @B Q\  ` DԔ?"> 0Xn8  HZ  T\% |2 >\B T ?" HZ 2 R\B N ?" HN 2 S\@ N ?" B U\ T DԔ?"@ N B V\@ T DԔ?"@ HB W\@ T DԔ?" ^fB X\ T DԔ?"< . B Y\@ T DԔ?"j\H \ 0޽h ? MMM̙___PPT10i.keVV+D=' = @B +   0 @#`(  ` ` T?"L I CONCLUSIONS" 0 $ ` S  d2   ``8H ` 0޽h ? MMM̙80___PPT10.pv$ 0 4(  d  c $Dp   #  s *;D KW  #  H  0xlZ ? ̙3380___PPT10. 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