Legistic Regression在社會科學研究的應用

全文

(1)Logistic Regression tEit.,,*"M"~J::.~llIm. 25. Logistic Regression. 1.i~J:~14-*~1LJ:.a~]!, ffl. 3::.A:lIsc.(a*MNlm.ti) It J,I.:!:AIISC. ~Ck~mtB9±~ § ,*f4¥Wf~J:.B9)J!tffl. '. B9 ' ::fl::1t-*B Logistic Regression:tEit 0J~1Q:f\5. Linear Regression B9 /F ~ ; -. :. . . Logistic Regression fO. " Odds Ratio B9 ~ lIE ;. =... The Simple Logistic Regression; gg . . The Multiple Logistic Regression; 1£" tm0jl.ljZfiSm~. ~. ;. . . Spsspc+. f~. ~~!Y3o. -. .. Logistic Regresslon~Linear Regressionl¥-J:f=1ii.J ? ~M~M~~Hm~. lIM~~~£B9W~~1:7oo*;;fi: (-)m~B9~~. ;~~~H~B9%~m~;p.

(2) 26. li'!iI:lr.i66Et*.(fJt'M!iUR.}~=M. S'9 #i. m. Linear Regression pJf ~ variable ) ,Q;\~:Ji'1::~lfE~~lt;m:lJi til§~~:1;. §. ( interval. ( dependent or ratio. •. 't::/G. ; Logistic Regression Jllj ±. (nominal). R#i.m~:Ji'1::~~M.§S'9:1;§.~olt;~·~H.M~~·m 1;).ti:,*fi:}~iW.*miQU-MA.:Ji'1:::;§Wr/~L\.m? tEP¥:miM~~ .1:JmiQUMA.:Ji'1::Uf~~:;}pUf~. i!& fr!i M ~ nonvoter). ,Jtlj Jl} .1:J. ? pJf 1;).. ( reader. iQU ~ J?fL. or nonreader) ?. ~ ~ :;}p. , Logistic regression. :Qi~1r1*Jij Logistic Regression. ~. Jl}.1:J miR:. gression /GtiI§~~#i..~:Ji'1:::1; § .~S'9rlm!§. 9=t '. ,. a. ( voter. or. Linear Re. tEIftl:Wrf3HJ!M~. S'9tA-M'. PJf~S'9~.lz:. .~m:Ji'1::~lfE~~lt;.~'~:Ji'1::~S'9~.lz:m~:Ji'1::~lfE~~lt;m ~'S'9:Ji'1:::1;§. 'ffi#i..~:Ji'1::R~~M.§S'9:1;§.~o. ml*~1r~M~i:f::j%. 1H!1*. ,'*. ( AGE ) ~/~JL\.m. Linear Regression ~rr7t;f1T. terplot *~71'~~M.~S'9IH!1*. ,. ( CHD ) Zrl3jS'9. ~fr~Wr:$t;Jij Scat. a. . .. ......... "...................... .. 1.0 .. 0.8 ~ >.. 0.6. o. 0.4. ~. 0.2 0.0. 10. 20. ao. 40 AGE(x). III. . 50. 60. 70.

(3) Logistic Regression :tU:l:..*,"..m~J:.I¥:lJ/lf13. III!-m~. : (1)if.~1ili~'tA~,'IM~SJl:t17lJ~{!£ ' .l:t17lJ~~. 27. if.*1il~A~-,'lMj~SJ. 0. (2){R~~~mJiPjM.13 (if'L'lMf~. '\. &if'L'IM~). (3)tiI!9=tJiPjM~~SJMl1*~;;r--t-5tm~. (4)tiI!9=tM7r. '. JID'L'IM~SJ~it~:II:. if SJif. ~ Pi tfIH~*. 0. 0. (Variability) :fEJ'iJf. 0. ~~~• • %'W~1im~.re.ft~~(if.~)5t~.. HI. '. (. ~~t~>et-*.RJmA:.t'IM~SJf~.. ~i!f}i!:i,IL'IM~. ) SJVariation '. 0. ~;fl~m l;.l7J~:}'{R~~. fqJ~*l~JiPjM~~ra~Ml1*SJ. ~.oreif.ti5tm~SJ.%~$~~-,reif.~5tm~,~re. if.ti;fOJIDIL'IM~SJMl1*. ~-. ' ff.I Scatterplot m~. (. ). 0. CHD Age Group 20-29 30-34 35-39 40-44 45-49 SO-54 55-59 60-69 Total. n 10 15 12 15 13 8 17 10 100. Absent 9 13 9 10 7 3 4 2 57. Present 1 2 3 5 6 5 13 8 43. Mean (Proportion) 0.10 0.13 0.25 0.33 0.46 0.63 0.76 0.80 0.43. 1.0 0.8. ;>-. ~ 0. 0.6 0.4 0.2 O.O...I.J,'. 1. 20. i. 30. 40. 50. AGE(x). II. =. 60. 70.

(4) 28. l111La~*ar.<~~~Iff.}.=Wl. :& iii! -. 1k.. ~ 7l". gression l¥J±~~F8J. t±I Logistic Regression ~ Linear Re. 0. fflLogistic Regression~ff7}tiT~ , EB~{tR~Jj;{::R::Rff~ M~§l¥J~§~~,~~{tR~Jj;{Y~M~~:E(Y/X)~. ~1l-~. 0 fIJ 1 ZFa'J ; ffi):tE Linear Regression. 9=t '. {tR~~~~. ~~~~~Jj;{·~~E(Y/X)~.1l-~OfIJ1Z~o. 17lJ : ~~. 1tt~1rrlitf~1f-ti'flJAt~A~J'If~Fa'Jl¥JIHJf*~ , 1f-ti'~~.lr. x ' ::R::i!:fl3!1A:J'If~~{tR~Jj;{ y. 0. Logistic Regression :JJfi~~ E ( Y /X ) = Bo + B1X ~IDt. Bo=0.055 B 1=0.20. 1lt X=l (20-29~) ~. E(Y/X) =0.055+0.20(1). 1lt X=5 (45-49~) ~. E CY IX) =0.055+0.20(5)= 1.055. 0.255. Y~M~~*~l'EB~{tR~Jj;{::R::~M~§~~§~Jj;{,. M~~~1l-~OfIJ1Z~'~~*t±I~M~~~.~~~~~ ;f§~. , ~Di@~:JJfi~FfifJUJtU~iB:.~~#:tE ' PI J! Linear Re. gression :tE{tR~~::R::~ § ~~~m~r~~~ffl. 0. {:::)~~IHJf*7}#fil¥J~~~F8J. (l)Linear Regression ~~J~,ft. ' Linear Regression. ~.~~o~~f*.::R::m. ~~IHJf*B97}#fi~~. ~.lr~~X~.l.&. ~,{tR~~Y~Z~.~.&oaX~1~.~2~'. ~::R::EB5~.~6~'Y~Z~.~.&;f§F8Jo. (2)Logistic Regression. tm ~ -. Ffi ~ • X lfIIt «;. 1f- ti' ' Y lfIIt 1. 7l" lifiA~...'. If.

(5) Logistic Regression :tEn..f4,!f!,.pff~J:.~lJlm. , O~.iJ';&~}j!~A:'J'.~ ~1mf*?t#Pl¥J~~~.. 0. :tE Logistic. Regression. 29. q:. ,. s MotE 20 ~IJ 34 ~Zr~' , ~~'¥~. ~~~'.Ml¥J • • tt&~ • • l¥J*~;~35~Z.'. n~.~*~'.~l¥J.$.~'-fi~~~z.'~ .~T*o&ft~~,. .~5.D~6~'Yn. J@'jitl! rPJ. ~)~1. X(. .Dl¥J~ffl~~m~;. X iIiIb l¥J jj.fj ~ ~ , Y l¥J.D it ~ /J". (::;)Jtn.~£. ( Random. D~2~'. X. 0. Error ) l¥Jffii~~[qJ. (1 )Linear Regression. ~.~~ : E(X/Y). jt;q:.Jt. E. Bo+BlX+. ~ tL Tl¥JW~. CD~';¥;~?t~c. ®jt;SjZ~1t. :. ( normal. ( mean. E. distribution). ) ~Jk 0 ;. ( variance). 1E'I¥;1t ( constant). (2)Logistic Regression. ~~~ : E(X/Y)=Bo+ BIX. Y=E(Y/X)+ ~. +. E. E. ' Y ~~. Logistic Regression. 1R 0 ' ftft J;J. E. E. ®~. E. ~ll:t,. E. 1- E(Y IX). E(Y IX). l¥J5}«ti~~'I¥;~?t~c. '. 0. = " Odds Ratio. ( binomial. ffiHj~:~lJ;[?t~c. distribution) , ~~ Linear Regression W~ ~c r:lFH~fi~ [qJ. ft. & ~~j:ifj:fmm :. CD1it Y= l ' Y=O'. Jk 1 '. E. ~ 'I¥;~.

(6) 30 1II1l:i&~*¥<.fijf~il.IRHft=.ltI!. :tE Linear Regression r.p ,. fi1f~*flI*~$fl::::i®.{,*Ik". ~$fl::::i®.1*l1(5fOR square *M.~~flJ{ra'B"JIJm{'*;. Regression r.p , JlU3::.~flI Odds Ratio *1JlltJM~. Logistic 0. .I.;""rr~lit. :. Odds Ratio &l~-&ml=JJl (-)'ffij 1l'-The odds ratio. ~~~~-.#~~~B"J~~*~U~~~~B"J~~. (The odds is simply the ratio of the probability of an event occurring versus the probability of it not occurring) /;'...-? "b.. ProbeeventL o A -;p...,4;o!J • Prob(no event). .{91JW;l3J3tnrT : tm. *. CW!~=). fl(; 1r~ 5t VT 11: JJIj. l}il1¥f~*re;m¥l:*€lf,(11:. ~= (JtNfrN:~~i!Ilf1,() ,-~~. ~ ~ 1'1?iI. rl3' B"J mm 1* '. l.Ii:t PJ U flI odds *JJIlUM~. ratio. ~. ~--~~. /G.• ir~t-. 0. ~. 1,(. ir~t·. A:47 C:69 116. B:81 D:39 120 -. 128 108 236. -. (1)~ffifU11:JJIJ ' ~W**re~¥l:*€ltelf}f,(B"J.H::{91J ' ~~*re~~. MiMf:ff,(B"J 1.18. (128/108= 1.18). (2)re11:JJIj~l3:~~. ,. l1t~~t-.B"J~. 0. conditional odds:. OO~A*re.¥l:Mi.f,(B"J~~'~~*¥l:*€l.f,(B"J~~~. 0.68 m ( 47/69=0.68. I. 0. ®f,(A*re.¥l:*€l.f,(B"J~~'~~*¥l:*€l.f,(B"J~~B"J. 2.08. ( 81/39=2.08). 0. (3)M~!l:11:JJljrl3'B"J.H:~ ,l1t~~t.B"J. the ratio of 2 con. ditional odds : m~11:*re.¥l:Mif,(11:B"J~~,~f,(11:*re.¥l:*€lf,(11:B"J.

(7) Logistic Regression =a:.it.,*"'iJf~J:.(I{J.m. lt19lJS"J 0.328 fg 0 A . B AD 47x39. r-;-ty=-gc-. 01 v. 31. 0.328. co. ®~fi*m~R~~fiS"Jlt19lJ'~~fi*m~R~~fiS"J. lt17lJS"J 3.049 fg 0 B . A Be 81X69. ty-;-c:-=~=. 3.049. A'·h./ <>0. h)flJffl i!§Mr1*1$(* ill odds ratio ( 'If ) Logistic Regression ~ , the odds ' l$(~ff9bt~ In ( 'If) In. 0. = BI ; BI ~i!§Mr1*1$( ,. 'If. ~P'IfS"JJtl$(~:tn. ~lI:t. S"J 45 ~ii.l PLj Log of. Linear Regression 9=tS"Ji!§Mr1*1$( ;. BI ''If360=e 'e ~ml$( ( exponential). 0. ~:~.M.A~~~~x(~'.) ~.~~JfrlH~A{&~~ y ( ~ , •. +. 2~,.m~.~~. ). •• S"Jlt19lJ'~~~.~. a9jipjfgo. =. . . The Simple Logistic Regression tEn!:fT Simple Logistic Regression. ~. , ~~ !t:.I;).l"'=;oo. 11fM: (-)~~~~~~jipjMM. § S"J45 §!Q~ ( dichotomous). 17lJ: (J!~=Et~gg) ~~~~A1f.~ ~i!f~JL'.~. (. ( 5tmG55it.l;).J::Et.l;).l"'jipj&) , ). 0. lU odds ratio ~jipj;oo*~. <Dw. 21X51. 8.11 22x6. f.R!Q~A.

(8) liI:rr.iar~*.(,"~il.lflHI~=M. 32. -m. ®W. eBl=e2.094=8.11. fW~ :. 55 ~tJJ.:~IL'.~~Jt.{9lj , f! 55 ~t1."""F~~ 8.11. o. .=. AGE(X) 55(1). CHD(y). <55(0). Total. Present(1). 21. 22. 43. Absent(O). 6. 51. 57. Total. 27. 73. 100. .Im. Estimated Standard Variable AGE Constant. Coefficient. Error. Coeff.lSE. W. 2.094. 0.529 0.255. 3.96 -3.30. 8.1. -0.841. H~~ftlflJif!mmm. 17IJ:. 13 tJJ.:tr9;:g 13~:lJi (polytomous). (J!~.n:). ~ft~:lJi~~~'~~~A'~A'~~~A'~~~M ml3'~~:lJi~f!~~G.~(~.~)o ~~it~~.ffl. design variable (. -mm indicator variable). ~~~'~~li~:lJitr9~ml3m~~~o§~'~~~~mm. 13 q:t ,. ~~-m$~~~11. ( reference group ). 'lI}~~m. 13 .ffl m ft/. Linear Regression q:t tr9 Dummy variable . ' (J!~~'~f!t1.~A~~~~II) •. .n:&~~q:t~~~"""Fft • •. ~~. 0. :. ®t1.~A~~~~R'Mt1.~A.~tr9o~sm~(W) ~. 1. 0.

(9) Logistic Regression ~ti.~.!!J!..JiJf~J:.~.m. ® g:§~ ~ A,~WI E8 "l'. 15X20 5XI0. 33. "l' = e Bl = e1.386. 6.00. =6.00) ,. g:§~~A ~ic..'IitWlE8j:t{11j~. A,~WI E8"l' = 250~\2~. AE8~ffi. 8.00 (. 8.00) ']!PM'LA.f~ic..'Iit!~E8j:t{9lJ~. .1i. CHD Status Present Absent Total Odds Ratio rIP) 95% CI In ('q,). White 5 20 25 1.0 0.0. Black 20 10 30 8.0 (2.3,27.6) 2.08. Hispanic 15 10 25 6.0 (1.7,21.3) 1.79. "l'. 0. e. Bl. AE8/\@. Other .10 10 20 40 (1.1,14.9) 1.39. = e1. 792 = 0. Total 50 50 100. 111\. White(l) Black(2) Hispanic(3) Other(4). Design Variables Dz Ds 0 0 1 0 0 1 0 0 0 0 1. Dl 0. IIi:; Variable RACE(I) RACE(2) RACE(3) Constant. '--. . ......... Estimated Coefficient 2.079 1.792 1.386 -1.386. Standard Error 0.633 0.646 0.671 0.500. Coeff.lSE 3.29 2.78 2.07 -2.77. .q, 8.0 6.0 4.0.

(10) 1 34. lII.:ll:.aj~*.<iJf~~Bfl.H'~=M. t:)1it~:lzJ!:f9Hi'dm.. ( continuous ). ~lJi. : ~/\~~ • ~n:~lJi~1:F-ft ' 1:/{~lJi~~~li!i{"'\Jit~ J!t~~J[;* I±l R~ *{4 JtX:-A~. ( J~A~"'\Jitf~ ). t39~~ ,. eBO+BIX. : Prob (Event). 0. 1+eBO + B1X. 1. 1+e-(BO+BIX). o. Logistic Regression t39:1Jf.'f:.~~. g(X)=In[ 1-ir(X~. ir( ) ]. Bo+BIX. -5.31O+0.111(age). tllJ*1:F-ft=20~ ,. JtIJ g(X)= -5.310+0.111 (20)= -3.09. ~IL\.~. Prob (. 1. ). 1 +e -(BO+BIX) 1 1 +e -(-3.09). = .0435. ~}\. Variable AGE Constant. Estimated Coefficient. Standard Error. 0.111 -5.310. 0.024 1.134. !!P 20 ~,",/L\.~t39~ *l'iJfj~. Coeff.!SE. 4.61 -4.68. 0.0435 ( 4.35% ) , ~sp.. 0. 1:F-ft~.Ib-~~·n~,W<I~~t39~.1a/J' ,. 3.03' !!P1:F-ft4a:ttitm 10 1:F- • ~IL'.fiH~t39. lOX lll .. fft • Jtfj'l". e. :m:~i:t:tti fJrJ. 3.03. tlO*l;J, 10 1:F-~¥. 0.

(11) Logistic Regression «iitt.,*¥.fiJf~J:.B<Jlfiffl. 35. 1m .. The Multiple Logistic Regression ~n:. ~/F. --MI¥JIJij:~, it~ Jf.I ~Ij The Multiple. Logistic Regression. 0. f71J : {&~~~ Nodes: 1ft: BWJt*5~ ( 11i!::~¥:E ' o1i!::ft ¥t) ~n:~~:flEM. 1.. ' 5t5.1iJ1i!:: :. :q::l& : Age. ~.~~. 2.1frrm-,*,l¥JliJf~m~ : Acid-i\!iU.~~. 3. x :J'(:;~~*6 ~ : Xray. 11i!::~¥:E ' 0 1i!::~¥:E. 4. m8.~¥tijl(;~¥:E : Grade-11i!::~¥:E ' 0 1i!::~¥:E 5. J.It~I¥JR~~~. 0 ft~~-~~. : Stage. , 1 ft~. ~=~~ If~ Spsspc. +. ~. l:B I¥J Logistic Regression 5t:tIT *6 ~ ill]. r: ~:JL. LOGISTIC REGRESSION NODES WITH AGE ACID XRAY GRADE STAGE. ----------Variables in the Equation--------- B. S.E.. Wald. df. Sig. R. Exp(B). -.0693. .0579. 1.4320. 1. .2314. .0000. .9331. Variable. AGE ACID. .0243. .0132. 3.4229. .0643. .1423. 1.0246. XRAY GRADE STAGE. 2.0453. .8072. 6.4207. 1. .0113. .2509. 7.7317. .7614. .7708. .9758. 1. .3232. .0000. 2.1413. 1.5641. .7740. 4.0835. 1. .0433. .1722. 4.7783. Constant. .0618. 3.4599. .0003. 1. .9857. ~1Uf:~.n. ' Logistic Regression. g(X). 0.0618. =. -. 1¥J1J&A~. 0.0693(Age). +. :. O.0243(Acid). 2.0453(Xray) + 0.7614(Grade) + 1.5641(Stage). +.

(12) 36 1iJliI.ll:.iT&:iS*.(iJf~~IR.) M=M. <F,Ij~-)tlD*-MA 66 ~ 'Acid=48 ' Xray=O' Stage. o ' Grade=O $. ~* ~. (bl1il;f;E5toJt*s_;~i!:.~~ftf'8~. ?. 'JtUCDg(X). ? @:.tt odds ratio(-qr)= ?. : CDg(X) =0.0618-0.0693(66) + 0.0243(48)= -3.346 1. (blProb ( ~M: ). 1. 1 +e -(BO+BIX"'). 1 +e -(-3.346). =0.034 m~:. MA~BtoJt*S*. ~M:~~. R~. 0.034 0.034 1-0.034. J. .lV\11V CVCIH). 0035 .. m~:~MA~BtoJt*s*~~M:~~~~~atl l:t;17lJ~ .035*. .q,-. 0. 1-0.034 0.034. 2841. .. ~§z'~MA~BtoJt*S*~atl~~~~~~ M:~17lJ~ 28.41 *. 0. <F,.')~=>tlD*-MA 60 ~'Acid=62' Xray = 1 , Stage. =0' Grade=O ' JtU~ Grade EB 0 ~~ 1 ~~M:). ffif ( li!DB:PIEBaM:~. ':.tt~BtoJt*s*~~M:~ odds ratio ilr:l:tj1JQ~ffi. ~ grade=O ' Logistic Regression ~::1:1~ih:!,:;~. ?. :. g(X) = 0.0618 - 0.0693(60) + 0.0243(62) + 2.0453(1) + 0.7614(0)+ 1.5641(0)= -0.54 Prob ( ~M: ) odds ratio(-qr). 1. 1 +e -(-.54) 1 ~g:37. 0.37. 0.59. ~ Grade= 1 ' Logistic Regression ~::1:1~A~. :.

(13) Logistic Regression 1£it.,*"'{iJJ~J:.~lfIm. g(X) = 0.0618. 37. 0.0693(60) + 0.0243(62) + 2.0453(1) +. 0.7614(1)+ 1.5641(0)=0.22 1. Prob ( odds ratio('IJ'). ~;~. 0.555. 1 +e -.22. .551::51::1::. 1.25. =2.12. :.Grn&~0.~1_·~*BW~M*A~~~. odds ratio it:!:fi1Ju 2.12. *. 0. ~MIt.ilJJ;J.1jE~fL~ Exp(B). I:B • Exp(B) :it 'jt§!t;~ odds ratio • Grade 2.1413 • fOJ::rni~.I:B~ 2.1211Htl3lI:. ~-fj. ~ Exp(B). 0. 3i. ...[]fAJ~f.S.~:.I!1!!Hi.g.? (Assessing the Good ness of Fit of the Model) Logistic Regression w:i~. 1ft •. ~fi5m~~~~il~jj~1f. • E<:5t321ttmr : (-);fUffl Wald Statistics ~ffJj~~m. Wald Statistics =. C-£-) 2----·-.tLtltfR. Chi. Square(X2):5t#tJ ~ffJj~. Ho : b=O. 7iJf ~ ffJj ~ Ha : b 4= 0. li!P~:rrJf~~m§ffimU#(~::gr(. li!P ~ :rrW::gr( rtr J;A ffl mu{td~@::gr(. J;A~fLAf7lJ :. --Age ~ Wald Statistics = 1.4320 • AlPMtli?d~~ .2314 (p > .05) • IZSJ .tLt:tEIQ~**A .05 ~1lt~ r ~. 0. ·. m§tE~~ffJj. li!pif-~~m§ffimU*E,W~I¥9M*~~it~~M:. fl!ilJmJ.if-~~~:rr~::gr(Ift;ii;~o. 0. f'JfJ;A:tE.tLt.

(14) .,. 38. lII.ltif~jS*.(:/i}J~~!fl) ~=JUj. FJr 71J B9 ~ ~ 9=t • R::ff Stage ;fIJ Xray ~. , IW.L:J:tE~f~~.m~9=t '. ~~~. *. Stage;fIJ Xray ~MJi. n:~~o. WfUffl Log Likelihood. ffl Wald Statistics ~~*~. ,. ~fIj~~m. ~fIj~~. -)ifU. ' Iii'3!IDM1*. B. 3!IDM1*.B9~~~ SE t:!z"fr~~*. !btEm5Jtflj~. 0. :tE~~AA:¥R. r. ' tm!Lt-* '. 1J!Jf~. • Log likelihood ~.l:t~J:1fIj;B:J. o. Likelihood ~7T'~n:~~ 'j"/n 1 ' FJr .L;I,*1t~t~ JlX:~. lJlU. fl}.~':EB9 "'l~tt. '. ~ Likelihood B9mlfi~t. '. - 2 Log Likelihood ( film - 2LL) ,. slt. 2•. B9.m~. Chi-Square distribution;ftIiE[ •. ffl-2 Log Likelihood. *~1i5m~. 2LL B91:¥:~ • Jt9=t-MmA. .l:t~:ttf~M. 0. , ~.l:t~mMm. ~~.B9~~'. -flalm~. JtIjEH5~.B9~~ , ~mMmAB9-2LLZ.~flli •. M~.~~B9mA·~m.. 1Q. ~~.l:t*~M~.~~. ;m.mAz.-~LB9~mfflGm~7T'·~A~r:. G- -2 I [Likelihood without the variable] n Likelihood with the variable = - 2 [Log Likelihood without the variable. Log. Likelihood with the variable] .L:JGfj[ ( improvement ) 5Jtflj~~. ~fIj~~m :. Ho : Model n-l=Model n' Model n;fIJ Mod. el n-l B9fJllJllj11slt&1:¥:}jU 1Yf~fIj~~. 0. Ha: Model n-l=l=Model n' Model n B9fJl. lJllj 11 ::ff ~Hi!f B9 c&i1t. 0.

(15) Logistic Regression :t£it.",*m:~J:(J{J1fI.m. J.;J.~+ ~{7ljwtf!ij. 39. , mA 1.2.3.4.5. ~txWVfllFf±~~fflmU~. ( ~1t~*~~mflf~&:i&{~ ,. t!n:i&ml:lf~~~. , :Jt;ji!LAm. ~/T>:t!2f&FJf1f~m~. Model. -2LL. 1.. Constant. 70.25. 2.. Xray. 3.. , :R5tlJlJ. Improvement. d.f.. slg.. 59.00. 11.25. 1. .001. Xray,Stage. 53.35. 5.65. 1. .0175. 4.. Xray, Stage.. 51.05. 2.30. 1. .354. 5.. Saturated. 48.126. 2.92. 2. .425. Acid. I. (I)mALRt!2fi5m~. a. 2LL Et'11H~mA1.~ 70.25 ~~ 59.00'. a. ( improvement) 11.25 ' sig. 2LL=70.25. fWj Am~Mm~ Xray 'mAq:tt!2;J{5 Xray. (2):mA2. Constant. ( Constant)'. mm G. rr~. t!Lzt~wt. '. G1H~. 11.25. , tElim~*~ .001. ~. :g;. ~+q:t~. a. ffi'HEm~~. a'.~m=Mm~~m-MmA~ffl.~~o. Xray" Stage;f1J Constant ~. ,. a. Stage' lit ffil. 2LL Et'11H 59.00. 53.35 ' Q:f( ,. fjHr~1f JE~Et'1~!U.wt ' m:::::::MmA~m=MmA~fflmU~~. 0. a. sig. :(£1im~7j(_. ~3:?:. A q:t t!2;J{5. ffiliEm~w.~. 5.65. ml~. ~. ffl!!. (3)m A 3. q:t fWj A m -. .0175(p. .05). (4)mA4.q:tfWjAm-Mm~ Acid ' lItffilmArp1f=M~ TI:m~& m~. 0. -2LL 1Hffi 53.35 ~~ 51.05 '7lQ:f(. sig = .354(p > .05) , lim /T-;. lim ~ * _ .05 ffil •. 2.30. 0. ~ it iE m. mot!Lft~wt,ft~&1fJE~~ • • •~,m~M:mA~m. MmA~fJHlIU~tff. 0.

(16) 1iiI.n:i&~*¥OJt~j!,li) ~=#II. 40. (5);f!;it~5.::If::. !fJ. 0. -. Saturated ;f!;it~ • FJff:fa%l1ft~~Jq~11LA.;f!;itA:;. 1R Iil:. 2LL. 48.126 • R ~ ~ J 2.92. 0. sig = .425(p. .05) • M7I';(EM~Jtc~ .05 ~ • $I:;i*fE~~ffN~ ~4.slt$I:;:£~. 0. >. ;f!;it~5.:to~. 0. ~.%fi~ffl.~f:f~M~.~~m:-~~;f!;it~~m~ :i{i~~~;f!;it~ ( the best fitting model) • -::If::~;f!;it~J6,m* ~Miii. ( the most parsimonious model). 0. Linear Regression !fJ • ?itf~~iiH1jt;~H~~~:i{i~' " {El fjl§M~. ~~~..JI:~.A;. ITti;(E Logistic Regression !fJ • ill,. ~it;~illfi:rnUl.lJ • ~.tItiE~+!fJ • R1r'~~~=M.~ • .~mm~ffl~~~*~·®ffl~n~~~M;f!;it~slt$I:;~~o. 7;. ... SPSspc+:J:ti<df;i1t IJJj. (-)£*m~. +. Spsspc Regression. 0. ~. J1fi. *. •. 4.0 l;J.. :;:t. 00. ~. J:li!. Logistic. tlQ*R~fi~~j.m;IJ1*~%fi • mr7Uro~ • :gt. fjl§~l±l~~+:/!l!,t~~f:ft. :. Logistic Regression Nodes with Age Acid Xray Grade Stage.l:3:lli;m~!fJ • Logistic Regression *Wf.Jf~~t] Logis. tic Regression 5tfi • Nodes ::If::~~~ , with j;.J~::If::~ft~ ~. 0. tlt:l*~ft~~9=t ' f:f~M~ 13 l;J.l:~~ 13 ~~ • jlU'fl~ Jj. 7i-~ro~o {=:)~ffl;f!;itA~m~. Spsspc. + !fJ. • ~ ffl.. Backward ~ fi: 15 r.E: • ;(E.tIt. ~. PI l;J. ~ ~ Forward :to. 11' *i3. ~. Forward Stepwise.

(17) Logistic Regression :tEn.ft.jJf~J:.~J!lJij. Selection. 0. ;tt;.~J'ftzQr. 41. :. (l)~-lIIm~R l,g13-1it1Jt. ' ='1-qf!!jl , R. l,g13-1itIJtf'Bm~~1it. &~~.'~~~~Urm~~~~m~J'fo (2)'m~1if ffl~-t'-9f'B Score ' ~W~f~~H~:8:{j£. ). f'B~lJi{. ( occu ). ~A~={lI!!Im~. (. 0. (3)ffl Residual Chi-Square *~~~~~. 0. ~~~Ho:~~*~A~m~~~(*~~m~)Z~ lJi{f'B;@!mffilJtl$~7n~. 0. 1Ji(~f'Bm~T~~IE. ). 0. (!ilPiiJ1t~lJi{l$TA~f~f'BfJU:J{Uj],. ~~~~Ha:*~A;@!m~~~Z~lJi{f'B;@!mffiIJt9' ~o/~-lII/f~~7n~. 0. (!il~~j,'~-lII~lJi{AM~ffU:J{Uj]'. 1Ji(. ~f'Bm~~O/.M~A-lII~f'B~lJi{o). ~~~1ifM.m.~fi.:8:~f'B~lJi{~Ar-lIIm~9' J[JIjf'Jf~.. f'B~li~lJi{l$~~A;@!m. sidual Chi-Square f'Bm:TM.~~ll:. ~. 9'. ffij Re. 0. (:::;lit{7lj IDt !Y-1 tzQ;~Hx1l"~ffltl:5J!j. (sex) .... ~ (occu) ... 4~ (age) ... :ttl!G'[. ( manarea ) ... &.0 ( rank) ... 1L{II!!I~lJi{~~li~lJi{ ,. it< ~ lJi{. r:tE tit !Wi ~ /If) J:: ~ 51 ~ f'B ~. J. Spsspc + f'B Forward Stepwise Selection fjJ gression *S*tzQ~+-f'Jfjj~. :. *ffl. (form). te f'B Logistic. 0. Re.

(18) 42. f!IlII.n:j6(j~*¥(jJf~ifl.afl.> ~=M. Jl+-. SpSSPC + Printout <~-MmA>. Chi·Square 750.559 859.000. ·2 Log Likelihood Goodness of Fit. df 858 858. Significance .9965 .4840. Variables in the Equation B Variable S.E. Wald df Sig R EXlJ(B) Constant .0935 319.5282 ·1.6708 .0000 SPSS/PC+ ----------------------------- Variables not in the Equation--------------------------- Residual Chi Square 36.549 with 5 df Sig=.oooo. ~---------------------------. Variable SEX MANAREA AGE OCCU RANK. Score .9639 18.2019 1.6070 22.6631 11.5617. df. Sig .3262 .0000 .2049 .0000 .0007. R .0000 .1469 .0000 .1659 .1129. <~-MmA>. ·2 Log Likelihood Model Chi·Square Improvement Goodness of Fit. Chi·Square 726.987 23.572 23.572 858.995. df 857 1 857. Significance .9995 .0000. .0000 .4744. Variables in the Equation S.E. Wald df .2065 21.5708 172.2687 .1727 SPSS/Pc+ -------------------------- Variables not in the Residual Chi Square 15.249 with Sig=.0042 4 df. Variable OCCU Constant. B .9593 -2.2668. Variable SEX MANAREA AGE. Score .0041 14.4841 1.1306. df. 1. Sig. .9489 .0001 .2876. R .0000 .1290 .0000. Sig .0000. R .1615. 2.6098.

(19) Logistic Regression iEi:t."';H"iJf~l:.~J1Iffl. 43. <m=MmA) Chi·Square 710.124 40.435 16.862 853.313. -2 Log Likelihood Model Chi·Square Improvement Goodness of Fit. df 856 2 1 856. Significance .9999 .0000 .0000 .5195. -------------------------- Variables in the Equation ---------------------------. S.E. Variable B Wald df Sig R Exp(B) 1.1508 .3167 13.2044 MANAREA .0003 .1222 3.1607 .8717 .2087 17.4524 OCCU .0000 .1435 2.3910 Constant .3249 95.7767 ·3.1799 .0000 SPSS/PC+ -----------------------Variables not in the Equation-------------------- Residual Chi Square .744 with 3 df Sig=.8558 Score .0009 .0914 .6435. Variable SEX AGE RANK. ~+-~lr'. ( constant ) jJ. df. Sig .9757 .7624 .4224. R .0000 .0000 .0000. ' tEm-MmA9=t '. Spsspc+. 7t:;rem-l&. Ailm~jJ~A9=t' pJflefl¥J~llJif~:lt;J*tE~m. A 9=t ( variables not in the equation) ,. Jt 9=t. Residual. Chi Square = 36.549 ' sig=.OOOO(p<.OOl)' m:tlr'tEm:t~J.t<. .001rtif ' :fE~~1Nitit ' E!p*tEi!g[mjJ~A9=tI¥J~ll~:gr:[' 1f-MI¥Ji!g[m1*l&/G~~~ lll1~. 1&~~. 0. j.'. rltrtif ' iolU~wrffl Score *~~m:t. I¥J~~~~ (Occu. 3J.tA. m-MmAI¥J-2 Log Likelihood ~ 750.559. r -11!!!!mA. 0. 0. m=MmAm:tlr' ' jjg!m )JmA9=tI¥J~Jj4 ( variables in the equation). occu. jJ~A9=tI¥J~. constant' fm*. 1f sex" manarea " age "& rank. 0. Residual Chi Square. 15.249 ' sig=.0042 ' ~~{'E~.:j!f JJc$ .0042 (p ~1NID.!'. ' E!fJ{'E sex" manarea " age Ii. rank. .01) rtif ' :fE~. p:gM~~. ,~j.'.

(20) liIl.lr.a~*.(~~ilI.!flHIi=WI. 44. MJt{1{~f1JtJ't:lffflmd. ,. ~f~~m:JUt1~B<J~lJ,i. *m::ttB<J -. ~. manarea ~A ~ -Mm::tt. 0. ~m-Mm::ttB<J 750.559. 2 Log Likelihood. 726.987 ' q5(~7 23.572. III. m)f~fr ffl Score. 0. 0. m= Mm~1.m7F •. 9='B<J~lJ,i-El.fi5 occu ... man·. area ~ constant • rm*:tE~.. B<J~lJ,ilf sex'" age. Ii... II. rank. 0. Residual Chi Square. .774' sig =. 7F:tE1.m~J1(.$ .05 ~ ,. WJ ffl md {1{ ~ lJ,i. ~. 710.124 •. • .J;lP sex'" age :& rank. B<J -. 0. .l:tJ::-MmAB<J 726.987. 2 Log Likelihood. ' q5(~ 716.862. 1i1,1n*~A~.1J~:J!:; ~IH!~¥*.WJfflmd{1{~lJ,i. m.a~w~·. .8558(p > .05) •. ,. 0. sex'" age :& rank. Spsspc + ~A/f'fI}~:&~~~lJ,i. ,. •• ~~ft~'JUt.~ffl~{1{~lJ,iB<Jm::tt-El.~. ~~~:ttB@1~M~li~lJ,io. -I:: ... t!~fi. R1i'*B Logistic Regression. -Jl:t;..l:t• • • B<J~.'~~li.lJ,i~ MtJ.J::B<Jm § ~71-. '. .... ~r,,~.. B<J-Jl:t;.~*.~. ... {1{.lJ,i~*lfffi. ' JtIJ~4H~$~m J::B<J$~. §. ~16'~~111j§§J:I , tE@ii~9='5Iffl B<J[Ifl~9='. .... _ 3?: ~ /\.1* te. EJ. ,. 0. ' [Ifl- . .. David W. Hosmer & Stan. ley Lemeshow, Applied Logistic Regression, New York: John Wiley & Sons, 1989 ; rm~:fLJW W EJ Marija J. Norusis, Spsspc + Advanced Statistics Version 5.0, Chicago, IL: Spss Inc., 1992. 0.

(21) *J~.Z ~~. • Logistic. Logistic Regression :(£it.f4"iff~J::.tr.JJlIm. 45. Regression ~-:fI:ffi~:1:f ffl tt-Jki1EH1fi*. •. *tt-J~.~I§. WJ4§.{:ft~Logistic Regression:1:fJ1iW?17. tt-JQi{Mo. }\ .. e:1f_13 Agresti, A. (1990). Categorical data analysis. New York: Wiley. Aldrich, J. H.,& Nelson, F. D. (1984). Linear probability, logit, and probit models.. Guantitative Applications in. the Social Sciences (series no. 07-045). Beverly Hills and London: Sages Pubns. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis. Cambridge, MA: MIT. Brand, R,& Keirse, M. J. N. C. (1990).. Using Logistic Re. gression in perinatal epidemiology:An introduction for clinical researchers. Part. I : Basic concepts. Paediatric. and Perinantal epidemiology, 4, 22-38. Christensen,. R. (1990).. Log-linear models.. New. York:. Springer-Verlag. Cleary, P. D., & Angel, R (1984).. The analysis of relation. ships involving dichotomous dependent variable.. Jour. nal of Health and Social Behavior, 25, 334-348. Fienberg, S. E. (1981).. The analysis of cross-classified. Categorical data (2nd ed). Cambridge, MA: MIT. Fingleton, B. (1984).. Models of category counts. Cam.

(22) 46. 1Il:lr.i&~*¥(.jjff~il.ifl.) 3ft=Wl. bridge, England: Cambridge University Press. Fleiss, J. L., Williams, J. B., & Dubro, A. F. (1986). logistic regression analysis of psychiatric data.. The. Journal. of Psychiatric research, 20, 195·209. Haberman, S. J. (1978).. Analysis of quantitative data. (Vols. 1 & 2). New York: Academic Press. Hanushek, E. A., & methods. for. Jackson,. social. J. E. (1977).. scientists (ch.. 7).. Statistical. New. York:. Academic Press. Hosmer, D. W., & Lemeshow, D. (1989). regression (chapter 1-5).. Applied logistic. New York: John Wiley &. sons. King,. G.. (1989).. Unifying. political. methodology:. likelihood theory of statistical inference.. The. Cambridge,. England: Cambridge University Press. Kmenta, J. (1986). Elements of econometrics (2nd ed., sec tion 11·5). New York: MacMillan. Landwehr, J. M., Pregibon, D., & Shoemaker, A. C. (1984). Graphical methods for assessing logistic regression models. Journal of the American Statistical Association, 79, 61-71. McCullagh, P., & NeIder, J. A. (1989). Generalized Linear models (2nd ed).. London: Chapman and HalL. Upton, G. J. (1978). The analysis of cross-tabulated data. Chichester, England: Wiley..

(23)

(24)