Logistic Ppt

Not e sonLogi s t i cRe gr e s s i on

STAT4 3 3 0 / 8 3 3 0

I nt r oduc t i on Pr e vi ous l y ,youl e a r ne da boutodds r at i os( OR’ s ) . Wenow t r ans i t i onandbegi ndi s c us s i on ofbi nar yl ogi s t i cr e gr e s s i on.Wewi l ls e e t ha tOR’ spl a ya ni mpor t a ntr ol ei nt he r e s ul t sofbi nar yl ogi s t i cmo mode l s . STAT43 30 /83 30PRI ESTLEY

I nt r oduc t i on Pr e vi ous l y ,youl e a r ne da boutodds r at i os( OR’ s ) . Wenow t r ans i t i onandbegi ndi s c us s i on ofbi nar yl ogi s t i cr e gr e s s i on.Wewi l ls e e t ha tOR’ spl a ya ni mpor t a ntr ol ei nt he r e s ul t sofbi nar yl ogi s t i cmo mode l s . STAT43 30 /83 30PRI ESTLEY

Bi nar yLogi s t i cRe gr e s s i on Bi nar yLogi s t i cRe gr e s s i oni san appr opr i at ewhe n: 1 . Ther e s pons evar i abl ei sc at e gor i c a lw/2c at e gor i e s( bi nar y , di c hot omous , e t c . ) .Ther e s pons ec a t e gor i e sar eof t e nge ne r i c a l l y l abe l e d“s uc c e s s ”or“f ai l ur e ”. 2 . Oneormor ee x pl a na t or yv ar i a bl e sa r ei nv ol v e d.The s ec a nbe e i t he rquant i t at i veorc a t e gor i c a lorami xt ur eofbot h. 3 . Onei si nt e r e s t e di na s s e s s i ngt her e l a t i ons hi pbe t we e nt he bi nar yr e s pons eandt hee xpl anat or yvar i abl e sand/orpr e di c t i ng t her e s pons ec a t e gor yba s e dont heva l ue ( s )oft hee xpl a na t or y v a r i a b l e ( s ) . STAT43 30 /83 30PRI ESTLEY

TheMode lEquat i on

STAT43 30 /83 30PRI ESTLEY

TheMode lEquat i on Af e w poi nt s : 1 . E( y)c a nne v e rf a l lbe l ow 0ora bove1 ( Re me mbe r : i ti sapr obabi l i t y! ) . 2 . Themode li snotal i ne a rf unc t i onoft heβ par ame t e r s .Thi si sat ypeofnonlinear r e gr e s s i onmode l .


TheMode lFunc t i on


TheMode lEquat i on Al t e r nat i ve l y ,t heequat i onc a nbe t r a ns f or me dt os how t ha ti tmode l st he na t ur a ll oga r i t hm oft heoddso f =1. y


TheMode lEquat i on

Thel e f ts i dei sc al l e dt he“l ogi t ”


TheMode lEquat i on I nge ne r a l ,t heb e s t i ma t e st hec ha ngei nt hel ogodds i whe nxi i si nc r e as e dby1uni t ,hol di ngal lot he rx’ si n t hemode lfixe d. The r e f or e ,e xp( )e s t i ma t e st heORofas uc c e s sf or b i e ac haddi t i onal1uni ti nc r e as ei nxi. Fur t he r mor e , ( e x p( ) 1) * 100gi ve st hepe r c e nt b i i nc r e as ei nt heoddsofas uc c e s sf ore ac h1 uni t i nc r e as ei nxi. STAT43 30 /83 30PRI ESTLEY

Mode lFi tSt at i s t i c s

Al loft he s es t at i s t i c sa s s e s st hemode lfit t hr ought hequa l i t yoft hee xpl anat or y c a pa c i t yoft hemode l .



2LogL The2LogLi ke l i hoodi sa t r ans f or mat i onoft heLi ke l i hoodf unc t i on( L) . Li saqua nt i fic a t i onofho w we l lt hemode lfit s t hes a mpl eda t a .



Bot hAI C& SCar ede vi ant soft he2Log Lt ha tpe na l i z ef ormode lc ompl e xi t y ( t henumbe rofpr e di c t orvar i abl e s ) .



AI C Akai keI nf or mat i onCr i t er i on. Us edt o c ompa r enonne s t e dmode l s . Sma l l e ri sbe t t e r . AI Ci sonl yme a ni ngf uli nr e l a t i ont oa not he r mode l ’ sAI Cval ue .



SC Sc hwar zCr i t e r i on.Ve r ymuc hl i ke AI C,howe ve rt hepe na l i z at i oni s di ffe r e nt .SCt e ndst of a vors i mpl e r mode l st hanAI C. STAT43 30 /83 30PRI ESTLEY


Choos eei t herAI CorSC( notbot h)and us et heval uesundert heheadi ng ‘ I nt e r c e ptandCovar i at e s ’t oc ompar et o c ompe t i ngmode l s . STAT43 30 /83 30PRI ESTLEY

Themode le quat i on.


I nf e r e nc e : TheCoe ffic i e nt s .

I ns t e adofat t e s tf ort hes i gni fic anc eofa c oe ffic i e nt( l i kei nl i ne arr e gr e s s i on) ,we ha veaWal dChi Squar edt es t .



Remember ,t ypi c al l ywedonote val uat e t hei nt e r c e pt ,butr at he rf oc usont het e s t f ore ac hpr e di c t or .



I nt hi sc as e,agei sas t at i s t i c al l y s i gni fic antpr e di c t orofdi s e as es t at usa t t heα=. 05l e ve l ,X2(1)=11. 53, p=. 0007. STAT43 30 /83 30PRI ESTLEY

I nf e r e nc e : TheCoe ffic i e nt s . Onec a na l s oobt ai nCI ’ sf ort he pa r a me t e re s t i ma t e sus i ngCLopt i oni n t heMODELs t at e me ntofPROC LOGI STI C.



Aswef oundi nl i ne a rr e gr e s s i on,wec a n c onc l udet hatagi ve npr e di c t ori s s t at i s t i c al l ys i gni fic antatt heα=. 05i ft he 9 5 % CIdoe snoti nc l udet henul lva l ueof 0. STAT43 30 /83 30PRI ESTLEY


The r e f or e ,ourbe s te s t i mat eoft he c hangei nt hel ogoddsf oragei s0. 0285, howe ver ,wear e95% c onfide ntt hatt hat c ha ngel i e sbe t we e n0 . 0 12 0a nd0 . 0 44 9f or t hepopul a t i on. STAT43 30 /83 30PRI ESTLEY

I nf e r e nc e : TheCoe ffic i e nt s . Fur t he r mor e :e xp( . 0 28 5)=1 . 0 29 e xp( . 0120)=1. 012 e xp( . 0449)=1. 046 The r e f or e ,wee s t i ma t eape r s on’ soddsof c ont r ac t i ngt hedi s e as ei nc r e as e1 . 029t i me s f ore ver yyeart he yageandwear e95 % confident t hatt hi si nc r e as er ange sbe t we e n ( 1. 012, 1. 046)f ort hepop. STAT43 30 /83 30PRI ESTLEY

I nf e r e nc e : TheCoe ffic i e nt s . Ofc our s e ,wenol ongerha vet oc omput e t he s eoddsr a t i oe s t i ma t e sbyha nd, be c aus eS ASpr ovi de st he mf orus .


I nf e r e nc e : TheCoe ffic i e nt s . Fur t her mor e: ( e x p( . 0 28 5) 1 ) * 1 00 % =2 . 8 9%. ( e xp( . 01 20) 1 ) * 100 % =1. 21 % ( e xp( . 04 49) 1 ) * 100 % =4. 59 %

Wec a ns t a t et ha tt heoddsofc ont r a c t i ng t hedi s e a s ei nc r e a s eby2 . 8 9% wi t he a c h addi t i onalyeari nageandwear e95% c onfide ntt hatt hi si nc r e as er ange s be t we e n( 1. 21%, 4. 59%)f ort hepop. STAT43 30 /83 30PRI ESTLEY

Fi nalNot e :Mode lFi t t i ng Re al i zet hati nor de rt oe s t i mat et he mode lpa r a me t e r s ,t heda t amus tc ons i s t ofas ubs t a nt i a lnumbe rofe a c hr e s pons e c a t e gor y . Fore xa mpl e ,onewi l lnotbe abl et oe s t i mat et her i s kofc ont r ac t i nga di s e as ei ft hedat as e tdoe snotc ont ai n anyi ndi vi dual swhoha vebee n di a gnos e dwi t ht hedi s e a s e . STAT43 30 /83 30PRI ESTLEY

Fi nalNot e :Mode lFi t t i ng Es s e nt i al l y ,t he n,i nor de rt oe s t i mat et he pr obabi l i t yofe i t he ras uc c es sorf ai l ur e , t hedat as e tmus tc ont ai nas ubs t ant i al numbe r( >30i sbe s t )ofobs e r vat i onst ha t e xpe r i e nc e das uc c e s sandas ubs t ant i al numbe rt ha te xpe r i e nc e daf a i l ur e .


Mor eaboutout put . PROCLOGI STI Cpr ovi de smor e i nf or mat i onc onc e r ni nghow t hemode l fit st hes a mpl eda t a .


Mor eaboutMode lFi t Per c entConc or dant Apa i rofobs e r va t i onswi t hdi ffe r e nt obs e r ve dr e s pons e si sc ons i de r e dc onc or da nti f t heobs e r va t i onwi t ht hel owe ror de r e d r e s pons eva l ueha sal owe rpr e di c t e dva l ue t ha nt heobs e r va t i onwi t hahi ghe ror de r e d r e s pons eva l ue .


Mor eaboutMode lFi t Pe r c e ntDi s c or da nt A pa i ri sc ons i de r e dd i fan i s c o r d a n t obs e r va t i onwi t hal owe ror de r e d r e s pons eva l ueha sahi ghe rpr e di c t e d va l uet ha na nobs e r va t i onwi t hahi ghe r or de rr e s pons e .


Mor eaboutMode lFi t Pe r c e ntTi e d A pa i rwi t hdi ffe r e ntr e s pons e si s c o n s i d e r e dt fi ti sne i t he rc onc or dant i e di nordi s c or da nt .


Mor eaboutMode lFi t Some r ’ sD,Gamma,& Ta ua The s ear es t at i s t i c st hatme as ur et he s t r e ngt handdi r e c t i onoft her e l at i ons hi p be t we e npai r s .


Mor eaboutMode lFi t Some r ’ sD& Taua L i k er ,t he s evar ybe t we e n1. 0( al l pai r sdi s c or dant )& +1. 0( al lpai r sa r e c o n c o r d a n t ) . Some r ’ sD=t hedi ffe r e nc ebe t we e n t he% c onc or dantandt he% di s c or dant* 100. STAT43 30 /83 30PRI ESTLEY

Mor eaboutMode lFi t Gamma Gammai sas i mi l ars t at i s t i c :i t ’ s va l ue sa l s or a ngebe t we e n1 . 0& +1 . 0 , howe ve rt hei nt e r pr e t at i onoft he s e val ue si sdi ffe r e nt :1. 0=noas s oc i at i on & +1. 0=pe r f e c tas s oc i at i on.


Pr e di c t e dVa l ue s Theout putofal ogi tmode li st he pr e di c t e dpr obabi l i t yofas uc c e s sf or e a c hobs e r va t i on.


Pr e di c t e dVa l ue s The s ea r eobt a i ne da nds t or e di na s e par at eS ASdat as e tus i ngt heOUTPUT s t at e me nt( s e et hef ol l owi ngc ode ) .


Pr e di c t e dVa l ue s PROCLOGI STI Cout put st hepr e di c t e dval ue s a nd9 5% CIl i mi t st oa nout putda t as e tt ha t al s oc ont ai nst heor i gi nalr a w dat a.


Pr e di c t e dVa l ue s Us et hePREDPROBS=Iopt i oni nor de r t oobt ai nt hepr e di c t e dc at e gor y( whi c h i ss a ve di nt he_ I NTO_va r i a bl e ) .


Pr e di c t e dVa l ue s _FROM_=Theobs e r ve dr e s pons e c at egor y=Thes ameval ueast he r e s pons evar i abl e .


Pr e di c t e dVa l ue s _I NTO_=Thepr e di c t e dr e s pons e c a t e g o r y .


Pr e di c t e dVa l ue s I P_1=TheI ndi vi dua lPr oba bi l i t yofa r e s pons eof1 .


Sc or i ngObs e r va t i onsi nS AS Obt a i ni ngpr e di c t e dpr obabi l i t i e sa nd/or pr e di c t e dout c ome s( c a t e gor i e s )f orne w obs e r vat i ons( i . e . ,s c or i ngne w obs e r vat i ons )i sdonei nl ogi tmode l i ng us i ngt hes amepr oc e dur eweus e di n s c or i ngne w obs e r vat i onsi nl i ne ar r e gr e s s i on. STAT43 30 /83 30PRI ESTLEY

Sc or i ngObs e r va t i onsi nS AS 1.Cr e a t eane w da t as e twi t ht hede s i r e d val ue soft hexvar i abl e sandt hey var i abl es e tt omi s s i ng. 2.Mer get hene w dat as etwi t ht he or i gi naldat as e t . fitt hefinalmode lus i ngPROC 3.Re LOGI STI Cus i ngt heOUTPUT s t a t e me nt . STAT43 30 /83 30PRI ESTLEY

Cl a s s i fic at i onTa bl e&Ra t e s A Cl as s i fic at i onTa bl ei sus e dt o s ummar i zet her e s ul t soft hepr e di c t i ons andt oul t i mat e l ye val uat et hefit ne s sof t hemode l . Obt a i nac l a s s i fic a t i ont a bl eus i ngPROC FREQ.


Cl a s s i fic at i onTa bl e&Ra t e s Theobs e r ve d( orac t ual )r e s pons ei si n r owsa ndt hepr e di c t e dr e s pons ei si n c ol umns .


Cl a s s i fic at i onTa bl e&Ra t e s Cor r e c tc l a s s i fic a t i onsa r es umma r i z e d ont hemai ndi agonal .


Cl a s s i fic at i onTa bl e&Ra t e s Thet ot a lnumbe rofc or r e c t c l as s i fic at i ons( i . e . ,‘ hi t s ’ )i st hes um of t hema i ndi a gona lf r e que nc i e s . O =130+9=139


Cl a s s i fic at i onTa bl e&Ra t e s Thet ot al gr ouphi tr at ei st her at i oofO andN.HR=13 9/196=. 698


Logistic Ppt

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