REGRESSION / 9장 로지스틱 회귀 ... - wolfpack.hnu.ac.kr

1 REGRESSION / 9 . 193. Chapter 9 . (metric) . (binary: / , / . 2 ) (Logistic REGRESSION ) . K.. ( ) .. 0, 1( : , ) .. C. (ordinal) .. ( , , ) . PA.. 3 LOGISTIC . CATMOD . CATMD CATegorical data MODeling , LOGISTIC CATMOD .. LF. y i = f ( x) = + 1 x1i + 2 x 2i + .. + p x pi + ei , ei ~ iidN (0, 2 ). 0 1 ( . ) ( R 2 ) ( , Likert . O. ) F- t- , .. yi ( 0, 1 ) OLS .. W.. ODDS. p ODDs = p ( ) . 1 p . 2002 16 1/9 Odds . 1$ . 9$ . 2002 16 . 4 Odds . 4$ 1$ . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 194. p ODDS transformation p* =.

2 1 p y i = p i = Pr(Y = 1) . pi ( Y = 1 ) . odds Odds . p *i =. 1 pi p i (0,1) p *i (0, ) . ln( p *i ) . (- , ) ei ~ Normal (0, 2 ) ( ) . K.. Logistic . pi yi = ln( ) = + 1x1i + 2 x2i + .. + p x pi + ei , ei ~ Normal (0, 2 ) --- ( ). C. 1 pi . PA. p i = Pr(Y = 1 | x) =. e 1+ e { + 1x1i + 2 x2i +..+ p x pi }. { + 1x1i + 2 x2i +..+ p x pi }. pi ( : Y = 1 , event) . + ei* =. 1+ e 1. { + 1x1i + 2 x2i +..+ p x pi }. + ei*. pi .. LF.. 2 Log L , AIC(Akaike Information Criterion) Schwartz Criterion . (Adjusted ) Wald Chi-square . O.. W. EXAMPLE (cell, smear, infil, li, blast, temp) (REMISS, ).

3 Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 195.. remiss=1 . remiss=0 . REMISS, 0 1( ) (binary, dichotomous) .. 1 , 0 . K. OLS . C. OLS (Li ) .. OLS . PA. LF. Li . ( ) .. Re miss = + * Li . Li .. O. OLS .. W. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 196. o ??? C K.. PA. LF. O. W. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 197. ( ). OLS Li .. Descending SAS event( , ) . non-event . 1 ( event ) . K. descending . OUTPUT . ( Y ) OUT2.

4 C. PA Event( ). non-event( ). Descending REMISS 1 event( ) 0 non-event .. descending profile . LF. Probability modeled is remiss=0 event ( . ) 0( ) . O. W. 2 - . p- Li . 0 1 . Yi = p i = Pr(Y = 1 | x) ( (event, ) ) 0. 1 . Li ( ) . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 198. 1. y i = p i = Pr(Y = Re miss | x) =. ( + Li ). 1+ e ( 2 ).. stepwise . SLS SLE . K.. SLS= ~ ) SLE= . C. PA. LF. O. 1. y i = p i = Pr(Y = Re miss | x) = Cell . ( + + Li ). 1+ e , Li , Temp . W. ( ) .. Pearson Residuals Deviance residual .. 2.

5 ? .. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 199. C K. ( , , , ).. ( ). PA. (event , ) .. LF. O. W. 1. PRED y i = p i = Pr(Y = Re miss | x) = . ( + + Li ). 1+ e .. STB . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 200. K. CELL LI TEMP . C..( ) . PA. ( ) . ( ).. LF. O. W. 206 200-1 .. EXAMPLE (OXYGEN) , . , . (ordinal) . RANK . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 201. OXYGEN 3 (0, 1, 2) . C K. PA. , OXYGEN_G .. LF.. O. W.

6 RUNTIME .. 1. Pr(Oxygen _ G = 0 | x) = ( ). ( + ). 1+ e 1. Pr(Oxygen _ G 1 | x) = ( & ). ( + ). 1+ e Pr(Y = 2 | x) = 1 Pr(Oxygen _ G 1). Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 202.. 3 .. K. 3 . 0 . 0 1 .. (runtime ) . C. ( ) = , . 0 . PA. 11 .. RUNTIME 11 .. LF. O. 0 , 1 ( )= , 2 . 11 1 ( ) . W. HOMEWORK #11 ( ) ( ) Due 6 1 ( ).. X1=( / ), X2=( / ), X3=( / ) . Y 0(2 ), 1(2 ) .. , , 2 .. X1=20, X2=10, X3=1 2 ( ) . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 203. ( ).. K.

7 0 0. 1 1 . C. PA. LF.. B Wald Exp(B). O. X4 1 .015 1 .006 .023. y i = Pr(Y = 1 | x) 0 1 . W.. ( / . ) . Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 204. PRE_* PGR_* . X4= .. cut-off .. K. 7 .. 44% .. cut-off . C. PA .. Y. 0 1 %. 1 Y 0 16 2 LF. 1 5 4 % ( ), .. ( ) . O.. X4 .. W. ( ). : , , , , , , ( ).. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9 . 205. ( ) . 3 ( . , , ) .. C K. PA.. ( ) . default .. ( ) . LF.. O. W. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring REGRESSION / 9.

8 206. K.. C. PA. 1. Pr(Oxygen _ G = 1| x) = ( ). ( ). 1+ e 1. LF. Pr(Oxygen _ G 2 | x ) = ( , ). ( ). 1+ e Pr(Y = 3 | x) = 1 Pr(Oxygen _ G 2) ( ). , . ( EST*) .. O.. W. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring 200-1. REGRESSION / 9 . 207. K. Prob. Level Logit Pr(Event) Event . Pr(Event) Event . EVENT 19 . C. Event non-EVENT 18 Event . Correct Event(Domestic) Event Non-event Non-event . PA. In-Correct Event(Domestic) non-Event Non-event event . Correct . Sensitivity Event( ) Event( ) . False Pos. Event( ) non-Event( ) , . Sensitivity + False Pos.

9 1 . LF. Specificity non-Event( ) non-Event( ) . False Neg. non-Event( ) Event( ) , . Specificity + False Neg. 1 . CORECT Prob. Level . O. W. Prof. Sehyug Kwon, Dept. of Statistics, HANNAM University @2005 Spring