SASéé¢å¯ä»¥ä½¿ç¨PROC GENMODæ¥å¤çPoisson Regression(åç¦æ¾åå½)ã
Poisson regression主è¦ä½¿ç¨å¨è®¡æ¬¡æ计æ°èµæåæä¸ï¼å±äºGeneralized linear modelï¼å¹¿ä¹çº¿æ§æ¨¡åï¼çä¸æ¯ï¼èä¸ä¼ä»¤æ们çY(outcome, independent variable)èåçåå¸ä¸ºPoissonåå¸ã
ç¹å«æ¯è¥ç¨å¨åè表åæ(contingency tables)æ¶ï¼å称为 Log-linear modelã
Modelç®åç示æ为 Log(E(Y|x))=a+bx
ä¸é¢æ们æ¥çä¸ä¸ªSAS helpéé¢çèä¾
èµæèæ¯ï¼è¿æ¯Aitkinç人äº1989å¹´åºçç书å
æå°çä¾åï¼æ¯å¯¹äºä¿é©èµå¿(insurance claims)èµæ建模åã
åénæ¯ä¿é©æ¥æ人æ°éãåécæ¯ä¿é©èµå¿çæ°éãåécaråä½ä¸ç»åå«ä¸ºsmall, mediumä¸largeãèä¿é©æ¥æ人çå¹´é¾åæ两ç»(åéage)ã
data insure;
input n c car $ age;
ln=log(n);
cards;
500 42 small 1
1200 37 medium 1
100 1 large 1
400 101 small 2
500 73 medium 2
300 14 large 2
;
run;
proc genmod data=insure;
class car age;
model c=car age /dist=poisson link=log offset=ln;
run;
æ们æéè¦çæ令å¦ä¸è¿°ï¼å
¶ä¸class åé¢æ¯èµæå
çç±»å«åé(car,age)ï¼
æ¥çå¨model statement åé¢å
æä¸æ³ççoutcomeåé(c,èµå¿èµæ)ï¼
çå·å³è¾¹æ¾å
¥æ³è°æ´ä¸ªdependent variables(å¦æ¤èä¾çcar,age)ã
æéè¦çæ¯å¨modelåé¢é¢çoption设å®ï¼éè¦åè¯SASä½ å设çèµæåå¸dist为ï¼
以æ¤ä¸ºä¾æ¯Poisson regressionï¼å æ¤è¾å
¥å
³é®åpoissonï¼èlinkè¦è®¾å®poisson regressionæ对åºç
log-linear modelï¼å æ¤å
³é®å为logãæ¥çè¿æoffsetè¦è®¾å®ï¼offsetæ¯æé对æ¯ä¸ªè§å¯å¼å»è®¾å®çä¸ä¸ªå¸¸æ°åå½ç³»æ°(constant coefficient)ã
ç»æå¦ä¸
æ¥è¡¨ç¬¬ä¸é¨åä¼å
æ述使ç¨è
æåç设å®ï¼å
å«æ设å®çèååå¸(poisson)ãlink function(Log)ãOutcome(c)以åoffsetåéï¼
æåæ¯è¯»å
¥çè§å¯å¼ç¬æ°ï¼ä»¥åxåé们åç»ç说æã
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