用SAS进行泊松，零膨胀泊松和有限混合Poisson模型分析
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原文链接：http://tecdat.cn/?p=6145
泊松模型
proc fmm data = tmp1 tech = trureg;
??model majordrg = age acadmos minordrg logspend / dist = truncpoisson;
??probmodel age acadmos minordrg logspend;
/*
Fit Statistics
?
-2 Log Likelihood???????????? 8201.0
AIC? (smaller is better)????? 8221.0
AICC (smaller is better)????? 8221.0
BIC? (smaller is better)????? 8293.5
?
Parameter Estimates for 'Truncated Poisson' Model
??
????????????????????????????????Standard
Component? Effect???? Estimate???? Error? z Value? Pr > |z|
?
????????1? Intercept?? -2.0706??? 0.3081??? -6.72??? <.0001
????????1? AGE???????? 0.01796? 0.005482???? 3.28??? 0.0011
????????1? ACADMOS??? 0.000852? 0.000700???? 1.22??? 0.2240
????????1? MINORDRG???? 0.1739?? 0.03441???? 5.05??? <.0001
????????1? LOGSPEND???? 0.1229?? 0.04219???? 2.91??? 0.0036
?
Parameter Estimates for Mixing Probabilities
??
?????????????????????????Standard
Effect?????? Estimate?????? Error??? z Value??? Pr > |z|
?
Intercept???? -4.2309????? 0.1808???? -23.40????? <.0001
AGE?????????? 0.01694??? 0.003323?????? 5.10????? <.0001
ACADMOS????? 0.002240??? 0.000492?????? 4.55????? <.0001
MINORDRG?????? 0.7653???? 0.03842????? 19.92????? <.0001
LOGSPEND?????? 0.2301???? 0.02683?????? 8.58????? <.0001
*/
?
*** HURDLE POISSON MODEL WITH NLMIXED PROCEDURE ***;
proc nlmixed data = tmp1 tech = trureg maxit = 500;
??parms B1_intercept = -4 B1_age = 0 B1_acadmos = 0 B1_minordrg = 0 B1_logspend = 0
????????B2_intercept = -2 B2_age = 0 B2_acadmos = 0 B2_minordrg = 0 B2_logspend = 0;
?
??eta1 = B1_intercept + B1_age * age + B1_acadmos * acadmos + B1_minordrg * minordrg + B1_logspend * logspend;
??exp_eta1 = exp(eta1);
??p0 = 1 / (1 + exp_eta1);
??eta2 = B2_intercept + B2_age * age + B2_acadmos * acadmos + B2_minordrg * minordrg + B2_logspend * logspend;
??exp_eta2 = exp(eta2);
??if majordrg = 0 then _prob_ = p0;
??else _prob_ = (1 - p0) * exp(-exp_eta2) * (exp_eta2 ** majordrg) / ((1 - exp(-exp_eta2)) * fact(majordrg));
??ll = log(_prob_);
??model majordrg ~ general(ll);
run;
/*
Fit Statistics
?
-2 Log Likelihood???????????????? 8201.0
AIC (smaller is better)?????????? 8221.0
AICC (smaller is better)????????? 8221.0
BIC (smaller is better)?????????? 8293.5
?
Parameter Estimates
??
??????????????????????????Standard
Parameter????? Estimate????? Error???? DF?? t Value?? Pr > |t|
?
B1_intercept??? -4.2309???? 0.1808??? 1E4??? -23.40???? <.0001
B1_age????????? 0.01694?? 0.003323??? 1E4????? 5.10???? <.0001
B1_acadmos???? 0.002240?? 0.000492??? 1E4????? 4.55???? <.0001
B1_minordrg????? 0.7653??? 0.03842??? 1E4???? 19.92???? <.0001
B1_logspend????? 0.2301??? 0.02683??? 1E4????? 8.58???? <.0001
============
B2_intercept??? -2.0706???? 0.3081??? 1E4???? -6.72???? <.0001
B2_age????????? 0.01796?? 0.005482??? 1E4????? 3.28???? 0.0011
B2_acadmos???? 0.000852?? 0.000700??? 1E4????? 1.22???? 0.2240
B2_minordrg????? 0.1739??? 0.03441??? 1E4????? 5.05???? <.0001
B2_logspend????? 0.1229??? 0.04219??? 1E4????? 2.91???? 0.0036
*/零膨胀泊松模型
*** ZERO-INFLATED POISSON MODEL WITH FMM PROCEDURE ***;
proc fmm data = tmp1 tech = trureg;
??model majordrg = age acadmos minordrg logspend / dist = poisson;
??probmodel age acadmos minordrg logspend;
run;
/*
Fit Statistics
?
-2 Log Likelihood???????????? 8147.9
AIC? (smaller is better)????? 8167.9
AICC (smaller is better)????? 8167.9
BIC? (smaller is better)????? 8240.5
?
Parameter Estimates for 'Poisson' Model
??
????????????????????????????????Standard
Component? Effect???? Estimate???? Error? z Value? Pr > |z|
?
????????1? Intercept?? -2.2780??? 0.3002??? -7.59??? <.0001
????????1? AGE???????? 0.01956? 0.006019???? 3.25??? 0.0012
????????1? ACADMOS??? 0.000249? 0.000668???? 0.37??? 0.7093
????????1? MINORDRG???? 0.1176?? 0.02711???? 4.34??? <.0001
????????1? LOGSPEND???? 0.1644?? 0.03531???? 4.66??? <.0001
?
Parameter Estimates for Mixing Probabilities
??
?????????????????????????Standard
Effect?????? Estimate?????? Error??? z Value??? Pr > |z|
?
Intercept???? -1.9111????? 0.4170????? -4.58????? <.0001
AGE????????? -0.00082??? 0.008406????? -0.10????? 0.9218
ACADMOS????? 0.002934??? 0.001085?????? 2.70????? 0.0068
MINORDRG?????? 1.4424????? 0.1361????? 10.59????? <.0001
LOGSPEND????? 0.09562???? 0.05080?????? 1.88????? 0.0598
*/
?
*** ZERO-INFLATED POISSON MODEL WITH NLMIXED PROCEDURE ***;
proc nlmixed data = tmp1 tech = trureg maxit = 500;
??parms B1_intercept = -2 B1_age = 0 B1_acadmos = 0 B1_minordrg = 0 B1_logspend = 0
????????B2_intercept = -2 B2_age = 0 B2_acadmos = 0 B2_minordrg = 0 B2_logspend = 0;
?
??eta1 = B1_intercept + B1_age * age + B1_acadmos * acadmos + B1_minordrg * minordrg + B1_logspend * logspend;
??exp_eta1 = exp(eta1);
??p0 = 1 / (1 + exp_eta1);
??eta2 = B2_intercept + B2_age * age + B2_acadmos * acadmos + B2_minordrg * minordrg + B2_logspend * logspend;
??exp_eta2 = exp(eta2);
??if majordrg = 0 then _prob_ = p0 + (1 - p0) * exp(-exp_eta2);
??else _prob_ = (1 - p0) * exp(-exp_eta2) * (exp_eta2 ** majordrg) / fact(majordrg);
??ll = log(_prob_);
??model majordrg ~ general(ll);
run;
/*
Fit Statistics
?
-2 Log Likelihood???????????????? 8147.9
AIC (smaller is better)?????????? 8167.9
AICC (smaller is better)????????? 8167.9
BIC (smaller is better)?????????? 8240.5
?
Parameter Estimates
??
??????????????????????????Standard
Parameter????? Estimate????? Error???? DF?? t Value?? Pr > |t|
?
B1_intercept??? -1.9111???? 0.4170??? 1E4???? -4.58???? <.0001
B1_age???????? -0.00082?? 0.008406??? 1E4???? -0.10???? 0.9219
B1_acadmos???? 0.002934?? 0.001085??? 1E4????? 2.70???? 0.0068
B1_minordrg????? 1.4424???? 0.1361??? 1E4???? 10.59???? <.0001
B1_logspend???? 0.09562??? 0.05080??? 1E4????? 1.88???? 0.0598
============
B2_intercept??? -2.2780???? 0.3002??? 1E4???? -7.59???? <.0001
B2_age????????? 0.01956?? 0.006019??? 1E4????? 3.25???? 0.0012
B2_acadmos???? 0.000249?? 0.000668??? 1E4????? 0.37???? 0.7093
B2_minordrg????? 0.1176??? 0.02711??? 1E4????? 4.34???? <.0001
B2_logspend????? 0.1644??? 0.03531??? 1E4????? 4.66???? <.0001
*/两类有限混合Poisson模型
*** TWO-CLASS FINITE MIXTURE POISSON MODEL WITH FMM PROCEDURE ***;
proc fmm data = tmp1 tech = trureg;
??model majordrg = age acadmos minordrg logspend / dist = poisson k = 2;
run;
/*
Fit Statistics
?
-2 Log Likelihood???????????? 8136.8
AIC? (smaller is better)????? 8166.8
AICC (smaller is better)????? 8166.9
BIC? (smaller is better)????? 8275.7
?
Parameter Estimates for 'Poisson' Model
??
????????????????????????????????Standard
Component? Effect???? Estimate???? Error? z Value? Pr > |z|
?
????????1? Intercept?? -2.4449??? 0.3497??? -6.99??? <.0001
????????1? AGE???????? 0.02214? 0.006628???? 3.34??? 0.0008
????????1? ACADMOS??? 0.000529? 0.000770???? 0.69??? 0.4920
????????1? MINORDRG??? 0.05054?? 0.04015???? 1.26??? 0.2081
????????1? LOGSPEND???? 0.2140?? 0.04127???? 5.18??? <.0001
????????2? Intercept?? -8.0935??? 1.5915??? -5.09??? <.0001
????????2? AGE???????? 0.01150?? 0.01294???? 0.89??? 0.3742
????????2? ACADMOS??? 0.004567? 0.002055???? 2.22??? 0.0263
????????2? MINORDRG???? 0.2638??? 0.6770???? 0.39??? 0.6968
????????2? LOGSPEND???? 0.6826??? 0.2203???? 3.10??? 0.0019
?
Parameter Estimates for Mixing Probabilities
??
?????????????????????????Standard
Effect?????? Estimate?????? Error??? z Value??? Pr > |z|
?
Intercept???? -1.4275????? 0.5278????? -2.70????? 0.0068
AGE????????? -0.00277???? 0.01011????? -0.27????? 0.7844
ACADMOS????? 0.001614??? 0.001440?????? 1.12????? 0.2623
MINORDRG?????? 1.5865????? 0.1791?????? 8.86????? <.0001
LOGSPEND???? -0.06949???? 0.07436????? -0.93????? 0.3501
*/
?
*** TWO-CLASS FINITE MIXTURE POISSON MODEL WITH NLMIXED PROCEDURE ***;
proc nlmixed data = tmp1 tech = trureg maxit = 500;
????????B2_intercept = -8 B2_age = 0 B2_acadmos = 0 B2_minordrg = 0 B2_logspend = 0
?
??eta1 = B1_intercept + B1_age * age + B1_acadmos * acadmos + B1_minordrg * minordrg + B1_logspend * logspend;
??exp_eta1 = exp(eta1);
??prob1 = exp(-exp_eta1) * exp_eta1 ** majordrg / fact(majordrg);
??eta2 = B2_intercept + B2_age * age + B2_acadmos * acadmos + B2_minordrg * minordrg + B2_logspend * logspend;
??exp_eta2 = exp(eta2);
??prob2 = exp(-exp_eta2) * exp_eta2 ** majordrg / fact(majordrg);
??eta3 = B3_intercept + B3_age * age + B3_acadmos * acadmos + B3_minordrg * minordrg + B3_logspend * logspend;
??exp_eta3 = exp(eta3);
??p = exp_eta3 / (1 + exp_eta3);
??_prob_ = p * prob1 + (1 - p) * prob2;
??ll = log(_prob_);
??model majordrg ~ general(ll);
run;
/*
Fit Statistics
?
-2 Log Likelihood???????????????? 8136.8
AIC (smaller is better)?????????? 8166.8
AICC (smaller is better)????????? 8166.9
BIC (smaller is better)?????????? 8275.7
?
Parameter Estimates
??
??????????????????????????Standard
Parameter????? Estimate????? Error???? DF?? t Value?? Pr > |t|
?
B1_intercept??? -2.4449???? 0.3497??? 1E4???? -6.99???? <.0001
B1_age????????? 0.02214?? 0.006628??? 1E4????? 3.34???? 0.0008
B1_acadmos???? 0.000529?? 0.000770??? 1E4????? 0.69???? 0.4920
B1_minordrg???? 0.05054??? 0.04015??? 1E4????? 1.26???? 0.2081
B1_logspend????? 0.2140??? 0.04127??? 1E4????? 5.18???? <.0001
============
B2_intercept??? -8.0935???? 1.5916??? 1E4???? -5.09???? <.0001
B2_age????????? 0.01150??? 0.01294??? 1E4????? 0.89???? 0.3742
B2_acadmos???? 0.004567?? 0.002055??? 1E4????? 2.22???? 0.0263
B2_minordrg????? 0.2638???? 0.6770??? 1E4????? 0.39???? 0.6968
B2_logspend????? 0.6826???? 0.2203??? 1E4????? 3.10???? 0.0020
============
B3_intercept??? -1.4275???? 0.5278??? 1E4???? -2.70???? 0.0068
B3_age???????? -0.00277??? 0.01011??? 1E4???? -0.27???? 0.7844
B3_acadmos???? 0.001614?? 0.001440??? 1E4????? 1.12???? 0.2623
B3_minordrg????? 1.5865???? 0.1791??? 1E4????? 8.86???? <.0001
B3_logspend??? -0.06949??? 0.07436??? 1E4???? -0.93???? 0.3501
*/
内容总结
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