Analysis of Poisson Model for Poisson by SAS

By Software Design

Link to the original text: http://tecdat.cn/?p=6145

Poisson model

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proc fmm data = tmp1 tech = trureg;

Model majordrg = age acadmos minordrg logspend / dist = truncpoisson;

 
Probmodel age acadmos minordrg logspend;

 
/*

Fit Statistics

To

-2 Log Likelihood 8201.0

AIC (smaller is better) 8221.0

AICC (smaller is better) 8221.0

BIC (smaller is better) 8293.5

To

Parameter Estimates for ‘Truncated Poisson’ Model

To

Standard

Component Effect Estimate Error z Value Pr> |z|

To

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

To

Parameter Estimates for Mixing Probabilities

To

Standard

Effect Estimate Error z Value Pr> |z|

To

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

*/

To

*** 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;

To

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

To

-2 Log Likelihood 8201.0

AIC (smaller is better) 8221.0

AICC (smaller is better) 8221.0

BIC (smaller is better) 8293.5

To

Parameter Estimates

To

Standard

Parameter Estimate Error DF t Value Pr> |t|

To

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

*/

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Zero expansion Poisson model

*** 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

To

-2 Log Likelihood 8147.9

AIC (smaller is better) 8167.9

AICC (smaller is better) 8167.9

BIC (smaller is better) 8240.5

To

Parameter Estimates for ‘Poisson’ Model

To

Standard

Component Effect Estimate Error z Value Pr> |z|

To

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

To

Parameter Estimates for Mixing Probabilities

To

Standard

Effect Estimate Error z Value Pr> |z|

To

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 0.0598 1.88

*/

To

*** 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;

To

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

To

-2 Log Likelihood 8147.9

AIC (smaller is better) 8167.9

AICC (smaller is better) 8167.9

BIC (smaller is better) 8240.5

To

Parameter Estimates

To

Standard

Parameter Estimate Error DF t Value Pr> |t|

To

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

*/

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Two types of limited hybrid Poisson model

*** 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

To

-2 Log Likelihood 8136.8

AIC (smaller is better) 8166.8

AICC (smaller is better) 8166.9

BIC (smaller is better) 8275.7

To

Parameter Estimates for ‘Poisson’ Model

To

Standard

Component Effect Estimate Error z Value Pr> |z|

To

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

To

Parameter Estimates for Mixing Probabilities

To

Standard

Effect Estimate Error z Value Pr> |z|

To

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

*/

To

*** 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

 
To

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

To

-2 Log Likelihood 8136.8

AIC (smaller is better) 8166.8

AICC (smaller is better) 8166.9

BIC (smaller is better) 8275.7

To

Parameter Estimates

To

Standard

Parameter Estimate Error DF t Value Pr> |t|

To

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

*/

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proc fmm data = tmp1 tech = trureg;

  model majordrg = age acadmos minordrg logspend / dist = truncpoisson;

 
  probmodel age acadmos minordrg logspend;

 
/*

Fit Statistics

To

-2 Log Likelihood             8201.0

AIC  (smaller is better)      8221.0

AICC (smaller is better)      8221.0

BIC  (smaller is better)      8293.5

To

Parameter Estimates for ‘Truncated Poisson‘ Model

To

                                Standard

Component  Effect     Estimate     Error  z Value  Pr > |z|

To

        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

To

Parameter Estimates for Mixing Probabilities

To

                         Standard

Effect       Estimate       Error    z Value    Pr > |z|

To

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

*/

To

*** 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;

To

  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

To

-2 Log Likelihood                 8201.0

AIC (smaller is better)           8221.0

AICC (smaller is better)          8221.0

BIC (smaller is better)           8293.5

To

Parameter Estimates

To

                          Standard

Parameter      Estimate      Error     DF   t Value   Pr > |t|

To

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

*/

分享图片

*** 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

To

-2 Log Likelihood             8147.9

AIC  (smaller is better)      8167.9

AICC (smaller is better)      8167.9

BIC  (smaller is better)      8240.5

To

Parameter Estimates for ‘Poisson‘ Model

To

                                Standard

Component  Effect     Estimate     Error  z Value  Pr > |z|

To

        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

To

Parameter Estimates for Mixing Probabilities

To

                         Standard

Effect       Estimate       Error    z Value    Pr > |z|

To

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

*/

To

*** 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;

To

  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

To

-2 Log Likelihood                 8147.9

AIC (smaller is better)           8167.9

AICC (smaller is better)          8167.9

BIC (smaller is better)           8240.5

To

Parameter Estimates

To

                          Standard

Parameter      Estimate      Error     DF   t Value   Pr > |t|

To

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

*/

分享图片

*** 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

To

-2 Log Likelihood             8136.8

AIC  (smaller is better)      8166.8

AICC (smaller is better)      8166.9

BIC  (smaller is better)      8275.7

To

Parameter Estimates for ‘Poisson‘ Model

To

                                Standard

Component  Effect     Estimate     Error  z Value  Pr > |z|

To

        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

To

Parameter Estimates for Mixing Probabilities

To

                         Standard

Effect       Estimate       Error    z Value    Pr > |z|

To

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

*/

To

*** 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

 
To

  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

To

-2 Log Likelihood                 8136.8

AIC (smaller is better)           8166.8

AICC (smaller is better)          8166.9

BIC (smaller is better)           8275.7

To

Parameter Estimates

To

                          Standard

Parameter      Estimate      Error     DF   t Value   Pr > |t|

To

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

*/

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