Avec SAS-GENMOD:
Voici ce que contient le fichier gamma11:
1 2 33.11
2 1 2.5
3 0 0.4
4 1 0.1
5 2 0.2
Programme:
data gamma11;
infile "gamma11";
input x1 x2 y;
proc genmod data=gamma11;
model y=x1 x2 x1*x2/ dist = gamma
link = log
type1;
run;
Sortie:
The GENMOD Procedure
Model Information
Description Value
Data Set WORK.GAMMA11
Distribution GAMMA
Link Function LOG
Dependent Variable Y
Observations Used 5
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 1 0.5444 0.5444
Scaled Deviance 1 5.0890 5.0890
Pearson Chi-Square 1 0.4831 0.4831
Scaled Pearson X2 1 4.5157 4.5157
Log Likelihood . -1.1838 .
Analysis Of Parameter Estimates
Parameter DF Estimate Std Err ChiSquare Pr>Chi
INTERCEPT 1 4.5925 1.7973 6.5289 0.0106
X1 1 -1.9416 0.5931 10.7178 0.0011
X2 1 0.0072 0.9475 0.0001 0.9940
X1*X2 1 0.3321 0.3105 1.1444 0.2847
SCALE 1 9.3475 5.8094 . .
NOTE: The scale parameter was estimated by maximum likelihood.
LR Statistics For Type 1 Analysis
Source Deviance DF ChiSquare Pr>Chi
INTERCEPT 20.6509 0 . .
X1 3.6002 1 10.6236 0.0011
X2 0.6669 1 8.8827 0.0029
X1*X2 0.5444 1 1.0343 0.3091
___________________________________________________________________
Programme:
proc genmod data=gamma11;
model y=x1 x2/ dist = gamma
link = log
corrb
covb
waldci
lrci;
run;
Sortie:
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 2 0.6669 0.3334
Scaled Deviance 2 5.1086 2.5543
Pearson Chi-Square 2 0.5200 0.2600
Scaled Pearson X2 2 3.9832 1.9916
Log Likelihood . -1.7010 .
Analysis Of Parameter Estimates
Parameter DF Estimate Std Err ChiSquare Pr>Chi
INTERCEPT 1 2.7315 0.4252 41.2643 0.0001
X1 1 -1.3166 0.1106 141.6343 0.0001
X2 1 1.0021 0.1933 26.8660 0.0001
SCALE 1 7.6605 4.7432 . .
NOTE: The scale parameter was estimated by maximum likelihood.
Estimated Covariance Matrix
Parameter
Number PRM1 PRM2 PRM3 Scale
PRM1 0.18081 -0.03517 -0.04099 -1.26E-10
PRM2 -0.03517 0.01224 -0.001288 3.672E-11
PRM3 -0.04099 -0.001288 0.03738 7.134E-11
Scale -1.26E-10 3.672E-11 7.134E-11 22.49774
Estimated Correlation Matrix
Parameter
Number PRM1 PRM2 PRM3 Scale
PRM1 1.0000 -0.7477 -0.4986 -0.0000
PRM2 -0.7477 1.0000 -0.0602 0.0000
PRM3 -0.4986 -0.0602 1.0000 0.0000
Scale -0.0000 0.0000 0.0000 1.0000
Normal Confidence Intervals For Parameters
Two-Sided Confidence Coefficient: 0.9500
Parameter Confidence Limits
PRM1 Lower 1.8981
PRM1 Upper 3.5649
PRM2 Lower -1.5334
PRM2 Upper -1.0998
PRM3 Lower 0.6232
PRM3 Upper 1.3810
Scale Lower -1.6359
Scale Upper 16.9570