[Data] Marijuana Use Data: comes from a survey conducted by the Wright State University School of Medicine and the United Health Services in Dayton, Ohio. The survey asked students in their final year of a high school near Dayton, Ohio whether they had ever used alcohol, cigarettes, or marijuana.
[Goal] Study association of alcohol, cigarettes, and marijuana use.
[Specification]
data Druguse;
input Alcohol $ Cigarette $ Drug $ Count;
datalines;
Yes Yes Yes 911
Yes Yes No 538
Yes No Yes 44
Yes No No 456
No Yes Yes 3
No Yes No 43
No No Yes 2
No No No 279
;
run;
Proc Genmod data=Druguse;
Class Alcohol (ref="No") Cigarette (ref="No") Drug(ref="No")/ param = ref ;
Model Count = Alcohol Cigarette Drug Alcohol*Cigarette
Cigarette*Drug Alcohol*Drug/obstats dist=poi link=log ;
run;
The GENMOD Procedure
Model Information
Data Set WORK.DRUGUSE
Distribution Poisson
Link Function Log
Dependent Variable Count
Number of Observations Read 8
Number of Observations Used 8
Class Level Information
Design
Class Value Variables
Alcohol No 0
Yes 1
Cigarette No 0
Yes 1
Drug No 0
Yes 1
Parameter Information
Parameter Effect Alcohol Cigarette Drug
Prm1 Intercept
Prm2 Alcohol Yes
Prm3 Cigarette Yes
Prm4 Drug Yes
Prm5 Alcohol*Cigarette Yes Yes
Prm6 Cigarette*Drug Yes Yes
Prm7 Alcohol*Drug Yes Yes
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 1 0.3740 0.3740
Scaled Deviance 1 0.3740 0.3740
Pearson Chi-Square 1 0.4011 0.4011
Scaled Pearson X2 1 0.4011 0.4011
Log Likelihood 12010.6124
Full Log Likelihood -24.7087
AIC (smaller is better) 63.4174
AICC (smaller is better) .
BIC (smaller is better) 63.9735
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Standard Wald 95% Wald
Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq
Intercept 1 5.6334 0.0597 5.5164 5.7504 8903.96 <.0001
Alcohol Yes 1 0.4877 0.0758 0.3392 0.6362 41.44 <.0001
Cigarette Yes 1 -1.8867 0.1627 -2.2055 -1.5678 134.47 <.0001
Drug Yes 1 -5.3090 0.4752 -6.2404 -4.3777 124.82 <.0001
Alcohol*Cigarette Yes Yes 1 2.0545 0.1741 1.7134 2.3957 139.32 <.0001
Cigarette*Drug Yes Yes 1 2.8479 0.1638 2.5268 3.1690 302.14 <.0001
Alcohol*Drug Yes Yes 1 2.9860 0.4647 2.0753 3.8968 41.29 <.0001
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.
Observation Statistics
Standard
Error of
the
Predicted Linear Linear
Observation Count Alcohol Cigarette Drug Value Predictor Predictor HessWgt
Std
Raw Pearson Deviance Deviance
Lower Upper Residual Residual Residual Residual
Std DFBETA_
Pearson Likelihood DFBETA_ Alcohol
Residual Residual Leverage CookD Intercept Yes
DFBETA_
Alcohol DFBETA_ DFBETA_
DFBETA_ Yes Cigarette Alcohol
Cigarette DFBETA_ Cigarette YesDrug YesDrug DFBETAS_
Yes DrugYes Yes Yes Yes Intercept
DFBETAS_
Alcohol DFBETAS_ DFBETAS_
DFBETAS_ DFBETAS_ Yes Cigarette Alcohol
Alcohol Cigarette DFBETAS_ Cigarette YesDrug YesDrug
Yes Yes DrugYes Yes Yes Yes
1 911 Yes Yes Yes 910.38317 6.8138656 0.0331254 910.38317
853.15473 971.45041 0.6168304 0.0204434 0.0204411 0.6332534
0.6333249 0.6333248 0.998958 54.934889 0.002206 -0.003561
-0.01676 -0.44816 0.0192594 0.6332582 0.4633397 0.0369506
-0.046993 -0.103011 -0.943104 0.1106452 3.8651156 0.9971201
2 538 Yes Yes No 538.61683 6.2890044 0.0430504 538.61683
495.03436 586.03627 -0.61683 -0.026578 -0.026583 -0.633446
-0.633325 -0.633325 0.9982388 32.478142 0.002206 -0.003561
-0.01676 -0.44816 -0.631001 0.6332582 0.4633397 0.0369506
-0.046993 -0.103011 -0.943104 -3.625103 3.8651156 0.9971201
3 44 Yes No Yes 44.61683 3.7981111 0.1481099 44.61683
33.375465 59.644459 -0.61683 -0.092346 -0.09256 -0.634793
-0.633325 -0.633356 0.9787392 2.6378038 0.002206 -0.003561
-0.01676 -0.44816 0.0192594 0.6332582 -0.186921 0.0369506
-0.046993 -0.103011 -0.943104 0.1106452 3.8651156 -0.402259
4 456 Yes No No 455.38317 6.1211392 0.0468122 455.38317
415.46112 499.14136 0.6168304 0.0289053 0.0288988 0.633182
0.6333249 0.6333246 0.9979169 27.450367 0.002206 0.6467
-0.01676 -0.44816 -0.631001 0.6332582 -0.186921 0.0369506
8.5353557 -0.103011 -0.943104 -3.625103 3.8651156 -0.402259
5 3 No Yes Yes 3.616831 1.2855982 0.4516316 3.616831
1.4924462 8.7651178 -0.616831 -0.324341 -0.334285 -0.652742
-0.633326 -0.638475 0.7377291 0.1611769 0.002206 -0.003561
-0.01676 -0.448161 0.0192594 -0.017002 0.4633402 0.0369507
-0.046993 -0.103012 -0.943105 0.1106454 -0.103775 0.9971212
6 43 No Yes No 42.38317 3.7467513 0.1518756 42.38317
31.471445 57.078189 0.6168304 0.0947478 0.0945193 0.631798
0.6333249 0.6332908 0.9776187 2.5028783 0.002206 -0.003561
0.6335009 -0.44816 -0.631001 -0.017002 0.4633397 0.0369506
-0.046993 3.8937473 -0.943104 -3.625103 -0.103775 0.9971201
7 2 No No Yes 1.3831699 0.3243779 0.476606 1.3831699
0.5434852 3.5201674 0.6168301 0.5244786 0.491342 0.5933111
0.6333247 0.6061677 0.3141916 0.026251 0.002206 -0.003561
-0.01676 0.2021004 0.0192594 -0.017002 -0.186921 0.0369506
-0.046993 -0.103011 0.4252981 0.1106452 -0.103774 -0.402259
8 279 No No No 279.61683 5.6334202 0.0597008 279.61683
248.74013 314.32632 -0.61683 -0.036888 -0.036901 -0.633558
-0.633325 -0.633326 0.9966075 16.833106 -0.648055 0.6467
0.6335009 0.2021004 -0.631001 -0.017002 -0.186921 -10.85503
8.5353557 3.8937473 0.4252982 -3.625103 -0.103775 -0.402259data Druguse;
input Alcohol $ Cigarette $ Drug $ Count;
datalines;
Yes Yes Yes 911
Yes Yes No 538
Yes No Yes 44
Yes No No 456
No Yes Yes 3
No Yes No 43
No No Yes 2
No No No 279
;
run;
Proc Genmod data=Druguse;
Class Alcohol (ref="No") Cigarette (ref="No") Drug(ref="No")/ param = ref ;
Model Count = Alcohol Cigarette Drug
Cigarette*Drug Alcohol*Drug/dist=poi link=log ;
run;
The GENMOD Procedure
Model Information
Data Set WORK.DRUGUSE
Distribution Poisson
Link Function Log
Dependent Variable Count
Number of Observations Read 8
Number of Observations Used 8
Class Level Information
Design
Class Value Variables
Alcohol No 0
Yes 1
Cigarette No 0
Yes 1
Drug No 0
Yes 1
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 2 187.7543 93.8772
Scaled Deviance 2 187.7543 93.8772
Pearson Chi-Square 2 177.6144 88.8072
Scaled Pearson X2 2 177.6144 88.8072
Log Likelihood 11916.9222
Full Log Likelihood -118.3989
AIC (smaller is better) 248.7977
AICC (smaller is better) 332.7977
BIC (smaller is better) 249.2744
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Standard Wald 95% Wald
Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq
Intercept 1 5.1921 0.0609 5.0727 5.3114 7273.54 <.0001
Alcohol Yes 1 1.1272 0.0641 1.0015 1.2529 309.01 <.0001
Cigarette Yes 1 -0.2351 0.0555 -0.3439 -0.1263 17.94 <.0001
Drug Yes 1 -6.6209 0.4737 -7.5493 -5.6924 195.35 <.0001
Cigarette*Drug Yes Yes 1 3.2243 0.1610 2.9088 3.5398 401.17 <.0001
Alcohol*Drug Yes Yes 1 4.1251 0.4529 3.2373 5.0128 82.94 <.0001
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.data Druguse;
input Alcohol $ Cigarette $ Drug $ Count;
datalines;
Yes Yes Yes 911
Yes Yes No 538
Yes No Yes 44
Yes No No 456
No Yes Yes 3
No Yes No 43
No No Yes 2
No No No 279
;
run;
Proc logistic data=Druguse;
Class Alcohol (ref="No") Cigarette (ref="No") Drug(ref="No")/ param = ref ;
Weight Count;
Model Drug= Alcohol Cigarette/aggregate scale=none ;
run;
The LOGISTIC Procedure
Model Information
Data Set WORK.DRUGUSE
Response Variable Drug
Number of Response Levels 2
Weight Variable Count
Model binary logit
Optimization Technique Fisher's scoring
Number of Observations Read 8
Number of Observations Used 8
Sum of Weights Read 2276
Sum of Weights Used 2276
Response Profile
Ordered Total Total
Value Drug Frequency Weight
1 No 4 1316.0000
2 Yes 4 960.0000
Probability modeled is Drug='Yes'.
Class Level Information
Design
Class Value Variables
Alcohol No 0
Yes 1
Cigarette No 0
Yes 1
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Deviance and Pearson Goodness-of-Fit Statistics
Criterion Value DF Value/DF Pr > ChiSq
Deviance 0.3740 1 0.3740 0.5408
Pearson 0.4011 1 0.4011 0.5265
Number of unique profiles: 4
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 3101.293 2261.840
SC 3101.372 2262.079
-2 Log L 3099.293 2255.840
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 843.4527 2 <.0001
Score 670.7849 2 <.0001
Wald 359.5451 2 <.0001
Type 3 Analysis of Effects
Wald
Effect DF Chi-Square Pr > ChiSq
Alcohol 1 41.2936 <.0001
Cigarette 1 302.1411 <.0001
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 -5.3090 0.4752 124.8221 <.0001
Alcohol Yes 1 2.9860 0.4647 41.2936 <.0001
Cigarette Yes 1 2.8479 0.1638 302.1411 <.0001
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
Alcohol Yes vs No 19.806 7.966 49.241
Cigarette Yes vs No 17.251 12.513 23.784
Association of Predicted Probabilities and Observed Responses
Percent Concordant 37.5 Somers' D 0.000
Percent Discordant 37.5 Gamma 0.000
Percent Tied 25.0 Tau-a 0.000
Pairs 16 c 0.500