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page 32 Table 2.1 An example of the coding of the design variables for race, coded at three levels.
data lowbwt1; set 'd:\hosmerdata\lowbwt'; if race = 1 then do; race2 = 0; race3 = 0; end; if race = 2 then do; race2 = 1; race3 = 0; end; if race = 3 then do; race2 = 0; race3 = 1; end; run; proc print data=lowbwt1 (obs=3); var race race2 race3; run;
Obs RACE race2 race3 1 2 1 0 2 3 0 1 3 1 0 0
page 36 Table 2.2 Estimated coefficients for a multiple logistic regression model using the variables age, weight at last menstrual period (lwt), race and number of first trimester physician visits from the low birth weight study.
NOTE: We have bolded the relevant output.
proc logistic data=lowbwt1 descending;
model low = age lwt race2 race3 ftv;
run;
quit;
The LOGISTIC Procedure
Model Information
Data Set WORK.LOWBWT1
Response Variable LOW < 2500g
Number of Response Levels 2
Number of Observations 189
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value LOW Frequency
1 1 59
2 0 130
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 236.672 234.573
SC 239.914 254.023
-2 Log L 234.672 222.573
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 12.0991 5 0.0335
Score 11.3876 5 0.0442
Wald 10.6964 5 0.0577
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 1.2953 1.0714 1.4616 0.2267
AGE 1 -0.0238 0.0337 0.4988 0.4800
LWT 1 -0.0142 0.00654 4.7428 0.0294
race2 1 1.0039 0.4979 4.0660 0.0438
race3 1 0.4331 0.3622 1.4296 0.2318
FTV 1 -0.0493 0.1672 0.0869 0.7681
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
AGE 0.976 0.914 1.043
LWT 0.986 0.973 0.999
race2 2.729 1.029 7.240
race3 1.542 0.758 3.136
FTV 0.952 0.686 1.321
Association of Predicted Probabilities and Observed Responses
Percent Concordant 65.1 Somers' D 0.308
Percent Discordant 34.3 Gamma 0.310
Percent Tied 0.6 Tau-a 0.133
Pairs 7670 c 0.654
page 38 Table 2.3 Estimated coefficients for a multiple logistic regression model using the variables lwt and race from the low birth weight study.
proc logistic data=lowbwt1 descending covout outest=lowbwt2;
model low = lwt race2 race3;
run;
quit;
The LOGISTIC Procedure
Model Information
Data Set WORK.LOWBWT1
Response Variable LOW < 2500g
Number of Response Levels 2
Number of Observations 189
Link Function Logit
Optimization Technique Fisher's scoring
Response Profile
Ordered Total
Value LOW Frequency
1 1 59
2 0 130
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 236.672 231.259
SC 239.914 244.226
-2 Log L 234.672 223.259
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 11.4129 3 0.0097
Score 10.7572 3 0.0131
Wald 10.1316 3 0.0175
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 0.8057 0.8452 0.9088 0.3404
LWT 1 -0.0152 0.00644 5.5886 0.0181
race2 1 1.0811 0.4881 4.9065 0.0268
race3 1 0.4806 0.3567 1.8156 0.1778
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
LWT 0.985 0.973 0.997
race2 2.948 1.133 7.672
race3 1.617 0.804 3.253
Association of Predicted Probabilities and Observed Responses
Percent Concordant 64.1 Somers' D 0.293
Percent Discordant 34.8 Gamma 0.296
Percent Tied 1.1 Tau-a 0.127
Pairs 7670 c 0.647
page 42 Table 2.4 Estimated covariance matrix of the estimated coefficients in Table 2.3.
proc print data=lowbwt2; where _type_='COV'; var _name_ intercept lwt race2 race3; run; Obs _NAME_ Intercept LWT race2 race3 2 Intercept 0.71430 -.005213648 0.02260 -0.10350 3 LWT -0.00521 0.000041465 -0.00065 0.00036 4 race2 0.02260 -.000647028 0.23819 0.05320 5 race3 -0.10350 0.000355854 0.05320 0.12722
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