page 32 Table 2.1 An example of the coding of the design variables for race, coded at three levels.
data lowbwt1; set 'd:hosmerdatalowbwt'; 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