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SAS Textbook Examples
Applied Logistic Regression, Second Edition by Hosmer and Lemeshow
Chapter 2: Multiple logistic regression

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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