Logistic Regression - NKNW Example 14.3
Logistic regression on Disease data

The LOGISTIC Procedure

Model Information
Data Set WORK.DISEASE
Response Variable Disease
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Number of Observations Read 98
Number of Observations Used 98

Response Profile
Ordered
Value		 Disease Total
Frequency
1 1 31
2 0 67

Probability modeled is Disease=1.


Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only		 Intercept
and
Covariates
AIC 124.318 111.054
SC 126.903 123.979
-2 Log L 122.318 101.054

R-Square 0.1950 Max-rescaled R-Square 0.2736

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 21.2635 4 0.0003
Score 20.4067 4 0.0004
Wald 16.6437 4 0.0023

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -2.3127 0.6426 12.9545 0.0003
Age 1 0.0297 0.0135 4.8535 0.0276
Status1 1 0.4088 0.5990 0.4657 0.4950
Status2 1 -0.3051 0.6041 0.2551 0.6135
sector 1 1.5746 0.5016 9.8543 0.0017

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
Age 1.030 1.003 1.058
Status1 1.505 0.465 4.868
Status2 0.737 0.226 2.408
sector 4.829 1.807 12.907

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 77.5 Somers' D 0.554
Percent Discordant 22.1 Gamma 0.556
Percent Tied 0.3 Tau-a 0.242
Pairs 2077 c 0.777

Partition for the Hosmer and Lemeshow Test
Group Total Disease = 1 Disease = 0
Observed Expected Observed Expected
1 10 0 0.79 10 9.21
2 10 1 1.02 9 8.98
3 11 2 1.51 9 9.49
4 10 1 1.78 9 8.22
5 10 3 2.34 7 7.66
6 10 4 3.09 6 6.91
7 10 7 3.91 3 6.09
8 11 3 5.51 8 5.49
9 10 5 6.32 5 3.68
10 6 5 4.75 1 1.25

Hosmer and Lemeshow Goodness-of-Fit
Test
Chi-Square DF Pr > ChiSq
9.1871 8 0.3268

Panel 1

Panel 2

Panel 3


Logistic Regression - NKNW Example 14.3
Listing of one kept value for each by group from Logistic Reg

Obs case Age Status1 Status2 sector Disease _LEVEL_ yhat lcl95 ucl95 resdev DFBETA_Intercept DFBETA_Age DFBETA_Status1 DFBETA_Status2 DFBETA_sector difdev
1 40 1 0 1 1 0 1 0.26630 0.09293 0.56251 -0.78696 -0.01939 0.09579 0.01031 -0.10891 -0.08726 0.65146
2 28 2 0 1 0 0 1 0.07187 0.02346 0.19976 -0.38621 -0.02297 0.02517 0.00406 -0.02016 0.01472 0.15105
3 37 3 1 0 1 0 1 0.44026 0.20277 0.70864 -1.07729 -0.03653 0.13065 -0.15334 -0.00929 -0.09777 1.23059
4 34 4 0 0 0 0 1 0.10031 0.03273 0.26867 -0.45980 -0.06299 0.03831 0.03101 0.03402 0.03349 0.21527
5 62 5 0 1 0 0 1 0.07805 0.02670 0.20716 -0.40315 -0.02281 0.02410 0.00395 -0.02219 0.01582 0.16460
6 3 6 0 0 0 0 1 0.10581 0.03573 0.27423 -0.47295 -0.06449 0.03745 0.03228 0.03561 0.03517 0.22774
7 91 7 0 1 0 0 1 0.08244 0.02904 0.21258 -0.41482 -0.02260 0.02318 0.00385 -0.02364 0.01660 0.17427
8 18 8 0 0 1 0 1 0.37751 0.18144 0.62395 -0.97368 -0.12774 0.11676 0.10849 0.08850 -0.07308 0.98811
9 14 9 0 0 0 1 1 0.11456 0.04062 0.28333 2.08167 0.51506 -0.27619 -0.26478 -0.29462 -0.29239 4.59669
10 24 11 1 0 1 0 1 0.49946 0.25967 0.73950 -1.17650 -0.00272 0.08844 -0.18022 -0.01563 -0.11255 1.46058
11 46 12 1 0 1 0 1 0.50690 0.26696 0.74370 -1.18915 0.00209 0.08229 -0.18374 -0.01651 -0.11446 1.49154
12 42 13 0 0 1 1 1 0.41304 0.21594 0.64260 1.32982 0.16963 -0.13835 -0.16158 -0.13291 0.11495 1.85198
13 25 14 0 1 1 0 1 0.34824 0.14743 0.62277 -0.92529 0.01835 0.05833 0.00400 -0.14741 -0.11664 0.89961
14 20 15 0 0 1 1 1 0.42754 0.23031 0.65085 1.30362 0.15429 -0.11829 -0.15489 -0.12785 0.11266 1.77482
15 23 16 0 0 1 1 1 0.43483 0.23757 0.65515 1.29058 0.14686 -0.10860 -0.15161 -0.12536 0.11150 1.73728
16 39 17 1 0 1 1 1 0.54397 0.30330 0.76572 1.10351 -0.02357 -0.04073 0.16920 0.01774 0.10412 1.27659
17 5 18 0 1 0 1 1 0.11082 0.04422 0.25134 2.09755 0.15482 -0.11485 -0.02231 0.26748 -0.17253 4.60704
18 96 19 0 1 0 0 1 0.11378 0.04577 0.25578 -0.49152 -0.01878 0.01312 0.00263 -0.03438 0.02201 0.24494
19 30 20 0 1 0 0 1 0.11682 0.04734 0.26041 -0.49845 -0.01822 0.01186 0.00247 -0.03545 0.02252 0.25194
20 21 21 1 0 1 1 1 0.57330 0.33160 0.78442 1.05485 -0.03820 -0.01341 0.16141 0.01876 0.09840 1.16292
21 16 22 0 0 1 1 1 0.47909 0.28142 0.68354 1.21315 0.10549 -0.05528 -0.13272 -0.11097 0.10445 1.52577
22 11 23 0 0 0 0 1 0.16403 0.06903 0.34176 -0.59860 -0.07437 0.01912 0.04453 0.05175 0.05261 0.36518
23 43 24 0 0 1 0 1 0.49395 0.29583 0.69399 -1.16715 -0.09070 0.03837 0.12371 0.10385 -0.09963 1.40958
24 81 25 1 0 0 0 1 0.23861 0.09829 0.47395 -0.73839 -0.03390 0.00011 -0.08578 0.01437 0.07126 0.56267
25 6 26 0 1 0 0 1 0.13653 0.05707 0.29233 -0.54184 -0.01385 0.00251 0.00128 -0.04256 0.02582 0.29819
26 13 27 0 0 0 0 1 0.18100 0.07840 0.36473 -0.63194 -0.07550 0.01099 0.04777 0.05627 0.05763 0.40740
27 70 28 0 0 0 0 1 0.18545 0.08079 0.37099 -0.64051 -0.07569 0.00867 0.04860 0.05745 0.05895 0.41866
28 68 30 0 0 0 0 1 0.19461 0.08559 0.38416 -0.65792 -0.07592 0.00366 0.05028 0.05987 0.06166 0.44206
29 8 31 1 0 0 1 1 0.27253 0.11409 0.52147 1.61246 0.06279 0.06227 0.27211 -0.03847 -0.21553 2.76692
30 22 32 1 0 1 1 1 0.65079 0.40153 0.83810 0.92689 -0.06762 0.04432 0.13975 0.02029 0.08316 0.89443
31 1 33 0 0 0 0 1 0.20898 0.09281 0.40556 -0.68473 -0.07590 -0.00487 0.05285 0.06363 0.06591 0.47951
32 2 35 0 0 0 0 1 0.21898 0.09759 0.42094 -0.70308 -0.07561 -0.01128 0.05460 0.06624 0.06888 0.50612
33 10 37 1 0 0 0 1 0.30931 0.12945 0.57423 -0.86030 -0.00925 -0.05360 -0.12060 0.01410 0.09116 0.77259
34 50 38 1 0 1 1 1 0.69019 0.43337 0.86648 0.86115 -0.07776 0.06620 0.12804 0.02044 0.07527 0.77207
35 57 39 0 0 1 0 1 0.60396 0.39037 0.78411 -1.36107 -0.02646 -0.08139 0.13312 0.11555 -0.12830 1.92752
36 49 40 1 0 1 1 1 0.70277 0.44296 0.87546 0.83992 -0.08033 0.07216 0.12419 0.02040 0.07271 0.73465
37 35 44 0 1 1 0 1 0.56602 0.28366 0.81117 -1.29210 0.19641 -0.15575 -0.02924 -0.26635 -0.20543 1.79985
38 69 46 0 0 0 0 1 0.28001 0.12255 0.51991 -0.81059 -0.06920 -0.05866 0.06465 0.08206 0.08725 0.67970
39 58 50 0 0 1 0 1 0.67901 0.43957 0.85086 -1.50754 0.04032 -0.19919 0.13590 0.12156 -0.15094 2.39781
40 84 51 0 1 0 0 1 0.24960 0.09562 0.51133 -0.75782 0.03299 -0.08525 -0.01037 -0.08886 0.04451 0.59705
41 74 52 0 0 0 1 1 0.31736 0.13470 0.58133 1.51506 0.13190 0.20421 -0.15128 -0.19742 -0.21258 2.45114
42 41 53 1 0 1 1 1 0.77682 0.49439 0.92531 0.71070 -0.08867 0.09691 0.10008 0.01925 0.05719 0.52764
43 65 59 0 1 0 1 1 0.29676 0.10555 0.60143 1.55875 -0.15028 0.32987 0.04183 0.26448 -0.12459 2.65895
44 4 60 0 0 0 0 1 0.37100 0.14908 0.66506 -0.96293 -0.04443 -0.15768 0.07794 0.10593 0.11613 0.98523
45 29 61 0 1 0 0 1 0.30932 0.10784 0.62395 -0.86032 0.07270 -0.15548 -0.01986 -0.11808 0.05478 0.78738
46 48 65 0 1 1 0 1 0.70895 0.35026 0.91671 -1.57116 0.40560 -0.43105 -0.07048 -0.36607 -0.27791 2.80759
47 17 67 0 0 1 1 1 0.77815 0.49016 0.92752 0.70829 -0.04972 0.12152 -0.03751 -0.03561 0.05310 0.52488
48 51 68 1 0 1 1 1 0.84467 0.53631 0.96236 0.58104 -0.08489 0.10238 0.07521 0.01660 0.04190 0.35400
49 44 70 0 0 1 1 1 0.79317 0.49700 0.93704 0.68076 -0.05250 0.12278 -0.03380 -0.03250 0.05013 0.48565
50 52 74 0 0 1 1 1 0.81201 0.50546 0.94806 0.64535 -0.05521 0.12315 -0.02928 -0.02867 0.04631 0.43731


Logistic Regression - NKNW Example 14.3
Plot of observed means (o) and predicted values (p) 

                                    Plot of yhat*Age.  Symbol used is 'x'.                                     
                                    Plot of mean*Age.  Symbol used is 'o'.                                     
                                                                                                               
          yhat |                                                                                               
               |                                                                                               
           1.0 +                                                                                               
                               o o o   o          o     o o           oo     o       oo o   o                  
               |                                                                                               
               |                                                                                               
               |                                                                                               
               |                                                                                               
               |                                                                      x                        
               |                                                                                               
           0.8 +                                                                        x   x                  
               |                                                       x             x                         
               |                                                                                               
               |                                          x                        x                           
               |                                        x           x                                          
               |                                  x                                                            
                                      o                                                                        
               |                                                                                               
           0.6 +                                         x                                                     
               |                       x                      x                                                
               |                   x                                                                           
               |              x                                                                                
                                  o     o   oo         o                           o                           
               |             x          x x                                                                    
               |                                                                                               
               |     x           xx                                                                            
           0.4 +               x                                                                               
               |          x                                                   x                                
               |                x                                                                              
                                o                o                                                             
               |                                       x              x        x                               
               |                                 x              x            x                                 
               |   x                                                 x                                         
                           o o                                                                                 
               |                           x         x                                                         
           0.2 +                                x  x                                                           
                                    o                                                                          
               |                         x   xx                                                                
               |                            x                                                                  
               |      x x  x        xxx                                                                        
                        o                                                                                      
               |    x  x x                                                                                     
               |                                                                                               
               |                                                                                               
           0.0 +                                                                                               
                   ooooo oo   o      o   ooo  o o  o o   o    o o   oo        oo                               
               |                                                                                               
               ---+---------+---------+---------+---------+---------+---------+---------+---------+--          
                  0        10        20        30        40        50        60        70        80            
                                                                                                               
                                                         Age                                                   
                                                                                                               
NOTE: 100 obs had missing values.