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SPSS Textbook Examples
Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow
Chapter 4: Model-building strategies and methods for logistic regression

page 105 Table 4.1 Univariable logistic regression models for the UIS  (n = 575).

NOTE: To obtain the values for G, subtract the log likelihoods (remember that the SPSS output gives the -2 log likelihoods, so you will need to divide the value given in the output by -2 before doing the subtraction).

Get file='d:\uis.sav'.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables AGE 1.406 1 .236
Overall Statistics 1.406 1 .236

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 1.398 1 .237
Block 1.398 1 .237
Model 1.398 1 .237

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 652.331 .002 .004


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) AGE .018 .015 1.403 1 .236 1.018 .988 1.049
Constant -1.660 .511 10.552 1 .001 .190

a Variable(s) entered on step 1: AGE.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER beck
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables BECK .633 1 .426
Overall Statistics .633 1 .426

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step .636 1 .425
Block .636 1 .425
Model .636 1 .425

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 653.092 .001 .002


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) BECK -.008 .010 .632 1 .426 .992 .972 1.012
Constant -.927 .200 21.428 1 .000 .396

a Variable(s) entered on step 1: BECK.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables NDRUGTX 9.759 1 .002
Overall Statistics 9.759 1 .002

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 11.839 1 .001
Block 11.839 1 .001
Model 11.839 1 .001

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 641.890 .020 .030


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) NDRUGTX -.075 .025 9.224 1 .002 .928 .884 .974
Constant -.768 .130 34.707 1 .000 .464

a Variable(s) entered on step 1: NDRUGTX.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ivhx2 ivhx3
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables IVHX2 .207 1 .649
IVHX3 9.737 1 .002
Overall Statistics 13.416 2 .001

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 13.352 2 .001
Block 13.352 2 .001
Model 13.352 2 .001

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 640.376 .023 .034


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) IVHX2 -.481 .266 3.277 1 .070 .618 .367 1.041
IVHX3 -.775 .217 12.798 1 .000 .461 .301 .704
Constant -.680 .142 22.998 1 .000 .507

a Variable(s) entered on step 1: IVHX2, IVHX3.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER race
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables RACE 4.779 1 .029
Overall Statistics 4.779 1 .029

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 4.624 1 .032
Block 4.624 1 .032
Model 4.624 1 .032

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 649.105 .008 .012


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) RACE .459 .211 4.735 1 .030 1.583 1.047 2.393
Constant -1.194 .114 109.395 1 .000 .303

a Variable(s) entered on step 1: RACE.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER treat
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables TREAT 5.163 1 .023
Overall Statistics 5.163 1 .023

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 5.178 1 .023
Block 5.178 1 .023
Model 5.178 1 .023

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 648.551 .009 .013


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) TREAT .437 .193 5.127 1 .024 1.548 1.061 2.260
Constant -1.298 .143 82.024 1 .000 .273

a Variable(s) entered on step 1: TREAT.
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER site
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables SITE 1.692 1 .193
Overall Statistics 1.692 1 .193

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 1.666 1 .197
Block 1.666 1 .197
Model 1.666 1 .197

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 652.063 .003 .004


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) SITE .264 .203 1.687 1 .194 1.302 .874 1.940
Constant -1.153 .117 96.939 1 .000 .316

a Variable(s) entered on step 1: SITE.

page 106 Table 4.2 Results of fitting a multivariable model containing the covariates significant at the 0.25 level in Table 4.1.

NOTE: To get the values listed in the column labeled z, you need to take the square root of the Wald statistics given in the SPSS output.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 race treat site.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables AGE 1.406 1 .236
NDRUGTX 9.759 1 .002
IVHX2 .207 1 .649
IVHX3 9.737 1 .002
RACE 4.779 1 .029
TREAT 5.163 1 .023
SITE 1.692 1 .193
Overall Statistics 32.679 7 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 34.481 7 .000
Block 34.481 7 .000
Model 34.481 7 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 619.248 .058 .086


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 421 7 98.4
1.00 144 3 2.0
Overall Percentage

73.7
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) AGE .050 .017 8.456 1 .004 1.052
NDRUGTX -.062 .026 5.759 1 .016 .940
IVHX2 -.603 .287 4.412 1 .036 .547
IVHX3 -.733 .252 8.432 1 .004 .481
RACE .226 .223 1.025 1 .311 1.254
TREAT .443 .199 4.930 1 .026 1.557
SITE .149 .217 .468 1 .494 1.160
Constant -2.405 .555 18.797 1 .000 .090
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX2, IVHX3, RACE, TREAT, SITE.

page 107 Figure 4.2 Univariable lowess smoothed logit versus age.

NOTE: We were unable to reproduce this graph.

page 107 Table 4.3 Results of the quartile analyses of age from the multivariable model containing the variable shown in the model in Table 4.2. 

#2 quartile regression.

SORT CASES BY age (A).

compute age1=($casenum<=148).
compute age2=($casenum>=149) and ($casenum<=292).
compute age3=($casenum>=293) and ($casenum<=458).
compute age4=($casenum>=459).
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age2 age3 age4 ndrugtx ivhx2 ivhx3 race treat site
  /PRINT=CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables AGE2 2.973 1 .085
AGE3 1.377 1 .241
AGE4 .246 1 .620
NDRUGTX 9.759 1 .002
IVHX2 .207 1 .649
IVHX3 9.737 1 .002
RACE 4.779 1 .029
TREAT 5.163 1 .023
SITE 1.692 1 .193
Overall Statistics 32.714 9 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 34.687 9 .000
Block 34.687 9 .000
Model 34.687 9 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 619.042 .059 .086


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 423 5 98.8
1.00 142 5 3.4
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B) 95.0% C.I.for EXP(B)
Lower Upper
Step 1(a) AGE2 -.166 .291 .325 1 .569 .847 .479 1.498
AGE3 .469 .271 3.007 1 .083 1.599 .941 2.718
AGE4 .596 .312 3.635 1 .057 1.814 .983 3.348
NDRUGTX -.059 .025 5.322 1 .021 .943 .897 .991
IVHX2 -.555 .285 3.776 1 .052 .574 .328 1.005
IVHX3 -.673 .252 7.131 1 .008 .510 .312 .836
RACE .279 .224 1.550 1 .213 1.321 .852 2.049
TREAT .443 .200 4.905 1 .027 1.557 1.052 2.305
SITE .158 .219 .523 1 .470 1.171 .763 1.799
Constant -1.055 .271 15.197 1 .000 .348

a Variable(s) entered on step 1: AGE2, AGE3, AGE4, NDRUGTX, IVHX2, IVHX3, RACE, TREAT, SITE.

page 108 Figure 4.3 Plot of estimated logistic regression coefficients versus approximate quartile midpoints of age.

data list list / age coeff.
begin data.
 24 0
30.5 -.165864
35.5 .4693399
47.5 .595771
end data.
execute.

IGRAPH
  /X1 = VAR(age)
  /Y = VAR(coeff)
  /LINE(MEAN) STYLE = DOTLINE INTERPOLATE = STRAIGHT.
Interactive Graph

page 109 Table 4.4 Summary of the use of the method of fractional polynomials for AGE.

NOTE: Deviance is the -2 log likelihood.

Get file='d:\uis.sav'.

NOTE: First row of table:

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx ivhx2 ivhx3 race treat site.
 
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables NDRUGTX 9.759 1 .002
IVHX2 .207 1 .649
IVHX3 9.737 1 .002
RACE 4.779 1 .029
TREAT 5.163 1 .023
SITE 1.692 1 .193
Overall Statistics 24.712 6 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 25.928 6 .000
Block 25.928 6 .000
Model 25.928 6 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 627.801 .044 .065


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) NDRUGTX -.052 .025 4.504 1 .034 .949
IVHX2 -.385 .273 1.992 1 .158 .680
IVHX3 -.499 .235 4.501 1 .034 .607
RACE .297 .220 1.817 1 .178 1.346
TREAT .412 .197 4.349 1 .037 1.509
SITE .179 .215 .689 1 .407 1.195
Constant -.947 .226 17.486 1 .000 .388
a Variable(s) entered on step 1: NDRUGTX, IVHX2, IVHX3, RACE, TREAT, SITE.

NOTE: Second row of table:

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 race treat site.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 575 100.0
Missing Cases 0 .0
Total 575 100.0
Unselected Cases 0 .0
Total 575 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 0 DFREE .00 428 0 100.0
1.00 147 0 .0
Overall Percentage

74.4
a Constant is included in the model.
b The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 0 Constant -1.069 .096 124.967 1 .000 .343

Variables not in the Equation

Score df Sig.
Step 0 Variables AGE 1.406 1 .236
NDRUGTX 9.759 1 .002
IVHX2 .207 1 .649
IVHX3 9.737 1 .002
RACE 4.779 1 .029
TREAT 5.163 1 .023
SITE 1.692 1 .193
Overall Statistics 32.679 7 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 34.481 7 .000
Block 34.481 7 .000
Model 34.481 7 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 619.248 .058 .086


Classification Table(a)

Predicted
DFREE Percentage Correct

Observed .00 1.00
Step 1 DFREE .00 421 7 98.4
1.00 144 3 2.0
Overall Percentage

73.7
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) AGE .050 .017 8.456 1 .004 1.052
NDRUGTX -.062 .026 5.759 1 .016 .940
IVHX2 -.603 .287