Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow, Chapter 4



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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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	AGE	.018	.015	1.403	1	.236	1.018	.988	1.049
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	BECK	-.008	.010	.632	1	.426	.992	.972	1.012
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	NDRUGTX	-.075	.025	9.224	1	.002	.928	.884	.974
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
	Variables	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	RACE	.459	.211	4.735	1	.030	1.583	1.047	2.393
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	TREAT	.437	.193	5.127	1	.024	1.548	1.061	2.260
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1(a)	SITE	.264	.203	1.687	1	.194	1.302	.874	1.940
Step 1(a)	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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	Percentage Correct
Step 1	DFREE	.00	421	7	98.4
	DFREE	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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)
		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	Percentage Correct
Step 1	DFREE	.00	423	5	98.8
	DFREE	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)
		B	S.E.	Wald	df	Sig.	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.

formats age (f2.0) coeff (f4.2).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= age coeff 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: coeff=col( source(s), name( "coeff" ) )
DATA: age=col( source(s), name( "age" ) )
GUIDE: axis( dim( 1 ), label( "AGE" ), start(0), delta(10) )
GUIDE: axis( dim( 2 ), label( "Coeff" ), start(0), delta(.25) )
GUIDE: form.line(position(*, 0), shape(shape.dash))
SCALE: linear( dim( 1 ), min(20), max(50) )
SCALE: linear( dim( 2 ), min(-.25), max(.75) )
ELEMENT: point( position( age * coeff ) )
ELEMENT: line( position( age * coeff ) )
END GPL.

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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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	Percentage Correct
Step 1	DFREE	.00	421	7	98.4
	DFREE	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.

NOTE: Third row of table:

compute agethree=age**3.
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER agethree 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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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(a)**
			Score	df	Sig.
Step 0	Variables	AGETHREE	1.959	1	.162
		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
a Residual Chi-Squares are not computed because of redundancies.

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	34.847	7	.000
	Block	34.847	7	.000
	Model	34.847	7	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	618.882	.059	.087

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	422	6	98.6
	DFREE	1.00	143	4	2.7
	Overall Percentage				74.1
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGETHREE	.000	.000	8.933	1	.003	1.000
	NDRUGTX	-.062	.026	5.817	1	.016	.940
	IVHX2	-.596	.287	4.318	1	.038	.551
	IVHX3	-.714	.250	8.163	1	.004	.490
	RACE	.236	.223	1.115	1	.291	1.266
	TREAT	.435	.199	4.763	1	.029	1.545
	SITE	.144	.217	.437	1	.509	1.155
	Constant	-1.303	.258	25.460	1	.000	.272
a Variable(s) entered on step 1: AGETHREE, NDRUGTX, IVHX2, IVHX3, RACE, TREAT, SITE.

NOTE: Fourth row of table:

compute age_2=age**(-2).
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER agethree age_2 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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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(a)**
			Score	df	Sig.
Step 0	Variables	AGETHREE	1.959	1	.162
		AGE_2	.891	1	.345
		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
a Residual Chi-Squares are not computed because of redundancies.

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	34.960	8	.000
	Block	34.960	8	.000
	Model	34.960	8	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	618.769	.059	.087

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	422	6	98.6
	DFREE	1.00	143	4	2.7
	Overall Percentage				74.1
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGETHREE	.000	.000	2.073	1	.150	1.000
	AGE_2	-153.863	457.593	.113	1	.737	.000
	NDRUGTX	-.062	.026	5.821	1	.016	.940
	IVHX2	-.606	.288	4.419	1	.036	.546
	IVHX3	-.726	.253	8.270	1	.004	.484
	RACE	.228	.224	1.037	1	.308	1.256
	TREAT	.439	.200	4.838	1	.028	1.552
	SITE	.146	.217	.450	1	.502	1.157
	Constant	-1.050	.796	1.740	1	.187	.350
a Variable(s) entered on step 1: AGETHREE, AGE_2, NDRUGTX, IVHX2, IVHX3, RACE, TREAT, SITE.

page 110 Figure 4.4 Univariable lowess smoothed logit versus number of previous drug treatments (NDRGTX).

NOTE: We were unable to reproduce this graph.

page 110 Table 4.5 Results of the design variable analysis of number of previous drug treatments (NDRGTX) from the multivariable model containing the variables shown in the model in Table 4.2.

compute group=ndrugtx.
recode group (0=1) (1,2=2) (3 thru 15=3) (16 thru highest=4).
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age group ivhx2 ivhx3 race treat site
  /CONTRAST (group)=Indicator(1).

**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

**Categorical Variables Codings**
		Frequency	Parameter coding
		Frequency	(1)	(2)	(3)
GROUP	1.00	79	.000	.000	.000
	2.00	173	1.000	.000	.000
	3.00	294	.000	1.000	.000
	4.00	29	.000	.000	1.000

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		GROUP	11.493	3	.009
		GROUP(1)	8.241	1	.004
		GROUP(2)	6.336	1	.012
		GROUP(3)	2.224	1	.136
		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		34.597	9	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	35.091	9	.000
	Block	35.091	9	.000
	Model	35.091	9	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	618.638	.059	.087

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	423	5	98.8
	DFREE	1.00	140	7	4.8
	Overall Percentage				74.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.051	.017	8.551	1	.003	1.052
	GROUP			7.491	3	.058
	GROUP(1)	.406	.309	1.726	1	.189	1.501
	GROUP(2)	-.154	.312	.243	1	.622	.858
	GROUP(3)	-.584	.620	.887	1	.346	.558
	IVHX2	-.648	.290	4.995	1	.025	.523
	IVHX3	-.795	.254	9.787	1	.002	.451
	RACE	.241	.224	1.155	1	.283	1.273
	TREAT	.420	.200	4.421	1	.035	1.522
	SITE	.162	.221	.539	1	.463	1.176
	Constant	-2.660	.606	19.267	1	.000	.070
a Variable(s) entered on step 1: AGE, GROUP, IVHX2, IVHX3, RACE, TREAT, SITE.

page 111 Figure 4.5 Plot of estimated logistic regression coefficients from Table 4.4 versus the midpoints of number of previous drug treatment groups.

data list list / midpt coeff.
begin data.
 0 0
1.5 .406
9 -.154
28 -.585
end data.
execute.

formats midpt (f2.0) coeff (f5.3).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= midpt coeff 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: coeff=col( source(s), name( "coeff" ) )
DATA: midpt=col( source(s), name( "midpt" ) )
GUIDE: axis( dim( 1 ), label( "Number of Previous Drug Treatments" ), start(0), delta(10) )
GUIDE: axis( dim( 2 ), label( "Coeff" ), start(0), delta(.25) )
GUIDE: form.line(position(*, 0), shape(shape.dash))
ELEMENT: point( position( midpt * coeff ) )
ELEMENT: line( position( midpt * coeff ) )
END GPL.

page 112 Figure 4.6 Plot of the univariable lowess smoothed logit (o) and the multivariable adjusted logit (+) from the J = 2 fractional polynomial model versus number of previous drug treatments (NDRGTX).

NOTE: We were unable to reproduce this graph.

page 113 Table 4.7 Results of fitting the multivariable model with the two term fractional polynomial transformation of ndrgtx.

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

compute ndrgfp1=1/((ndrugtx+1)/10).
compute ndrgfp2=ndrgfp1*ln((ndrugtx+1)/10).
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		NDRGFP1	6.074	1	.014
		NDRGFP2	4.115	1	.043
		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		38.703	8	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	40.278	8	.000
	Block	40.278	8	.000
	Model	40.278	8	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	613.451	.068	.100

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	422	6	98.6
	DFREE	1.00	140	7	4.8
	Overall Percentage				74.6
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.054	.017	9.693	1	.002	1.056
	NDRGFP1	.981	.289	11.545	1	.001	2.668
	NDRGFP2	.361	.110	10.805	1	.001	1.435
	IVHX2	-.609	.291	4.374	1	.036	.544
	IVHX3	-.724	.256	8.021	1	.005	.485
	RACE	.248	.224	1.220	1	.269	1.281
	TREAT	.422	.200	4.444	1	.035	1.526
	SITE	.173	.221	.614	1	.433	1.189
	Constant	-4.314	.792	29.633	1	.000	.013
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE.

page 115 Table 4.9 Preliminary final model containing significant main effects and interactions.

compute nage=ndrgfp1*age.
compute racesite=race*site.
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		NDRGFP1	6.074	1	.014
		NDRGFP2	4.115	1	.043
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		RACE	4.779	1	.029
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
		NAGE	5.573	1	.018
		RACESITE	.144	1	.705
	Overall Statistics		52.071	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	55.766	10	.000
	Block	55.766	10	.000
	Model	55.766	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	597.963	.092	.136

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	417	11	97.4
	DFREE	1.00	131	16	10.9
	Overall Percentage				75.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.117	.029	16.317	1	.000	1.124
	NDRGFP1	1.669	.407	16.804	1	.000	5.307
	NDRGFP2	.434	.117	13.762	1	.000	1.543
	IVHX2	-.635	.299	4.514	1	.034	.530
	IVHX3	-.705	.262	7.263	1	.007	.494
	RACE	.684	.264	6.708	1	.010	1.982
	TREAT	.435	.204	4.556	1	.033	1.545
	SITE	.516	.255	4.101	1	.043	1.676
	NAGE	-.015	.006	6.419	1	.011	.985
	RACESITE	-1.429	.530	7.280	1	.007	.239
	Constant	-6.844	1.219	31.504	1	.000	.001
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

page 123 Table 4.11 Log-likelihood for the model at each step and likelihood ratio test statistics (G), degrees-of-freedom (df), and p-values for two methods of selecting variables for a final model from a summary table.

NOTE: G is calculated by hand because it follows the book.

NOTE: The following code gives the log likelihood and the values for method 1.

compute x=1.
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER x
  /noconst.

**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,c)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	0	428	.0
	DFREE	1.00	0	147	100.0
	Overall Percentage				25.6
a No terms in the model.
b Initial Log-likelihood Function: -2 Log Likelihood = 797.119
c The cut value is .500

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	137.323	1	.000
Step 0	Overall Statistics		137.323	1	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	143.390	1	.000
	Block	143.390	1	.000
	Model	143.390	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	653.729	.221	.294

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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)	X	-1.069	.096	124.967	1	.000	.343
a Variable(s) entered on step 1: X.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
Step 0	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	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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	-.075	.025	9.224	1	.002	.928
Step 1(a)	Constant	-.768	.130	34.707	1	.000	.464
a Variable(s) entered on step 1: NDRUGTX.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx treat.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
	Variables	TREAT	5.163	1	.023
	Overall Statistics		14.892	2	.001

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	16.869	2	.000
	Block	16.869	2	.000
	Model	16.869	2	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	636.860	.029	.043

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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	-.074	.024	9.126	1	.003	.929
	TREAT	.435	.195	4.983	1	.026	1.545
	Constant	-.999	.169	34.916	1	.000	.368
a Variable(s) entered on step 1: NDRUGTX, TREAT.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx treat ivhx2 ivhx3.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
	Overall Statistics		22.391	4	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	23.678	4	.000
	Block	23.678	4	.000
	Model	23.678	4	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	630.051	.040	.059

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	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	-.054	.025	4.837	1	.028	.947
	TREAT	.421	.197	4.600	1	.032	1.524
	IVHX2	-.403	.271	2.206	1	.138	.669
	IVHX3	-.580	.229	6.431	1	.011	.560
	Constant	-.772	.188	16.893	1	.000	.462
a Variable(s) entered on step 1: NDRUGTX, TREAT, IVHX2, IVHX3.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER ndrugtx treat ivhx2 ivhx3 age.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		AGE	1.406	1	.236
	Overall Statistics		31.156	5	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	33.142	5	.000
	Block	33.142	5	.000
	Model	33.142	5	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	620.587	.056	.082

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	426	2	99.5
	DFREE	1.00	144	3	2.0
	Overall Percentage				74.6
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	NDRUGTX	-.064	.026	6.190	1	.013	.938
	TREAT	.451	.199	5.165	1	.023	1.570
	IVHX2	-.624	.285	4.799	1	.028	.536
	IVHX3	-.806	.245	10.853	1	.001	.447
	AGE	.053	.017	9.338	1	.002	1.054
	Constant	-2.333	.548	18.095	1	.000	.097
a Variable(s) entered on step 1: NDRUGTX, TREAT, IVHX2, IVHX3, AGE.

NOTE: The following code gives the values for G for method 2.

-2*(-326.864-(-310.293))=33.142

-2*(-320.945-(-310.293))=21.304

-2*(-318.430-(-310.293))=16.274

-2*(-315.025-(-310.293))=9.464

page 126 Table 4.12 Results of applying stepwise variable selection using the score test to select and maximum likelihood test to remove covariates at each step to the UIS data. Results are presented at each step in terms of the p-values to enter (below the horizontal line), and the p-value to remove (above the horizontal line) in each column. The asterisk denotes the maximum p-value to remove at each step.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=FSTEP(COND) ivhx age ndrugtx treat race site beck
  /CONTRAST (ivhx)=Indicator(1)
  /CRITERIA PIN(.15) POUT(.20) ITERATE(20) CUT(.5).

**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

**Categorical Variables Codings**
		Frequency	Parameter coding
		Frequency	(1)	(2)
IVHX	1.00	223	.000	.000
	2.00	109	1.000	.000
	3.00	243	.000	1.000

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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	IVHX	13.416	2	.001
		IVHX(1)	.207	1	.649
		IVHX(2)	9.737	1	.002
		AGE	1.406	1	.236
		NDRUGTX	9.759	1	.002
		TREAT	5.163	1	.023
		RACE	4.779	1	.029
		SITE	1.692	1	.193
		BECK	.633	1	.426
	Overall Statistics		32.680	8	.000

**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
Step 2	Step	7.280	1	.007
	Block	20.632	3	.000
	Model	20.632	3	.000
Step 3	Step	7.292	1	.007
	Block	27.924	4	.000
	Model	27.924	4	.000
Step 4	Step	5.218	1	.022
	Block	33.142	5	.000
	Model	33.142	5	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	640.376	.023	.034
2	633.096	.035	.052
3	625.805	.047	.070
4	620.587	.056	.082

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	1.00	147	0	.0
	Overall Percentage				74.4
Step 2	DFREE	.00	427	1	99.8
	DFREE	1.00	146	1	.7
	Overall Percentage				74.4
Step 3	DFREE	.00	426	2	99.5
	DFREE	1.00	145	2	1.4
	Overall Percentage				74.4
Step 4	DFREE	.00	426	2	99.5
	DFREE	1.00	144	3	2.0
	Overall Percentage				74.6
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	IVHX			13.157	2	.001
	IVHX(1)	-.481	.266	3.277	1	.070	.618
	IVHX(2)	-.775	.217	12.798	1	.000	.461
	Constant	-.680	.142	22.998	1	.000	.507
Step 2(b)	IVHX			18.618	2	.000
	IVHX(1)	-.681	.279	5.952	1	.015	.506
	IVHX(2)	-1.002	.236	18.081	1	.000	.367
	AGE	.045	.017	7.216	1	.007	1.046
	Constant	-2.033	.527	14.909	1	.000	.131
Step 3(c)	IVHX			11.834	2	.003
	IVHX(1)	-.590	.283	4.352	1	.037	.554
	IVHX(2)	-.820	.244	11.316	1	.001	.441
	AGE	.051	.017	8.781	1	.003	1.052
	NDRUGTX	-.063	.026	6.026	1	.014	.939
	Constant	-2.041	.530	14.842	1	.000	.130
Step 4(d)	IVHX			11.622	2	.003
	IVHX(1)	-.624	.285	4.799	1	.028	.536
	IVHX(2)	-.806	.245	10.853	1	.001	.447
	AGE	.053	.017	9.338	1	.002	1.054
	NDRUGTX	-.064	.026	6.190	1	.013	.938
	TREAT	.451	.199	5.165	1	.023	1.570
	Constant	-2.333	.548	18.095	1	.000	.097
a Variable(s) entered on step 1: IVHX.
b Variable(s) entered on step 2: AGE.
c Variable(s) entered on step 3: NDRUGTX.
d Variable(s) entered on step 4: TREAT.

**Model if Term Removed(a)**
Variable		Model Log Likelihood	Change in -2 Log Likelihood	df	Sig. of the Change
Step 1	IVHX	-326.912	13.448	2	.001
Step 2	IVHX	-326.268	19.439	2	.000
Step 2	AGE	-320.203	7.309	1	.007
Step 3	IVHX	-318.991	12.178	2	.002
	AGE	-317.367	8.930	1	.003
	NDRUGTX	-316.584	7.362	1	.007
Step 4	IVHX	-316.260	11.933	2	.003
	AGE	-315.049	9.512	1	.002
	NDRUGTX	-314.074	7.561	1	.006
	TREAT	-312.910	5.233	1	.022
a Based on conditional parameter estimates

**Variables not in the Equation**
			Score	df	Sig.
Step 1	Variables	AGE	7.327	1	.007
		NDRUGTX	4.933	1	.026
		TREAT	4.550	1	.033
		RACE	2.111	1	.146
		SITE	.558	1	.455
		BECK	.083	1	.774
	Overall Statistics		20.140	6	.003
Step 2	Variables	NDRUGTX	6.211	1	.013
		TREAT	5.007	1	.025
		RACE	1.422	1	.233
		SITE	.508	1	.476
		BECK	.002	1	.963
	Overall Statistics		12.853	5	.025
Step 3	Variables	TREAT	5.202	1	.023
		RACE	1.204	1	.273
		SITE	.242	1	.623
		BECK	.001	1	.974
	Overall Statistics		6.552	4	.162
Step 4	Variables	RACE	.884	1	.347
		SITE	.327	1	.568
		BECK	.000	1	.995
	Overall Statistics		1.349	3	.717

page 127 Table 4.13 Results of applying stepwise variable selection to interactions from the main effects model from the UIS data, using the maximum likelihood method presented at each step in terms of the p-values to enter (below the horizontal line), and the p-value to remove (above the horizontal line) in each column. The asterisk denotes the maximum p-value to remove at each step.

NOTE: We were unable to reproduce this table.

page 133 Table 4.14 Five best models identified using Mallows Cq. Model covariates, Mallows Cq, the Wald test and the likelihood ratio test for the excluded covariates, degrees-of-freedom and p-value.

NOTE: Each of the values shown in this table must be calculated by hand using the formulas in the text.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age beck ivhx2 ivhx3 ndrugtx 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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		BECK	.633	1	.426
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		NDRUGTX	9.759	1	.002
		RACE	4.779	1	.029
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
	Overall Statistics		32.680	8	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	34.481	8	.000
	Block	34.481	8	.000
	Model	34.481	8	.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	Percentage Correct
Step 1	DFREE	.00	421	7	98.4
	DFREE	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	8.389	1	.004	1.052
	BECK	.000	.011	.001	1	.980	1.000
	IVHX2	-.604	.288	4.406	1	.036	.547
	IVHX3	-.734	.255	8.278	1	.004	.480
	NDRUGTX	-.062	.026	5.757	1	.016	.940
	RACE	.226	.223	1.024	1	.312	1.254
	TREAT	.442	.199	4.929	1	.026	1.557
	SITE	.149	.218	.468	1	.494	1.161
	Constant	-2.411	.598	16.238	1	.000	.090
a Variable(s) entered on step 1: AGE, BECK, IVHX2, IVHX3, NDRUGTX, RACE, TREAT, SITE.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 treat.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
	Overall Statistics		31.156	5	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	33.142	5	.000
	Block	33.142	5	.000
	Model	33.142	5	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	620.587	.056	.082

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	426	2	99.5
	DFREE	1.00	144	3	2.0
	Overall Percentage				74.6
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.053	.017	9.338	1	.002	1.054
	NDRUGTX	-.064	.026	6.190	1	.013	.938
	IVHX2	-.624	.285	4.799	1	.028	.536
	IVHX3	-.806	.245	10.853	1	.001	.447
	TREAT	.451	.199	5.165	1	.023	1.570
	Constant	-2.333	.548	18.095	1	.000	.097
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX2, IVHX3, TREAT.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 treat race.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
		RACE	4.779	1	.029
	Overall Statistics		32.044	6	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	34.016	6	.000
	Block	34.016	6	.000
	Model	34.016	6	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	619.713	.057	.085

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	423	5	98.8
	DFREE	1.00	144	3	2.0
	Overall Percentage				74.1
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.051	.017	8.668	1	.003	1.052
	NDRUGTX	-.063	.026	6.070	1	.014	.939
	IVHX2	-.593	.286	4.284	1	.038	.553
	IVHX3	-.760	.249	9.318	1	.002	.468
	TREAT	.439	.199	4.859	1	.028	1.551
	RACE	.208	.221	.883	1	.347	1.231
	Constant	-2.356	.550	18.339	1	.000	.095
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX2, IVHX3, TREAT, RACE.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
	Overall Statistics		31.613	6	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	33.467	6	.000
	Block	33.467	6	.000
	Model	33.467	6	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	620.262	.057	.083

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	424	4	99.1
	DFREE	1.00	143	4	2.7
	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)	AGE	.052	.017	9.208	1	.002	1.054
	NDRUGTX	-.062	.026	5.935	1	.015	.939
	IVHX2	-.635	.286	4.940	1	.026	.530
	IVHX3	-.786	.247	10.120	1	.001	.456
	TREAT	.455	.199	5.247	1	.022	1.577
	SITE	.123	.215	.326	1	.568	1.131
	Constant	-2.373	.553	18.430	1	.000	.093
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX2, IVHX3, TREAT, SITE.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx2 ivhx3 treat beck.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		TREAT	5.163	1	.023
		BECK	.633	1	.426
	Overall Statistics		31.157	6	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	33.142	6	.000
	Block	33.142	6	.000
	Model	33.142	6	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	620.587	.056	.082

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	426	2	99.5
	DFREE	1.00	144	3	2.0
	Overall Percentage				74.6
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.053	.017	9.256	1	.002	1.054
	NDRUGTX	-.064	.026	6.184	1	.013	.938
	IVHX2	-.624	.285	4.790	1	.029	.536
	IVHX3	-.806	.247	10.608	1	.001	.447
	TREAT	.451	.199	5.164	1	.023	1.570
	BECK	.000	.011	.000	1	.995	1.000
	Constant	-2.334	.590	15.655	1	.000	.097
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX2, IVHX3, TREAT, BECK.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrugtx ivhx3 treat.

**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	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	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
		IVHX3	9.737	1	.002
		TREAT	5.163	1	.023
	Overall Statistics		25.962	4	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	28.140	4	.000
	Block	28.140	4	.000
	Model	28.140	4	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	625.589	.048	.070

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	426	2	99.5
	DFREE	1.00	145	2	1.4
	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)	AGE	.043	.016	6.684	1	.010	1.043
	NDRUGTX	-.070	.026	7.387	1	.007	.932
	IVHX3	-.564	.219	6.661	1	.010	.569
	TREAT	.428	.197	4.699	1	.030	1.534
	Constant	-2.177	.540	16.243	1	.000	.113
a Variable(s) entered on step 1: AGE, NDRUGTX, IVHX3, TREAT.

page 134 Table 4.15 Five best models identified using the score test approximation to Mallows Cq, (S8 = 32.6798).

NOTE: We were unable to reproduce this table.

page 137 Table 4.16 A contingency table with a zero cell count and the result s of fitting a logistic regression model to this data.

data list list / x y1 y2 y3 cnt.
begin data.
1 1 0 0 7
1 0 1 0 12
1 0 0 1 20
0 1 0 0 13
0 0 1 0 8
end data.
execute.

weight by cnt.

CROSSTABS
  /TABLES=x  BY y1 y2 y3
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.

**Case Processing Summary**
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
X * Y1	60	100.0%	0	.0%	60	100.0%
X * Y2	60	100.0%	0	.0%	60	100.0%
X * Y3	60	100.0%	0	.0%	60	100.0%

**X * Y1 Crosstabulation**
Count
		Y1		Total
		.00	1.00	Total
X	.00	8	13	21
X	1.00	32	7	39
Total		40	20	60

**X * Y2 Crosstabulation**
Count
		Y2		Total
		.00	1.00	Total
X	.00	13	8	21
X	1.00	27	12	39
Total		40	20	60

**X * Y3 Crosstabulation**
Count
		Y3		Total
		.00	1.00	Total
X	.00	21		21
X	1.00	19	20	39
Total		40	20	60

NOTE: The values in the column labeled 1 are listed as the constant in the SPSS output.

LOGISTIC REGRESSION VAR=x
  /METHOD=ENTER y2 y3.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	5	100.0
	Missing Cases	0	.0
	Total	5	100.0
Unselected Cases		0	.0
Total		5	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
			X		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	X	.00	0	21	.0
	X	1.00	0	39	100.0
	Overall Percentage				65.0
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	.619	.271	5.230	1	.022	1.857

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	Y2	.330	1	.566
	Variables	Y3	16.155	1	.000
	Overall Statistics		18.903	2	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	24.874	2	.000
	Block	24.874	2	.000
	Model	24.874	2	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	52.820	.339	.467

**Classification Table(a)**
			Predicted
			X		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	X	.00	13	8	61.9
	X	1.00	7	32	82.1
	Overall Percentage				75.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	Y2	1.025	.654	2.452	1	.117	2.786
	Y3	10.822	36.733	.087	1	.768	50104.963
	Constant	-.619	.469	1.744	1	.187	.538
a Variable(s) entered on step 1: Y2, Y3.

page 137 Table 4.17 Stratified 2 by 2 contingency tables with a zero cell count within one stratum.

data list list / z x y cnt.
begin data.
1 1 1 5
1 1 0 5
1 0 1 2
1 0 0 8
2 1 1 10
2 1 0 2
2 0 1 2
2 0 0 6
3 1 1 15
3 0 1 1
3 0 0 4
end data.
execute.

weight by cnt.

CROSSTABS
  /TABLES=y  BY x  BY z
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.

**Case Processing Summary**
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Y * X * Z	60	100.0%	0	.0%	60	100.0%

**Y * X * Z Crosstabulation**
Count
			X		Total
Z			.00	1.00	Total
1.00	Y	.00	8	5	13
	Y	1.00	2	5	7
	Total		10	10	20
2.00	Y	.00	6	2	8
	Y	1.00	2	10	12
	Total		8	12	20
3.00	Y	.00	4		4
	Y	1.00	1	15	16
	Total		5	15	20

NOTE: The odds ratios in the bottom row of the table need to be calculated by hand.

page 138 Table 4.18 Results of fitting logistic regression models to the data in Table 4.17.

NOTE: Model 1:

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x z
  /CONTRAST (z)=Indicator(1).

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	11	100.0
	Missing Cases	0	.0
	Total	11	100.0
Unselected Cases		0	.0
Total		11	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

**Categorical Variables Codings**
		Frequency	Parameter coding
		Frequency	(1)	(2)
Z	1.00	4	.000	.000
	2.00	4	1.000	.000
	3.00	3	.000	1.000

**Classification Table(a,b)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	25	.0
	Y	1.00	0	35	100.0
	Overall Percentage				58.3
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	.336	.262	1.651	1	.199	1.400

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	20.549	1	.000
		Z	8.366	2	.015
		Z(1)	.034	1	.853
		Z(2)	5.794	1	.016
	Overall Statistics		24.547	3	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	27.591	3	.000
	Block	27.591	3	.000
	Model	27.591	3	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	53.912	.369	.496

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	18	7	72.0
	Y	1.00	5	30	85.7
	Overall Percentage				80.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	2.768	.716	14.959	1	.000	15.928
	Z			5.433	2	.066
	Z(1)	1.189	.812	2.144	1	.143	3.283
	Z(2)	2.038	.889	5.256	1	.022	7.676
	Constant	-2.319	.773	9.005	1	.003	.098
a Variable(s) entered on step 1: X, Z.

NOTE: Model 2:

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x z x*z
  /CONTRAST (z)=Indicator(1).

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	11	100.0
	Missing Cases	0	.0
	Total	11	100.0
Unselected Cases		0	.0
Total		11	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

**Categorical Variables Codings**
		Frequency	Parameter coding
		Frequency	(1)	(2)
Z	1.00	4	.000	.000
	2.00	4	1.000	.000
	3.00	3	.000	1.000

**Classification Table(a,b)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	25	.0
	Y	1.00	0	35	100.0
	Overall Percentage				58.3
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	.336	.262	1.651	1	.199	1.400

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	20.549	1	.000
		Z	8.366	2	.015
		Z(1)	.034	1	.853
		Z(2)	5.794	1	.016
		X * Z	24.468	2	.000
		X by Z(1)	3.857	1	.050
		X by Z(2)	14.286	1	.000
	Overall Statistics		26.811	5	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	32.816	5	.000
	Block	32.816	5	.000
	Model	32.816	5	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	48.687	.421	.567

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	18	7	72.0
	Y	1.00	5	30	85.7
	Overall Percentage				80.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	1.386	1.012	1.875	1	.171	4.000
	Z			.076	2	.963
	Z(1)	.288	1.137	.064	1	.800	1.333
	Z(2)	.000	1.369	.000	1	1.000	1.000
	X * Z			.814	2	.666
	X by Z(1)	1.322	1.514	.762	1	.383	3.750
	X by Z(2)	10.203	42.439	.058	1	.810	26979.595
	Constant	-1.386	.791	3.075	1	.080	.250
a Variable(s) entered on step 1: X, Z, X * Z .

page 139 Table 4.19 Estimated slope, constant, and estimated standard errors when the data have complete separation, quasicomplete separation, and overlap.

NOTE: The values for x = 5.5 and x = 6.0 are different from those shown in the text because of the complete separation and each statistical package handles complete separation differently. The point to note is that neither value is to be trusted.

data list list /  x y.
BEGIN DATA.
 1 0
 2 0
 3 0
 4 0
 5 0
 5.5 0
 6 1
 7 1
 8 1
 9 1
 10 1
 11 1
END DATA.

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.439	1	.004
Step 0	Overall Statistics		8.439	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	16.636	1	.000
	Block	16.636	1	.000
	Model	16.636	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	.000	.750	1.000

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	6	0	100.0
	Y	1.00	0	6	100.0
	Overall Percentage				100.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	63.218	7651.169	.000	1	.993	2851911423513431000000000000.000
Step 1(a)	Constant	-363.451	43936.851	.000	1	.993	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=6.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.182	1	.004
Step 0	Overall Statistics		8.182	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	13.863	1	.000
	Block	13.863	1	.000
	Model	13.863	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	2.773	.685	.913

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	6	0	100.0
	Y	1.00	1	5	83.3
	Overall Percentage				91.7
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	10.826	158.574	.005	1	.946	50293.209
Step 1(a)	Constant	-64.954	951.443	.005	1	.946	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=6.05.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.154	1	.004
Step 0	Overall Statistics		8.154	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	13.587	1	.000
	Block	13.587	1	.000
	Model	13.587	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	3.048	.678	.904

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	5	1	83.3
	Y	1.00	1	5	83.3
	Overall Percentage				83.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	4.345	6.087	.510	1	.475	77.082
Step 1(a)	Constant	-26.173	36.720	.508	1	.476	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=6.10.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.127	1	.004
Step 0	Overall Statistics		8.127	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	13.374	1	.000
	Block	13.374	1	.000
	Model	13.374	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	3.261	.672	.896

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	5	1	83.3
	Y	1.00	1	5	83.3
	Overall Percentage				83.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	3.634	4.181	.755	1	.385	37.852
Step 1(a)	Constant	-21.967	25.373	.750	1	.387	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=6.15.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.099	1	.004
Step 0	Overall Statistics		8.099	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	13.184	1	.000
	Block	13.184	1	.000
	Model	13.184	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	3.452	.667	.889

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	5	1	83.3
	Y	1.00	1	5	83.3
	Overall Percentage				83.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	3.220	3.332	.934	1	.334	25.032
Step 1(a)	Constant	-19.530	20.340	.922	1	.337	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=6.20.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	8.070	1	.004
Step 0	Overall Statistics		8.070	1	.004

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	13.007	1	.000
	Block	13.007	1	.000
	Model	13.007	1	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	3.629	.662	.882

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	5	1	83.3
	Y	1.00	1	5	83.3
	Overall Percentage				83.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	2.927	2.818	1.079	1	.299	18.669
Step 1(a)	Constant	-17.803	17.298	1.059	1	.303	.000
a Variable(s) entered on step 1: X.

if $casenum = 6 x=8.
LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	12	100.0
	Missing Cases	0	.0
	Total	12	100.0
Unselected Cases		0	.0
Total		12	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	0	6	.0
	Y	1.00	0	6	100.0
	Overall Percentage				50.0
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	.000	.577	.000	1	1.000	1.000

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X	6.897	1	.009
Step 0	Overall Statistics		6.897	1	.009

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	9.076	1	.003
	Block	9.076	1	.003
	Model	9.076	1	.003

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	7.560	.531	.707

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	5	1	83.3
	Y	1.00	1	5	83.3
	Overall Percentage				83.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X	.966	.531	3.310	1	.069	2.629
Step 1(a)	Constant	-6.124	3.585	2.918	1	.088	.002
a Variable(s) entered on step 1: X.

page 140 Table 4.20 Data displaying near collinearity among the independent variables and constant.

data list list /  subj x1 x2 x3 y.
BEGIN DATA.
1 .225 .231 1.026 0
2 .487 .489 1.022 1
3 -1.080 -1.070 1.074 0
4 -.87 -.87 1.091 0
5 -.58 -.57 1.095 0
6 -.64 -.64 1.01 0
7 1.614 1.619 1.087 0
8 .352 .355 1.095 1
9 -1.025 -1.018 1.008 0
10 .929 .937 1.057 1
end data.

list subj x1 x2 x3 y.

    SUBJ       X1       X2       X3        Y

    1.00      .23      .23     1.03      .00
    2.00      .49      .49     1.02     1.00
    3.00    -1.08    -1.07     1.07      .00
    4.00     -.87     -.87     1.09      .00
    5.00     -.58     -.57     1.10      .00
    6.00     -.64     -.64     1.01      .00
    7.00     1.61     1.62     1.09      .00
    8.00      .35      .36     1.10     1.00
    9.00    -1.02    -1.02     1.01      .00
   10.00      .93      .94     1.06     1.00

Number of cases read:  10    Number of cases listed:  10

page 141 Table 4.21 Estimated coefficients and standard errors from fitting logistic regression models to the data in Table 4.20.

NOTE: column 2.

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x1.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	10	100.0
	Missing Cases	0	.0
	Total	10	100.0
Unselected Cases		0	.0
Total		10	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	7	0	100.0
	Y	1.00	3	0	.0
	Overall Percentage				70.0
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	-.847	.690	1.508	1	.220	.429

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X1	2.380	1	.123
Step 0	Overall Statistics		2.380	1	.123

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	2.475	1	.116
	Block	2.475	1	.116
	Model	2.475	1	.116

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	9.743	.219	.311

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	6	1	85.7
	Y	1.00	2	1	33.3
	Overall Percentage				70.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X1	1.380	1.005	1.885	1	.170	3.976
Step 1(a)	Constant	-1.002	.829	1.459	1	.227	.367
a Variable(s) entered on step 1: X1.

NOTE: column 3 (note that there is likely a typo in this column).

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x1 x2.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	10	100.0
	Missing Cases	0	.0
	Total	10	100.0
Unselected Cases		0	.0
Total		10	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	7	0	100.0
	Y	1.00	3	0	.0
	Overall Percentage				70.0
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	-.847	.690	1.508	1	.220	.429

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X1	2.380	1	.123
	Variables	X2	2.375	1	.123
	Overall Statistics		2.504	2	.286

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	2.775	2	.250
	Block	2.775	2	.250
	Model	2.775	2	.250

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	9.443	.242	.344

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	6	1	85.7
	Y	1.00	2	1	33.3
	Overall Percentage				70.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X1	146.354	276.979	.279	1	.597	3.637982827113263E+63
	X2	-144.869	276.614	.274	1	.600	.000
	Constant	-.370	1.362	.074	1	.786	.690
a Variable(s) entered on step 1: X1, X2.

NOTE: column 4 (note that there is likely a typo in this column).

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x3.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	10	100.0
	Missing Cases	0	.0
	Total	10	100.0
Unselected Cases		0	.0
Total		10	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	7	0	100.0
	Y	1.00	3	0	.0
	Overall Percentage				70.0
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	-.847	.690	1.508	1	.220	.429

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X3	.008	1	.929
Step 0	Overall Statistics		.008	1	.929

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	.008	1	.929
	Block	.008	1	.929
	Model	.008	1	.929

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	12.209	.001	.001

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	7	0	100.0
	Y	1.00	3	0	.0
	Overall Percentage				70.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X3	1.788	19.971	.008	1	.929	5.976
Step 1(a)	Constant	-2.737	21.128	.017	1	.897	.065
a Variable(s) entered on step 1: X3.

NOTE: column 5.

LOGISTIC REGRESSION VAR=y
  /METHOD=ENTER x1 x2 x3.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	10	100.0
	Missing Cases	0	.0
	Total	10	100.0
Unselected Cases		0	.0
Total		10	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
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	Y	.00	7	0	100.0
	Y	1.00	3	0	.0
	Overall Percentage				70.0
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	-.847	.690	1.508	1	.220	.429

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	X1	2.380	1	.123
		X2	2.375	1	.123
		X3	.008	1	.929
	Overall Statistics		2.511	3	.473

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	2.796	3	.424
	Block	2.796	3	.424
	Model	2.796	3	.424

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	9.421	.244	.346

**Classification Table(a)**
			Predicted
			Y		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	Y	.00	6	1	85.7
	Y	1.00	2	1	33.3
	Overall Percentage				70.0
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	X1	142.922	282.156	.257	1	.612	1.176048465167391E+62
	X2	-141.405	281.804	.252	1	.616	.000
	X3	-3.620	24.953	.021	1	.885	.027
	Constant	3.422	26.155	.017	1	.896	30.615
a Variable(s) entered on step 1: X1, X2, X3.

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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

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