Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 2: Multiple Logistic Regression

page 32 Table 2.1 An example of the coding of the design variables for
race, coded at three levels.

get file='lowbwt.sav'.
recode race (2=1) (else=0) into race2.

recode race (3=1) (else=0) into race3.

execute.
list race race2 race3

 / cases=from 1 to 3.
     RACE    RACE2    RACE3
     2.00     1.00      .00

     3.00      .00     1.00

     1.00      .00      .00
Number of cases read:  3    Number of cases listed:  3

page 36 Table 2.2 Estimated coefficients for a multiple logistic regression
model using the variables age, weight at last menstrual period (lwt),
race and
number of first trimester physician visits from the low birth weight study.

LOGISTIC REGRESSION VAR=low

  /METHOD=ENTER age lwt race2 race3 ftv

  /PRINT=SUMMARY.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	189	100.0
	Missing Cases	0	.0
	Total	189	100.0
Unselected Cases		0	.0
Total		189	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
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	< 2500g	.00	130	0	100.0
	< 2500g	1.00	59	0	.0
	Overall Percentage				68.8
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	-.790	.157	25.327	1	.000	.454

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	2.674	1	.102
		LWT	5.438	1	.020
		RACE2	1.727	1	.189
		RACE3	1.797	1	.180
		FTV	.749	1	.387
	Overall Statistics		11.388	5	.044

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	12.099	5	.033
	Block	12.099	5	.033
	Model	12.099	5	.033

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	222.573	.062	.087

**Classification Table(a)**
			Predicted
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	< 2500g	.00	125	5	96.2
	< 2500g	1.00	54	5	8.5
	Overall Percentage				68.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	-.024	.034	.499	1	.480	.976
	LWT	-.014	.007	4.741	1	.029	.986
	RACE2	1.004	.498	4.066	1	.044	2.729
	RACE3	.433	.362	1.430	1	.232	1.542
	FTV	-.049	.167	.087	1	.768	.952
	Constant	1.295	1.071	1.461	1	.227	3.651
a Variable(s) entered on step 1: AGE, LWT, RACE2, RACE3, FTV.

page 38 Table 2.3 Estimated coefficients for a multiple logistic regression
model using the variables lwt and race from the low birth weight study.

LOGISTIC REGRESSION VAR=low

  /METHOD=ENTER lwt race2 race3.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	189	100.0
	Missing Cases	0	.0
	Total	189	100.0
Unselected Cases		0	.0
Total		189	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
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	< 2500g	.00	130	0	100.0
	< 2500g	1.00	59	0	.0
	Overall Percentage				68.8
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	-.790	.157	25.327	1	.000	.454

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	LWT	5.438	1	.020
		RACE2	1.727	1	.189
		RACE3	1.797	1	.180
	Overall Statistics		10.757	3	.013

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	11.413	3	.010
	Block	11.413	3	.010
	Model	11.413	3	.010

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	223.259	.059	.082

**Classification Table(a)**
			Predicted
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	< 2500g	.00	124	6	95.4
	< 2500g	1.00	53	6	10.2
	Overall Percentage				68.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	LWT	-.015	.006	5.587	1	.018	.985
	RACE2	1.081	.488	4.906	1	.027	2.948
	RACE3	.481	.357	1.816	1	.178	1.617
	Constant	.805	.845	.908	1	.341	2.238
a Variable(s) entered on step 1: LWT, RACE2, RACE3.

page 42 Table 2.4 Estimated covariance matrix of the estimated coefficients
in Table 2.3.

LOGISTIC REGRESSION VAR=low

  /METHOD=ENTER lwt race2 race3

  /PRINT=SUMMARY corr.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	189	100.0
	Missing Cases	0	.0
	Total	189	100.0
Unselected Cases		0	.0
Total		189	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
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	< 2500g	.00	130	0	100.0
	< 2500g	1.00	59	0	.0
	Overall Percentage				68.8
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	-.790	.157	25.327	1	.000	.454

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	LWT	5.438	1	.020
		RACE2	1.727	1	.189
		RACE3	1.797	1	.180
	Overall Statistics		10.757	3	.013

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	11.413	3	.010
	Block	11.413	3	.010
	Model	11.413	3	.010

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	223.259	.059	.082

**Classification Table(a)**
			Predicted
			< 2500g		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	< 2500g	.00	124	6	95.4
	< 2500g	1.00	53	6	10.2
	Overall Percentage				68.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	LWT	-.015	.006	5.587	1	.018	.985
	RACE2	1.081	.488	4.906	1	.027	2.948
	RACE3	.481	.357	1.816	1	.178	1.617
	Constant	.805	.845	.908	1	.341	2.238
a Variable(s) entered on step 1: LWT, RACE2, RACE3.

**Correlation Matrix**
		Constant	LWT	RACE2	RACE3
Step 1	Constant	1.000	-.958	.055	-.343
	LWT	-.958	1.000	-.206	.155
	RACE2	.055	-.206	1.000	.306
	RACE3	-.343	.155	.306	1.000

NOTE: for the variances: var=(se)**2

NOTE: for the covariances: cov=corr*se*se

lwt/lwt: (.006)**2 = .00036
lwt/race2: (.006)*(.488)*(-.206) = -.000603168
lwt/race3: (.006)*(.357)*(.155) = .00033201
lwt/constant: (.006)*(.845)*(-.958) = -.00485706
race2/race2: (.488)*2 = .238144
race2/race3: (.488)*(.357)*(.306) = .053310096
race2/constant: (.488)*(.845)*(.055) = .0226798
race3/race3: (.357)**2 = .127449
race3/constant: (.357)*(.845)*(-.343) = -.103471095
constant/constant: (.845)**2 = .714025