Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 1: Introduction to the Logistic Regression Model | SPSS Textbook Examples

page 3 Table 1.1 Age and coronary heart disease (CHD) status of 100 subjects.

Get file='chdage.sav'.

compute agrp=age.
recode agrp (20 thru 29=1)(30 thru 34=2)(35 thru 39=3)(40 thru 44=4)(45 thru 49=5)(50 thru 54=6)(55 thru 59=7)(60 thru 69=8).
execute.

list id age agrp chd.


       ID       AGE     AGRP       CHD

     1.00     20.00     1.00       .00
     2.00     23.00     1.00       .00
     3.00     24.00     1.00       .00
     4.00     25.00     1.00       .00
     5.00     25.00     1.00      1.00
     6.00     26.00     1.00       .00
     7.00     26.00     1.00       .00
     8.00     28.00     1.00       .00
     9.00     28.00     1.00       .00
    10.00     29.00     1.00       .00
    11.00     30.00     2.00       .00
    12.00     30.00     2.00       .00
    13.00     30.00     2.00       .00
    14.00     30.00     2.00       .00
    15.00     30.00     2.00       .00
    16.00     30.00     2.00      1.00
    17.00     32.00     2.00       .00
    18.00     32.00     2.00       .00
    19.00     33.00     2.00       .00
    20.00     33.00     2.00       .00
    21.00     34.00     2.00       .00
    22.00     34.00     2.00       .00
    23.00     34.00     2.00      1.00
    24.00     34.00     2.00       .00
    25.00     34.00     2.00       .00
    26.00     35.00     3.00       .00
    27.00     35.00     3.00       .00
    28.00     36.00     3.00       .00
    29.00     36.00     3.00      1.00
    30.00     36.00     3.00       .00
    31.00     37.00     3.00       .00
    32.00     37.00     3.00      1.00
    33.00     37.00     3.00       .00
    34.00     38.00     3.00       .00
    35.00     38.00     3.00       .00
    36.00     39.00     3.00       .00
    37.00     39.00     3.00      1.00
    38.00     40.00     4.00       .00
    39.00     40.00     4.00      1.00
    40.00     41.00     4.00       .00
    41.00     41.00     4.00       .00
    42.00     42.00     4.00       .00
    43.00     42.00     4.00       .00
    44.00     42.00     4.00       .00
    45.00     42.00     4.00      1.00
    46.00     43.00     4.00       .00
    47.00     43.00     4.00       .00
    48.00     43.00     4.00      1.00
    49.00     44.00     4.00       .00
    50.00     44.00     4.00       .00

       ID       AGE     AGRP       CHD

    51.00     44.00     4.00      1.00
    52.00     44.00     4.00      1.00
    53.00     45.00     5.00       .00
    54.00     45.00     5.00      1.00
    55.00     46.00     5.00       .00
    56.00     46.00     5.00      1.00
    57.00     47.00     5.00       .00
    58.00     47.00     5.00       .00
    59.00     47.00     5.00      1.00
    60.00     48.00     5.00       .00
    61.00     48.00     5.00      1.00
    62.00     48.00     5.00      1.00
    63.00     49.00     5.00       .00
    64.00     49.00     5.00       .00
    65.00     49.00     5.00      1.00
    66.00     50.00     6.00       .00
    67.00     50.00     6.00      1.00
    68.00     51.00     6.00       .00
    69.00     52.00     6.00       .00
    70.00     52.00     6.00      1.00
    71.00     53.00     6.00      1.00
    72.00     53.00     6.00      1.00
    73.00     54.00     6.00      1.00
    74.00     55.00     7.00       .00
    75.00     55.00     7.00      1.00
    76.00     55.00     7.00      1.00
    77.00     56.00     7.00      1.00
    78.00     56.00     7.00      1.00
    79.00     56.00     7.00      1.00
    80.00     57.00     7.00       .00
    81.00     57.00     7.00       .00
    82.00     57.00     7.00      1.00
    83.00     57.00     7.00      1.00
    84.00     57.00     7.00      1.00
    85.00     57.00     7.00      1.00
    86.00     58.00     7.00       .00
    87.00     58.00     7.00      1.00
    88.00     58.00     7.00      1.00
    89.00     59.00     7.00      1.00
    90.00     59.00     7.00      1.00
    91.00     60.00     8.00       .00
    92.00     60.00     8.00      1.00
    93.00     61.00     8.00      1.00
    94.00     62.00     8.00      1.00
    95.00     62.00     8.00      1.00
    96.00     63.00     8.00      1.00
    97.00     64.00     8.00       .00
    98.00     64.00     8.00      1.00
    99.00     65.00     8.00      1.00
   100.00     69.00     8.00      1.00

Number of cases read:  100    Number of cases listed:  100

page 4 Figure 1.1 Scatterplot of CHD by AGE for 100 subjects.

formats chd (f2.1) age (2.0).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= chd age 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: chd=col( source(s), name( "chd" ) )
DATA: age=col( source(s), name( "age" ) )
GUIDE: axis( dim( 1 ), label( "AGE" ) )
GUIDE: axis( dim( 2 ), label( "Percent with CHD" ) )
ELEMENT: point( position( age * chd ) )
END GPL.

page 4 Table 1.2 Frequency table of age group by CHD.

CROSSTABS
  /TABLES=agrp BY chd
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.

Case Processing Summary

	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
AGRP * CHD	100	100.0%	0	.0%	100	100.0%

AGRP * CHD Crosstabulation
Count

		CHD		Total
		.00	1.00
AGRP	1.00	9	1	10
	2.00	13	2	15
	3.00	9	3	12
	4.00	10	5	15
	5.00	7	6	13
	6.00	3	5	8
	7.00	4	13	17
	8.00	2	8	10
Total		57	43	100

 

page 5 Figure 1.2 Plot of the percentage of subjects with CHD in each age group.

NOTE: agrp was used to make this graph instead of age as in the text.

aggregate outfile='table12.sav'
  / break=agrp / totn=n(chd)
  / present=sum(chd).
execute.

get file='table12.sav'.
compute prop=present/totn.
formats agrp (f1.0) prop (f2.1).
GGRAPH
  /GRAPHDATASET NAME="GraphDataset" VARIABLES= prop agrp 
  /GRAPHSPEC SOURCE=INLINE .
BEGIN GPL
SOURCE: s=userSource( id( "GraphDataset" ) )
DATA: prop=col( source(s), name( "prop" ) )
DATA: agrp=col( source(s), name( "agrp" ) )
GUIDE: axis( dim( 1 ), label( "AGE" ) )
GUIDE: axis( dim( 2 ), label( "Percent with CHD" ) )
SCALE: linear( dim( 1 ) )
SCALE: linear( dim( 2 ), min(0), max(1) )
ELEMENT: point( position( agrp * prop ) )
END GPL.

page 10 Table 1.3 Results of fitting the logistic regression model to the data in Table 1.1.

get file='chdage.sav'.

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER age.

Case Processing Summary

Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	100	100.0
	Missing Cases	0	.0
	Total	100	100.0
Unselected Cases		0	.0
Total		100	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
			CHD		Percentage Correct
	Observed		.00	1.00
Step 0	CHD	.00	57	0	100.0
		1.00	43	0	.0
	Overall Percentage				57.0
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	-.282	.202	1.947	1	.163	.754

Variables not in the Equation

			Score	df	Sig.
Step 0	Variables	AGE	26.399	1	.000
	Overall Statistics		26.399	1	.000

Omnibus Tests of Model Coefficients

		Chi-square	df	Sig.
Step 1	Step	29.310	1	.000
	Block	29.310	1	.000
	Model	29.310	1	.000

Model Summary

Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	107.353	.254	.341

Classification Table(a)

			Predicted
			CHD		Percentage Correct
	Observed		.00	1.00
Step 1	CHD	.00	45	12	78.9
		1.00	14	29	67.4
	Overall Percentage				74.0
a The cut value is .500

Variables in the Equation

		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.111	.024	21.254	1	.000	1.117
	Constant	-5.309	1.134	21.935	1	.000	.005
a Variable(s) entered on step 1: AGE.

page 20 Table 1.4 Estimated covariance matrix of the estimated coefficients in Table 1.3.

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER age
  /PRINT=SUMMARY corr.
 

Case Processing Summary

Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	100	100.0
	Missing Cases	0	.0
	Total	100	100.0
Unselected Cases		0	.0
Total		100	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
			CHD		Percentage Correct
	Observed		.00	1.00
Step 0	CHD	.00	57	0	100.0
		1.00	43	0	.0
	Overall Percentage				57.0
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	-.282	.202	1.947	1	.163	.754

Variables not in the Equation

			Score	df	Sig.
Step 0	Variables	AGE	26.399	1	.000
	Overall Statistics		26.399	1	.000

Omnibus Tests of Model Coefficients

		Chi-square	df	Sig.
Step 1	Step	29.310	1	.000
	Block	29.310	1	.000
	Model	29.310	1	.000

Model Summary

Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	107.353	.254	.341

Classification Table(a)

			Predicted
			CHD		Percentage Correct
	Observed		.00	1.00
Step 1	CHD	.00	45	12	78.9
		1.00	14	29	67.4
	Overall Percentage				74.0
a The cut value is .500

Variables in the Equation

		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.111	.024	21.254	1	.000	1.117
	Constant	-5.309	1.134	21.935	1	.000	.005
a Variable(s) entered on step 1: AGE.

Correlation Matrix

		Constant	AGE
Step 1	Constant	1.000	-.978
	AGE	-.978	1.000

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

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

age/age: (.024)**2 = .000579
constant/constant: (1.134)**2 = 1.218517
age/constant: (-.978)*(.024)*(1.134) = -0.026677