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SPSS Textbook Examples
Regression with Graphics by Lawrence Hamilton
Chapter 7: Logit regression

Limitations of linear regression

Page 218 Figure 7.1  Linear regression of a dichotomous Y variable (0 = open schools, 1 = close schools) on a measurement X variable (years lived in town).

GET FILE 'd:\apps\rwgdata\toxic.sav'.

IGRAPH
 /X1 = VAR(lived)
 /Y = VAR(close) type=scale
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL
 /SCATTER.

Interactive Graph

Interactive Graph

Page 219 Figure 7.2  Boxplots and oneway scatterplots of years lived in town, for respondents favoring closed and open schools.

compute const=.01.
execute.

EXAMINE  VARIABLES=lived BY close
 /PLOT=BOXPLOT
 /STATISTICS=NONE.

Explore

Total Sample

Case Processing Summary

Cases
Valid Missing Total
N Percent N Percent N Percent
years lived in Williamstown 153 100.0% 0 .0% 153 100.0%


years lived in Williamstown

Boxplot

schools should close

Case Processing Summary

Cases
Valid Missing Total

schools should close N Percent N Percent N Percent
years lived in Williamstown open 87 100.0% 0 .0% 87 100.0%
close 66 100.0% 0 .0% 66 100.0%


years lived in Williamstown

Boxplot

Page 222 Figure 7.4  Logit regression of school-closing opinion on years lived in town, also showing linear regression line.

NOTE:  SPSS will not allow you to graph two regression lines and the data points on the same graph.

Estimation

Page 224 Table 7.1  Logit regression of school-closing opinion on years lived in town.

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
Overall Statistics 12.683 1 .000


Block 1: Method = Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 13.944 1 .000
Block 13.944 1 .000
Model 13.944 1 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 195.267 .087 .117


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 59 28 67.8
close 29 37 56.1
Overall Percentage

62.7
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.041 .012 11.398 1 .001 .960
Constant .460 .263 3.069 1 .080 1.584
a Variable(s) entered on step 1: LIVED.


Hypothesis Tests and Confidence Intervals

Page 226 Table 7.2  Logit regression of school-closing opinion on years lived in town, education, contamination, and HSC meetings.

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived educ contam hsc.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
EDUC .221 1 .638
CONTAM 17.292 1 .000
HSC 39.337 1 .000
Overall Statistics 52.845 4 .000


Block 1: Method = Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 59.830 4 .000
Block 59.830 4 .000
Model 59.830 4 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 149.382 .324 .434


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 75 12 86.2
close 24 42 63.6
Overall Percentage

76.5
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.046 .015 9.698 1 .002 .955
EDUC -.166 .090 3.404 1 .065 .847
CONTAM 1.208 .465 6.739 1 .009 3.347
HSC 2.173 .464 21.919 1 .000 8.784
Constant 1.731 1.302 1.768 1 .184 5.649
a Variable(s) entered on step 1: LIVED, EDUC, CONTAM, HSC.

Page 227 Table 7.3  Logit regression of school-closing opinion on seven background variables.

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived educ contam hsc female kids nodad
  /PRINT=ITER(1) SUMMARY.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Iteration History(a,b,c)

-2 Log likelihood Coefficients
Iteration
Constant
Step 0 1 209.212 -.275
2 209.212 -.276
a Constant is included in the model.
b Initial -2 Log Likelihood: 209.212
c Estimation terminated at iteration number 2 because log-likelihood decreased by less than .010 percent.


Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
EDUC .221 1 .638
CONTAM 17.292 1 .000
HSC 39.337 1 .000
FEMALE 3.868 1 .049
KIDS 5.666 1 .017
NODAD 9.835 1 .002
Overall Statistics 57.038 7 .000


Block 1: Method = Enter

Iteration History(a,b,c,d)

-2 Log likelihood Coefficients
Iteration
Constant LIVED EDUC CONTAM HSC FEMALE KIDS NODAD
Step 1 1 147.028 1.565 -.027 -.130 .782 1.764 -.015 -.365 -1.074
2 141.482 2.538 -.041 -.187 1.147 2.239 -.037 -.580 -1.844
3 141.054 2.859 -.046 -.204 1.269 2.401 -.050 -.662 -2.184
4 141.049 2.893 -.047 -.206 1.282 2.418 -.052 -.671 -2.225
a Method: Enter
b Constant is included in the model.
c Initial -2 Log Likelihood: 209.212
d Estimation terminated at iteration number 4 because log-likelihood decreased by less than .010 percent.


Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 68.162 7 .000
Block 68.162 7 .000
Model 68.162 7 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 141.049 .359 .482


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 77 10 88.5
close 25 41 62.1
Overall Percentage

77.1
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.047 .017 7.549 1 .006 .954
EDUC -.206 .093 4.886 1 .027 .814
CONTAM 1.282 .481 7.093 1 .008 3.604
HSC 2.418 .510 22.507 1 .000 11.221
FEMALE -.052 .557 .009 1 .926 .950
KIDS -.671 .566 1.405 1 .236 .511
NODAD -2.225 .999 4.962 1 .026 .108
Constant 2.893 1.603 3.258 1 .071 18.054
a Variable(s) entered on step 1: LIVED, EDUC, CONTAM, HSC, FEMALE, KIDS, NODAD.

Page 228 Table 7.4  Reduced model with male/nonparent interaction term.

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived educ contam hsc nodad.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
EDUC .221 1 .638
CONTAM 17.292 1 .000
HSC 39.337 1 .000
NODAD 9.835 1 .002
Overall Statistics 56.279 5 .000


Block 1: Method = Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 66.559 5 .000
Block 66.559 5 .000
Model 66.559 5 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 142.652 .353 .473


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 76 11 87.4
close 25 41 62.1
Overall Percentage

76.5
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.040 .015 6.559 1 .010 .961
EDUC -.197 .093 4.509 1 .034 .821
CONTAM 1.298 .477 7.422 1 .006 3.664
HSC 2.278 .490 21.590 1 .000 9.762
NODAD -1.731 .725 5.695 1 .017 .177
Constant 2.182 1.330 2.691 1 .101 8.865
a Variable(s) entered on step 1: LIVED, EDUC, CONTAM, HSC, NODAD.

  Interpretation

Page 232 Figure 7.5  Conditional effects of years lived in town, at proclosing (top), average, and anticlosing levels of other X variables.

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived educ contam hsc nodad.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
EDUC .221 1 .638
CONTAM 17.292 1 .000
HSC 39.337 1 .000
NODAD 9.835 1 .002
Overall Statistics 56.279 5 .000


Block 1: Method = Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 66.559 5 .000
Block 66.559 5 .000
Model 66.559 5 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 142.652 .353 .473


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 76 11 87.4
close 25 41 62.1
Overall Percentage

76.5
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.040 .015 6.559 1 .010 .961
EDUC -.197 .093 4.509 1 .034 .821
CONTAM 1.298 .477 7.422 1 .006 3.664
HSC 2.278 .490 21.590 1 .000 9.762
NODAD -1.731 .725 5.695 1 .017 .177
Constant 2.182 1.330 2.691 1 .101 8.865
a Variable(s) entered on step 1: LIVED, EDUC, CONTAM, HSC, NODAD.

SORT CASES BY
  lived (A).

compute lhat1 = 3.17-.04*lived.
compute phat1 = 1/(1+exp(-lhat1)).
compute lhat2 = .387-.04*(lived).
compute phat2 = 1/(1+exp(-lhat2)).
compute lhat3 = -2.14-.04*(lived).
compute phat3 = 1/(1+exp(-lhat3)).
execute.

GRAPH
  /SCATTERPLOT(OVERLAY)=lived lived lived  WITH phat1 phat2 phat3 (PAIR).

Graph

Scatter of phat1 phat2 phat3 lived lived lived

Page 232 Figure 7.6  Conditional effects of contamination, at proclosing, average, and anticlosing levels of other X variables.

NOTE:  This graph does not look exactly like the one in the text because of scaling issues on the X-axis.

SORT CASES BY contam (A).
compute lhat4 = 3.22+1.3*(contam).
compute phat4 = 1/(1+exp(-lhat4)).
compute lhat5 = -.7681+1.3*(contam).
compute phat5 = 1/(1+exp(-lhat5)).
compute lhat6 = -6.79+1.3*(contam).
compute phat6 = 1/(1+exp(-lhat6)).
execute.

SORT CASES BY
  contam (A).

GRAPH
  /LINE(MULTIPLE)= VALUE( phat4 phat5 phat6 ) BY contam.

Graph

Line of value(phat4 phat5 phat6) by contam

Diagnostic graphs

Page 239 Figure 7.7  Poorness-of-fit statistic delta-chi-square(P) versus predicted probability of favoring closed schools; X patterns 131 and 3 are poorly fit (high delta-chi-square(P) values).

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived educ contam hsc nodad
  /SAVE PRED COOK LEVER ZRESID DEV.

Logistic Regression

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 153 100.0
Missing Cases 0 .0
Total 153 100.0
Unselected Cases 0 .0
Total 153 100.0
a If weight is in effect, see classification table for the total number of cases.


Dependent Variable Encoding
Original Value Internal Value
open 0
close 1


Block 0: Beginning Block

Classification Table(a,b)

Predicted
schools should close Percentage Correct

Observed open close
Step 0 schools should close open 87 0 100.0
close 66 0 .0
Overall Percentage

56.9
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 -.276 .163 2.864 1 .091 .759


Variables not in the Equation

Score df Sig.
Step 0 Variables LIVED 12.683 1 .000
EDUC .221 1 .638
CONTAM 17.292 1 .000
HSC 39.337 1 .000
NODAD 9.835 1 .002
Overall Statistics 56.279 5 .000


Block 1: Method = Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 66.559 5 .000
Block 66.559 5 .000
Model 66.559 5 .000


Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 142.652 .353 .473


Classification Table(a)

Predicted
schools should close Percentage Correct

Observed open close
Step 1 schools should close open 76 11 87.4
close 25 41 62.1
Overall Percentage

76.5
a The cut value is .500


Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LIVED -.040 .015 6.559 1 .010 .961
EDUC -.197 .093 4.509 1 .034 .821
CONTAM 1.298 .477 7.422 1 .006 3.664
HSC 2.278 .490 21.590 1 .000 9.762
NODAD -1.731 .725 5.695 1 .017 .177
Constant 2.182 1.330 2.691 1 .101 8.865
a Variable(s) entered on step 1: LIVED, EDUC, CONTAM, HSC, NODAD.

compute deltap=(zre_1)**2/(1-lev_1).
execute.
GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH deltap.

Graph

Scatter of deltap pre_1

Page 240 Figure 7.8  Poorness-of-fit statistic delta-chi-square(D) versus predicted probability of favoring closed schools; X patterns 131, 3, 27, 62, 115 are poorly fit (high delta-chi-square(D) values).

compute deltad=(dev_1)**2/(1-lev_1).
execute.

GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH deltad.

Graph

Scatter of deltad pre_1

Page 241 Figure 7.9  Influence statistic delta-B versus predicted probability of favoring closed schools; patterns 131, 3, 115, 44, and 94 are most influential (high delta-B values).

NOTE:  Delta-B is the Cook's D statistic.

GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH coo_1.

Graph

Scatter of coo_1 pre_1

Page 242 Figure 7.10  Delta-chi-square(D) versus P-hat with symbols proportional to delta-B; large, high circles indicate influential, poorly fit X patterns.

NOTE:  We do not know how to make the bubbles (symbols) proportional.

GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH deltad.

Graph

Scatter of deltad pre_1


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