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Statistical Methods and Data Analytics

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

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:appsrwgdatatoxic.sav'.

formats lived (f2.0) close (f2.1).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lived close
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: lived=col(source(s), name("lived"))
DATA: close=col(source(s), name("close"))
GUIDE: text.title( label( "Figure 7.1" ) )
GUIDE: form.line(position(*, 1), shape(shape.half_dash))
GUIDE: form.line(position(*, 0), shape(shape.half_dash))
GUIDE: axis(dim(1), label("Years Lived in Town"), delta(10))
GUIDE: axis(dim(2), label("Favor Closing Schools"), delta(.2))
SCALE: linear(dim(1), min(0), max(80))
SCALE: linear(dim(2), min(-.2), max(1))
ELEMENT: point(position(lived*close))
ELEMENT: line(position(smooth.linear(lived*close)), shape(shape.dash))
END GPL.

Image

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.
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%

Image

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%

Image

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

GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lived close
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: lived=col(source(s), name("lived"))
DATA: close=col(source(s), name("close"))
GUIDE: text.title( label( "Figure 7.4" ) )
GUIDE: form.line(position(*, 1), shape(shape.half_dash))
GUIDE: form.line(position(*, 0), shape(shape.half_dash))
GUIDE: axis(dim(1), label("Years Lived in Town"), delta(10))
GUIDE: axis(dim(2), label("Favor Closing Schools"), delta(.2))
SCALE: linear(dim(1), min(0), max(80))
SCALE: linear(dim(2), min(-.2), max(1))
ELEMENT: point(position(lived*close))
ELEMENT: line(position(smooth.linear(lived*close)), shape(shape.dash))
ELEMENT: line(position(smooth.quadratic(lived*close)))
END GPL.

Image

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

LOGISTIC REGRESSION VAR=close
  /METHOD=ENTER lived.

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

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

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.

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.

 

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

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
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.

 

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

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
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.

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

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

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.

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.
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

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

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.

formats lived (f2.0) phat1 phat2 phat3 (f2.1).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=lived phat1 phat2 phat3 
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: lived=col(source(s), name("lived"))
DATA: phat1=col(source(s), name("phat1"))
DATA: phat2=col(source(s), name("phat2"))
DATA: phat3=col(source(s), name("phat3"))
GUIDE: text.title( label( "Figure 7.5" ) )
GUIDE: axis(dim(1), label("Years Lived in Town"), delta(10))
GUIDE: axis(dim(2), label("Probability of Favoring School Closing"), delta(.2))
SCALE: linear(dim(1), min(0), max(80))
SCALE: linear(dim(2), min(0), max(1))
ELEMENT: line(position(smooth.spline(lived*phat1)), shape(shape.dash))
ELEMENT: line(position(smooth.spline(lived*phat2)))
ELEMENT: line(position(smooth.spline(lived*phat3)), shape(shape.half_dash))
END GPL.

Image

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

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).

value labels contam 0 "Not contaminated" 1 "Contaminated".
formats contam (f1.0) phat4 phat5 phat6 (f2.1).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=contam phat4 phat5 phat6 
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: contam=col(source(s), name("contam"), unit.category() )
DATA: phat4=col(source(s), name("phat4"))
DATA: phat5=col(source(s), name("phat5"))
DATA: phat6=col(source(s), name("phat6"))
GUIDE: text.title( label( "Figure 7.6" ) )
GUIDE: axis(dim(1), label(" "))
GUIDE: axis(dim(2), label("Probability of Favoring School Closing"), delta(.2))
SCALE: linear(dim(2), min(-.2), max(1))
ELEMENT: line(position(smooth.spline(contam*phat4)), shape(shape.dash))
ELEMENT: line(position(smooth.spline(contam*phat5)))
ELEMENT: line(position(smooth.spline(contam*phat6)), shape(shape.half_dash))
END GPL.

Image

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.

 

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
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

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.

formats pre_1 (f2.1) deltap (f2.0).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pre_1 deltap
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: deltap=col(source(s), name("deltap"))
DATA: pre_1=col(source(s), name("pre_1"))
GUIDE: text.title( label( "Figure 7.7" ) )
GUIDE: axis(dim(1), label("P-hat"), delta(.2))
GUIDE: axis(dim(2), label("Delta P"), delta(5))
SCALE: linear(dim(1), min(0), max(1))
SCALE: linear(dim(2), min(0), max(30))
ELEMENT: point(position(pre_1*deltap))
END GPL.

Image

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.

formats deltad (f2.0).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pre_1 deltad
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: deltad=col(source(s), name("deltad"))
DATA: pre_1=col(source(s), name("pre_1"))
GUIDE: text.title( label( "Figure 7.8" ) )
GUIDE: axis(dim(1), label("P-hat"), delta(.2))
GUIDE: axis(dim(2), label("Delta D"), delta(1))
SCALE: linear(dim(1), min(0), max(1))
SCALE: linear(dim(2), min(0), max(7))
ELEMENT: point(position(pre_1*deltad))
END GPL.

Image

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. 

formats coo_1 (f2.1).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pre_1 coo_1
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: coo_1=col(source(s), name("coo_1"))
DATA: pre_1=col(source(s), name("pre_1"))
GUIDE: text.title( label( "Figure 7.9" ) )
GUIDE: axis(dim(1), label("P-hat"), delta(.2))
GUIDE: axis(dim(2), label("Delta B"), delta(.1))
SCALE: linear(dim(1), min(0), max(1))
SCALE: linear(dim(2), min(0), max(.7))
ELEMENT: point(position(pre_1*coo_1))
END GPL.

Image

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. 

GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=pre_1 deltad coo_1
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: deltad=col(source(s), name("deltad"))
DATA: pre_1=col(source(s), name("pre_1"))
DATA: coo_1=col(source(s), name("coo_1"))
GUIDE: text.title( label( "Figure 7.10" ) )
GUIDE: axis(dim(1), label("P-hat"), delta(.2))
GUIDE: axis(dim(2), label("Delta D"), delta(1))
SCALE: linear(dim(1), min(0), max(1))
SCALE: linear(dim(2), min(0), max(7))
ELEMENT: point(position(pre_1*deltad), size(coo_1))
END GPL.

Image

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