Stat Computing > SPSS > Textbook Examples > Applied Regression Analysis, by Fox

SPSS Textbook Examples
Applied Regression Analysis by John Fox
Chapter 15: Logit and probit models

page 440 Figure 15.1 Scatterplot of voting intention (1 represents yes, 0 represents no) by a scale of support for the status quo, for a sample of Chilean voters surveyed prior to the 1988 plebiscite. The points are jittered vertically to minimize overlapping. The solid straight line shows the linear least-squares fit; the solid curved line shows the fit of the logistic regression model; the broken line represents a lowess nonparametric regression.

NOTE: SPSS will not allow the multiple regression lines to be placed on a single graph. Also, we do not know how to do a lowess non-parametric regression in SPSS.

GET FILE='D:\chile.sav'.
if intvote = 1 voting = 1.
if intvote = 2 voting = 0.

IGRAPH
 /X1 = VAR(statquo)
 /Y = VAR (voting)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL
 /SCATTER COINCIDENT = NONE.
   

page 452 Table 15.1 Deviances (-2 log likelihood) for several models fit to the women's labor force participation data. The following code is used for terms in the models: C constant; I husband's income; K presence of children; R region. The column labeled K + 1 gives the number of regressors in the model, including the constant.

GET FILE='D:\womenlf.sav'.

if workstat = 1 or workstat = 2 ws = 1.
if workstat = 0 ws = 0.
compute ik = husbinc*chilpres.
compute cons = 1.
compute rgn1 = 0.
if region = "Atlantic" rgn1 = 1.
compute rgn2 = 0.
if region = "BC" rgn2 = 1.
compute rgn3 = 0.
if region = "Ontario" rgn3 = 1.
compute rgn4 = 0.
if region = "Prairie" rgn4 = 1.
compute rgn5 = 0.
if region = "Quebec" rgn5 = 1.
execute.

model 0 with C:

NOTE: SPSS will not allow a regression without a predictor. (i.e., just the constant). Therefore, you need to create a variable - here we created const. Then we entered our constant with the /noconst subcommand, which, in effect, gives us a model with just a constant.

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER cons
 /noconst.
 

model 1 with C, I, K, R, I*K:

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER husbinc chilpres rgn2 rgn3 rgn4 rgn5 ik.
 

model 2 with C, I, K, R:

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER husbinc chilpres rgn2 rgn3 rgn4 rgn5.
 

model 3 with C, I, K, I*K:

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER husbinc chilpres ik.
 

model 4 with C, I, R:

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER husbinc rgn2 rgn3 rgn4 rgn5.
 

model 5: with C, K, R:

LOGISTIC REGRESSION VAR=ws
 /METHOD=ENTER chilpres rgn2 rgn3 rgn4 rgn5.
 

page 452 Table 15.2 Analysis of deviance table for terms in the logit model fit to the women's labor force participation data.

NOTE: To get the G**2 terms, subtract the deviances. 
Model 0 versus model 1: 356.16 - 316.54 = 39.62. 
Model 2 versus model 1: 317.30 - 316.54 = .76. 
Model 5 versus model 2: 322.44 - 317.30 = 5.14. 
Model 4 versus model 2: 347.86 - 317.30 = 30.56. 
Model 3 versus model 1: 319.12 - 316.54 = 2.58.

page 453 Figure 15.4 Fitted probability of young married women working outside the home, as a function of husband's income and presence of children. The solid line shows the logit model fit by maximum likelihood; the broken line shows the linear least-squares fit.

NOTE: The four lines in Figure 15.4 have been done in separate graphs.

logistic regression var = ws 
 /method=enter chilpres husbinc 
 /save pre. 

regression 
 /dep = ws 
 /method=enter chilpres husbinc 
 /save pre. 

if chilpres = 1 pw1 = pre_1.
if chilpres = 0 pw2 = pre_1.
if chilpres = 1 lw1 = pre_2.
if chilpres = 0 lw2 = pre_2.
execute.

SORT CASES BY husbinc (A).

IGRAPH
 /X1 = VAR(husbinc)
 /Y = VAR(pw1)
 /LINE(MEAN) STYLE = LINE INTERPOLATE = STRAIGHT.
   
IGRAPH
 /X1 = VAR(husbinc)
 /Y = VAR(pw2)
 /LINE(MEAN) STYLE = LINE INTERPOLATE = STRAIGHT.
   
IGRAPH
 /X1 = VAR(husbinc)
 /Y = VAR(lw1)
 /LINE(MEAN) STYLE = LINE INTERPOLATE = STRAIGHT.

IGRAPH
 /X1 = VAR(husbinc)
 /Y = VAR(lw2)
 /LINE(MEAN) STYLE = LINE INTERPOLATE = STRAIGHT.
   

page 459 Figure 15.5 Partial-residual plot for husband's income in the women's labor force participation data. The broken line gives the logit fit; the solid line shows a lowess smooth of the plot. Note the four bands due to the four combinations of values of the dichotomous dependent variable and the dichotomous independent variable presence of children. Because husband's income is also discrete, many points are overplotted.

NOTE: SPSS does not do lowess smoothing in IGRAPH, so that line is not done. The other two are done on separate graphs. 

NOTE: Leverage, studentized residuals and dfbetas are being saved here so that this regression only has to be run once.

logistic regression var=ws 
 /method=enter chilpres husbinc 
 /save pre lev sre dfbeta. 

NOTE: pre_3 is generated here.

compute par = (ws-pre_3)/(pre_3*(1-pre_3)) - .0423*husbinc.
regression 
 /dep=par 
 /method=enter husbinc 
 /save pre. 

IGRAPH
 /X1 = VAR(husbinc)
 /Y = VAR(pre_4)
 /LINE(MEAN) STYLE = LINE INTERPOLATE = STRAIGHT.
   
GRAPH
  /SCATTERPLOT(BIVAR)=husbinc WITH par.
   

page 461 Figure 15.6 Plot of studentized residuals versus hat values for the logit model fit to the women's labor force participation data. Vertical lines are drawn at twice and three times the average hat value. Many points are overplotted.

logistic regression var=ws 
 /method=enter chilpres husbinc 
 /save lev sre dfbeta. 

compute pr = (ws - pre_3)/sqrt(pre_3*(1 - pre_3)).

GRAPH
  /SCATTERPLOT(BIVAR)=lev_1 WITH sre_1.
   

page 462 Figure 15.7 Index plots of approximate influence of each observation on the coefficients of husband's income and presence of children.

Panel (a)

GRAPH
  /SCATTERPLOT(BIVAR)=obs WITH dfb2_1.
   
  

Panel (b)

GRAPH
  /SCATTERPLOT(BIVAR)=obs WITH dfb1_1.
   

page 469 Figure 15.8 Fitted probabilities for the polytomous logit model, showing women's labor force participation as a function of husband's income and presence of children. The upper panel is for children present, the lower panel for children absent.

NOTE: The scaling of the x-axis is very different than in the text.

Panel (a)

GET FILE='D:\womenlf.sav'.
compute w0 = 0.
if workstat = 0 w0 = 1.
compute w1 = 0.
if workstat = 1 w1 = 1.
compute w2 = 0.
if workstat = 2 w2 = 1.
execute.

logistic regression var=w0 
 /method=enter husbinc chilpres 
 /save pre.