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

SPSS Textbook Examples
Applied Regression Analysis by John Fox
Chapter 12: Diagnosing nonlinearity, nonconstant error variance, and nonnormality

page 297 Figure 12.1 The distribution of the studentized residuals from Ornstein's interlocking-directorate regression. A normal quanitle comparison plot is shown in (a). The 95% confidence envelope is based on the standard errors of the order statistics for an independent normal sample. A nonparametric density estimate is shown in (b).

NOTE: The dummy variables need to be calculated before the graphs can be made.

NOTE: We do not know how to do quantile-normal or density plots using SPSS.

page 298 Table 12.1 Regression of number of interlocking directorate and executive positions maintained by 248 dominant Canadian corporations on corporate assets, sector, and nation of control. The baseline category for sector is heavy manufacturing; for nation of control, Canada.

GET FILE='D:/ornstein.sav'.

compute sec1 = 0.
if sector = "AGR" sec1 = 1.
compute sec2 = 0.
if sector = "BNK" sec2 = 1.
compute sec3 = 0.
if sector = "CON" sec3 = 1.
compute sec4 = 0.
if sector = "FIN" sec4 = 1.
compute sec5 = 0.
if sector = "HLD" sec5 = 1.
compute sec6 = 0.
if sector = "MAN" sec6 = 1.
compute sec7 = 0.
if sector = "MER" sec7 = 1.
compute sec8 = 0.
if sector = "MIN" sec8 = 1.
compute sec9 = 0.
if sector = "TRN" sec9 = 1.
compute sec10 = 0.
if sector = "WOD" sec10 = 1.
compute nat1 = 0.
if nation = "CAN" nat1 = 1.
compute nat2 = 0.
if nation = "OTH" nat2 = 1.
compute nat3 = 0.
if nation = "UK" nat3 = 1.
compute nat4 = 0.
if nation = "US" nat4 = 1.
compute asset1 = sqrt(assets).
execute.

regression 
 /dep=intrlcks 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10 
 /save pre sre.

compute inter1 = sqrt(intrlcks + 1).
execute.

regression 
 /dep=inter1 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10.
 

page 299 Figure 12.2 The distribution of the studentized residuals from Orstein's interlocking-directorate regression, after transforming the dependent variable. A normal quantile comparison plot is shown in (a), a nonparametric density estimate in (b).

NOTE: We do not know how to do quantile-normal or density plots using SPSS.

page 303 Figure 12.3 Detecting nonconstant spread in Ornstein's interlocking-directorate regression. (a) A plot of studentized residuals versus fitted values. (b) A plot of log spread (log absolute studentized residuals) versus log level (log fitted values). The least-squares line is shown on the plot.

Panel (a)

GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH sre_1.

Panel (b)

compute abssre = abs(sre_1).
compute logsre = lg10(abssre).
compute logpre = lg10(pre_1 + 2).
execute.

IGRAPH
 /X1 = VAR(logpre)
 /Y = VAR(logsre)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
 /SCATTER COINCIDENT = NONE.
  

page 304 Figure 12.4 Plot of log spread versus log level for Ornstein's interlocking-directorate regression, after transforming the dependent variable. The least-squares line is shown on the plot.

regression 
 /dep=inter1 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10 
 /save pre sre.

compute logfit2 = lg10(pre_2).
compute abs2 = abs(sre_2).
compute logres2 = lg10(abs2).
execute.
regression 
 /dep=logres2 
 /method=enter logfit2. 

IGRAPH
 /X1 = VAR(logfit2)
 /Y = VAR(logres2)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
 /SCATTER COINCIDENT = NONE.
  

page 312 Figure 12.6 Partial-residual plots for the regression of occupational prestige on (a) education, (b) income, (c) percentage of women. The data are for 102 Canadian occupations in 1971. The least-squares line and a nonparamentric-regression smooth are shown on each plot.

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

regression 
 /dep=prestige 
 /method=enter percwomn educat income 
 /save res.

NOTE: We need to look at the output and get the coefficient for the variable education to complete the necessary calculation.

Panel (a)

compute resedu = res_1 + (4.187*educat).

IGRAPH
 /X1 = VAR(educat)
 /Y = VAR(resedu)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
 /SCATTER COINCIDENT = NONE.

  

Panel (b)

compute resedu2 = res_1 + (.0013*income).

IGRAPH
 /X1 = VAR(income)
 /Y = VAR(resedu2)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
 /SCATTER COINCIDENT = NONE.
   

Panel (c)

compute resedu3 = res_1 + (-.0089*percwomn).

IGRAPH
 /X1 = VAR(percwomn)
 /Y = VAR(resedu3)
 /FITLINE METHOD = REGRESSION LINEAR LINE = TOTAL MEFFECT
 /SCATTER COINCIDENT = NONE.
   

page 313 Formula in the middle of the page.

NOTE: The criteria=tolerance option needs to used in this example or else SPSS will throw out the variable edu2 because of low tolerance.

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

compute loginc = lg10(income)/lg10(2).
compute edu2 = educat*educat.
compute edu3 = educat**3.
compute w2 = percwomn*percwomn.
execute.
regression 
 /criteria=tolerance(0.0000001) 
 /dep=prestige /method=enter loginc percwomn w2 educat edu2 edu3 
 /save res.

page 314 Figure 12.7 The partial relationship between prestige and education, holding income and percentage of women at their average levels. The curve shows the cubic fit for education. The points are partial residuals, obtained by adding the least-squares residuals to the education fit.

DESCRIPTIVES
  VARIABLES=income percwomn
  /STATISTICS=MEAN STDDEV MIN MAX.

compute pm = 20.8+8.78*lg10(6797.902)/lg10(2)-0.179*28.979+0.0025*28.979*28.979-29.9*educat+2.91*edu2-.0807*edu3.
compute pmr = res_1 + pm.
execute.

NOTE: In order to get the cubic fit line on the plot, you need to use the code below, double-click on the resulting graph, select chart from the menu at the top, select options, click on fit line total, select fit options, select cubic, click on continue and OK. We do not know how to add the cubic fit line using code.

GRAPH
  /SCATTERPLOT(BIVAR)=educat WITH pmr.

page 319 Table 12.2 Analysis of variance for vocabulary test scores, showing the incremental F-test for nonlinearity of the relationship between vocabulary and education.

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

regression 
 /dep=vocab 
 /method=enter educ.

NOTE: The do-loop below is needed in order to create the dummy variables.

DO REPEAT A=e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e16 e17 e18 e19 e20 
/B=1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.
COMPUTE A=(educ=B).
END REPEAT.

regression 
 /dep=vocab 
 /method=enter e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e16 e17 e18 e19 e20.
 

NOTE: The nonlinear effect needs to be calculated by hand.

Sum of Squares for nonlinear effect: 1261.69399-1175.11129 = 86.5827 F-value: (86.57/18)/(3472.8/948) = 1.3128753 p-value: 17255134

page 324 Figure 12.8 Box-Cox transformations for Ornstein's interlocking-directorate regression. The maximized log likelihood is plotted against the transformation parameter lamda. The intersection of the line near the top of the graph with the log likelihood curve marks off the 95% confidence interval for lamda. The maximum of the log likelihood corresponds to the MLE of lamda.

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

compute asset1 = sqrt(assets).
compute dep1 = (intrlcks + 1).
compute logy = ln(dep1).
compute c1 = mean(logy).
compute c = exp(c1).

NOTE: The mean of c = 8.2501268.

compute cv = dep1*(ln(dep1/8.2501268)-1).
execute.

compute sec1 = 0.
if sector = "AGR" sec1 = 1.
compute sec2 = 0.
if sector = "BNK" sec2 = 1.
compute sec3 = 0.
if sector = "CON" sec3 = 1.
compute sec4 = 0.
if sector = "FIN" sec4 = 1.
compute sec5 = 0.
if sector = "HLD" sec5 = 1.
compute sec6 = 0.
if sector = "MAN" sec6 = 1.
compute sec7 = 0.
if sector = "MER" sec7 = 1.
compute sec8 = 0.
if sector = "MIN" sec8 = 1.
compute sec9 = 0.
if sector = "TRN" sec9 = 1.
compute sec10 = 0.
if sector = "WOD" sec10 = 1.
compute nat1 = 0.
if nation = "CAN" nat1 = 1.
compute nat2 = 0.
if nation = "OTH" nat2 = 1.
compute nat3 = 0.
if nation = "UK" nat3 = 1.
compute nat4 = 0.
if nation = "US" nat4 = 1.
compute asset1 = sqrt(assets).
execute.

regression 
 /dep=dep1 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10
 /method=test(cv).
 

page 324 Figure 12.9 Constructed-variable plot for the Box-Cox . transformation of Ornstein's interlocking- directorate regression. The least-squares line is shown on the plot.

regression 
 /dep=dep1 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10 
 /save res.

regression 
 /dep=cv 
 /method=enter asset1 nat2 nat3 nat4 sec1 sec2 sec3 sec4 sec5 sec7 sec8 sec9 sec10 
 /save res. 

regression 
 /dep=res_1 
 /method=enter res_2.