Breusch-Pagan & Koenker test

 

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* BREUSCH-PAGAN & KOENKER TEST MACRO *
* See 'Heteroscedasticity: Testing and correcting in SPSS'
* by Gwilym Pryce, for technical details.
* Code by Marta Garcia-Granero 2002/10/28.
 
* The MACRO needs 3 arguments:
* the dependent, the number of predictors and the list of predictors
* (if they are consecutive, the keyword TO can be used) .
 
* (1) MACRO definition (select an run just ONCE).
 
DEFINE bpktest(!POSITIONAL !TOKENS(1) /!POSITIONAL !TOKENS(1) /!POSITIONAL !CMDEND).
* Regression to get the residuals and residual plots.
REGRESSION
/STATISTICS R ANOVA
/DEPENDENT !1
/METHOD=ENTER !3
/SCATTERPLOT=(*ZRESID,*ZPRED)
/RESIDUALS HIST(ZRESID) NORM(ZRESID)
/SAVE RESID(residual) .
do if $casenum=1.
print /"Examine the scatter plot of the residuals to detect"
/"model misspecification and/or heteroscedasticity"
/""
/"Also, check the histogram and np plot of residuals "
/"to detect non normality of residuals "
/"Skewness and kurtosis more than twice their SE indicate non-normality ".
end if.
* Checking normality of residuals.
DESCRIPTIVES
VARIABLES=residual
/STATISTICS=KURTOSIS SKEWNESS .
* New dependent variable (g) creation.
COMPUTE sq_res=residual**2.
compute constant=1.
AGGREGATE
/OUTFILE='tempdata.sav'
/BREAK=constant
/rss = SUM(sq_res)
/N=N.
MATCH FILES /FILE=*
/FILE='tempdata.sav'.
EXECUTE.
if missing(rss) rss=lag(rss,1).
if missing(n) n=lag(n,1).
compute g=sq_res/(rss/n).
execute.
* BP&K tests.
* Regression of g on the predictors.
REGRESSION
/STATISTICS R ANOVA
/DEPENDENT g
/METHOD=ENTER !3
/SAVE RESID(resid) .
*Final report.
do if $casenum=1.
print /" BP&K TESTS"
/" ==========".
end if.
* Routine adapted from Gwilym Pryce.
matrix.
compute p=!2.
get g /variables=g.
get resid /variables=resid.
compute sq_res2=resid&**2.
compute n=nrow(g).
compute rss=msum(sq_res2).
compute ii_1=make(n,n,1).
compute i=ident(n).
compute m0=i-((1/n)*ii_1).
compute tss=transpos(g)*m0*g.
compute regss=tss-rss.
print regss
/format="f8.4"
/title="Regression SS".
print rss
/format="f8.4"
/title="Residual SS".
print tss
/format="f8.4"
/title="Total SS".
compute r_sq=1-(rss/tss).
print r_sq
/format="f8.4"
/title="R-squared".
print n
/format="f4.0"
/title="Sample size (N)".
print p
/format="f4.0"
/title="Number of predictors (P)".
compute bp_test=0.5*regss.
print bp_test
/format="f8.3"
/title="Breusch-Pagan test for Heteroscedasticity"
+ " (CHI-SQUARE df=P)".
compute sig=1-chicdf(bp_test,p).
print sig
/format="f8.4"
/title="Significance level of Chi-square df=P (H0:"
+ "homoscedasticity)".
compute k_test=n*r_sq.
print k_test
/format="f8.3"
/title="Koenker test for Heteroscedasticity"
+ " (CHI-SQUARE df=P)".
compute sig=1-chicdf(k_test,p).
print sig
/format="f8.4"
/title="Significance level of Chi-square df=P (H0:"
+ "homoscedasticity)".
end matrix.
!ENDDEFINE.
 
* (2) Sample data (replace by your own)*.
 
INPUT PROGRAM.
- VECTOR x(20).
- LOOP #I = 1 TO 50.
- LOOP #J = 1 TO 20.
- COMPUTE x(#J) = NORMAL(1).
- END LOOP.
- END CASE.
- END LOOP.
- END FILE.
END INPUT PROGRAM.
execute.
 
* x1 is the dependent and x2 TO x20 the predictors.
 
* (3) MACRO CALL (select and run).
 
BPKTEST x1 19 x2 TO x20.
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