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############### TWOWAY SIMPLE SLOPES MACRO ############################
###### Version 1.1 // 9.1.07 // by J. Ullrich #######################
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TWOWAY y= /x= /m= /z= /rs= /alpha= /n= /high= /low= .
EXE.
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# This is how the command works:
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# TWOWAY y= your dependent variable here
# /x= your focal predictor here
# /m= your moderator here
# /z= standardize predictors, yes (1) or no (0)?
# /rs= calculate region of significance, yes (1) or no (0)?
# /alpha= your desired alpha level for rs (e.g., .05)
# /n= your sample size (after listwise deletion of missings)
# /high= your high conditional value of m
# /low= your low conditional value of m.
# EXE.
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# The simplest way to use the command is to specify only the DV,
# the focal predictor variable, and the moderator variable,
# and set z to 1.
# The command will then standardize the predictor variables before
# computing the product term and use 1 SD below/above the mean as
# the conditional values of the moderator variable. There is no need to
# include more arguments (although SPSS will produce error message #4024,
# talking about omitted operands, which you may ignore).
# Note that the macro temporarily removes all missing values. However,
# the macro treats any user-defined missing values (i.e., anything other
# than the sysmis value of ',') as real data! So please check if your
# dataset involves any user-defined missing values and change them to
# ','.
# Optionally, you can set rs to 1 in order to get the limits of the
# region of significance for the focal predictor variable. In this case,
# you must provide the effective sample size (after listwise deletion of
# missing values) and the desired alpha level.
# If you wish to use other conditional values than 1 SD below/above the
# mean, set z to 0 and provide appropriate high and low conditional
# values.
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# See notes for details. Updates may appear on this website:
# http://web.uni-frankfurt.de/fb05/psychologie/Abteil/sozial/
# Comments and suggestions to ullrich at psych.uni-frankfurt.de
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# Run the rest of the syntax to define the macro for the current session.
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DEFINE TWOWAY
(y = !charend('/')
/x = !charend('/')
/m = !charend('/')
/z = !charend('/')
/rs = !charend('/') !default(0)
/alpha = !charend('/')
/n = !charend('/')
/high = !charend('/') !default(1)
/low = !charend('/') !default(1)).
DO IF (!rs=1).
COMPUTE tcrit = idf.t(1-!alpha/2,!n-4).
ELSE IF(!rs=0).
COMPUTE tcrit = 0.
END IF.
MATRIX.
get dd/variables = !y !x !m tcrit /names mmnms /missing = omit.
compute n = nrow(dd).
compute df = n - 4.
compute const = make(n,1,1).
compute data=dd.
compute yy=data(:,1).
compute xx=data(:,2).
compute mm=data(:,3).
compute tcrit=data(1,4).
compute meanx = msum(xx)/nrow(xx).
compute devx = xx - meanx.
compute sqx= mssq(devx).
compute sdx = sqrt(sqx/(n-1)).
compute xz = devx/sdx.
compute meanm = msum(mm)/nrow(mm).
compute devm = mm - meanm.
compute sqm= mssq(devm).
compute sdm = sqrt(sqm/(n-1)).
compute mz = devm/sdm.
compute xname = mmnms(1,2).
compute mname = mmnms(1,3).
compute he = t({"Constant", xname, mname, "Product"}).
do if (!z = 1).
compute xm = xz&*mz.
compute pred = {const,xz,mz,xm}.
compute b = inv(t(pred)*pred)*t(pred)*yy.
compute hat = pred * b.
compute err = cssq(hat - yy)/df.
compute vcov = err * inv(t(pred)*pred).
compute se = {sqrt(vcov(1,1)); sqrt(vcov(2,2)); sqrt(vcov(3,3));sqrt(vcov(4,4))}.
compute t1 = abs(b(1)/sqrt(vcov(1,1))).
compute t2 = abs(b(2)/sqrt(vcov(2,2))).
compute t3 = abs(b(3)/sqrt(vcov(3,3))).
compute t4 = abs(b(4)/sqrt(vcov(4,4))).
compute p1 = 2*(1-TCDF(t1,df)).
compute p2 = 2*(1-TCDF(t2,df)).
compute p3 = 2*(1-TCDF(t3,df)).
compute p4 = 2*(1-TCDF(t4,df)).
compute bt = {t1;t2;t3;t4}.
compute bp = {p1;p2;p3;p4}.
compute out = {b, se, bt, bp}.
print /title="+++ TWOWAY Moderated Multiple Regression Results +++".
print out /title=" "
/clabels = "b" "SE" "t" "p(>|t|)"/rnames = he /format f10.4.
print df /title="degrees of freedom (error)".
print vcov /title="Variances and covariances of predictors"/format=E12.0.
compute high=!high.
compute low=!low*-1.
compute sslowm = b(2)+(low * b(4)).
print /title="simple slope at low moderator value:".
compute sslowmse = sqrt(vcov(2,2) + (2*low*vcov(2,4)) + ((low**2)*vcov(4,4))).
compute tlow = abs(sslowm/sslowmse).
compute plow = 2*(1-TCDF(tlow,df)).
compute outm1 = {sslowm, sslowmse,tlow, plow}.
print outm1 /title = " "/clabels= "b" "SE" "t" "p(>|t|)"/format f10.4.
compute sshim = b(2)+(high * b(4)).
print /title="simple slope at high moderator value:".
compute sshise = sqrt(vcov(2,2) + (2*high*vcov(2,4)) + ((high**2)*vcov(4,4))).
compute thigh = abs(sshim/sshise).
compute phigh = 2*(1-TCDF(thigh,df)).
compute outm2 = {sshim, sshise, thigh, phigh}.
print outm2 /title = " "/clabels= "b" "SE" "t" "p(>|t|)"/format f10.4.
do if (!rs=1).
compute rsa = (((tcrit**2)*vcov(4,4))-b(4)**2).
compute rsb = (2*(((tcrit**2)*vcov(2,4))-(b(2)*b(4)))).
compute rsc = (((tcrit**2)*vcov(2,2))-b(2)**2).
compute rs1 = (-rsb + sqrt((rsb**2)-(4*rsa*rsc)))/(2*rsa).
compute rs2 = (-rsb - sqrt((rsb**2)-(4*rsa*rsc)))/(2*rsa).
compute rs12 = {rs1;rs2}.
print /title="+++ Region of Significance Results +++".
print rs12/title="focal predictor is significant between these moderator values:".
end if.
else if (!z = 0).
compute xm = xx&*mm.
compute pred = {const,xx,mm,xm}.
compute b = inv(t(pred)*pred)*t(pred)*yy.
compute hat = pred * b.
compute err = cssq(hat - yy)/df.
compute vcov = err * inv(t(pred)*pred).
compute se = {sqrt(vcov(1,1)); sqrt(vcov(2,2)); sqrt(vcov(3,3));sqrt(vcov(4,4))}.
compute out = {b, se}.
print /title="+++ TWOWAY Moderated Multiple Regression Results +++".
print out /title=" "
/clabels = "b" "SE" /rnames = he /format f10.4.
print df /title="degrees of freedom (error)".
print vcov /title="Variances and covariances of predictors"/format=E12.0.
compute high=!high.
compute low=!low.
compute sslowm = b(2)+(low * b(4)).
print /title="simple slope at low moderator value:".
compute sslowmse = sqrt(vcov(2,2) + (2*low*vcov(2,4)) + ((low**2)*vcov(4,4))).
compute tlow = abs(sslowm/sslowmse).
compute plow = 2*(1-TCDF(tlow,df)).
compute outm1 = {sslowm, sslowmse,tlow, plow}.
print outm1 /title = " "/clabels= "b" "SE" "t" "p(>|t|)"/format f10.4.
compute sshim = b(2)+(high * b(4)).
print /title="simple slope at high moderator value:".
compute sshise = sqrt(vcov(2,2) + (2*high*vcov(2,4)) + ((high**2)*vcov(4,4))).
compute thigh = abs(sshim/sshise).
compute phigh = 2*(1-TCDF(thigh,df)).
compute outm2 = {sshim, sshise, thigh, phigh}.
print outm2 /title = " "/clabels= "b" "SE" "t" "p(>|t|)"/format f10.4.
do if (!rs=1).
compute rsa = (((tcrit**2)*vcov(4,4))-b(4)**2).
compute rsb = (2*(((tcrit**2)*vcov(2,4))-(b(2)*b(4)))).
compute rsc = (((tcrit**2)*vcov(2,2))-b(2)**2).
compute rs1 = (-rsb + sqrt((rsb**2)-(4*rsa*rsc)))/(2*rsa).
compute rs2 = (-rsb - sqrt((rsb**2)-(4*rsa*rsc)))/(2*rsa).
compute rs12 = {rs1;rs2}.
print /title="+++ Region of Significance Results +++".
print rs12/title="focal predictor is significant between these moderator values:".
end if.
else.
print /title =" Wrong value specified for z. Use 1 or 0." .
end if.
END MATRIX.
delete variables tcrit.
!END DEFINE.
