David A. Kenny
January 28, 2010
Moderation Macro
This
moderation macro, called ModText, was written by David A. Kenny, Department of
Psychology,
Thank You!
I
thank my good friend Bob Calsyn for the sample data. Thanks to Amanda Snook, Stefano Livi, and
Brian Connolly for advice.
Download:
ModText.SPS
(You need SPSS to open this and the next 3 files.)
Macro
Output (You do not need SPSS to open this file. But if you do not use "wordwrap" it will look
ugly.)
To understand how
to run a macro return to the DataToText
page. The macro takes a few minutes to run and so be patient. Make sure
to backup the raw data file, as sometimes an error in the macro can alter the
data file.
PLEASE
READ THIS: Note that the
output (the text file you name) cannot be viewed in SPSS and is not written to
the SPSS output file. You need to view
it in text reader (e.g., Notepad). When viewing the file, make sure to use "wordwrap"
and Courier or New Courier font.
The Macro Call
This is the
statement for the sample data:
ModText x = Treatment/y = Housing/m = h_contact
/xn ='Treatment' yn
='Days Housed'
mn='Housing
Contacts' alpha =.05
ofile=
'C:\modtext.txt' clist='' directory='C:\'.
The defaults are
as follows:
x = X
y = Y
m = M
xn ='Causal Variable'
yn ='Outcome'
mn ='Moderator'
alpha =.05
ofile ='modtext.txt'
clist =
directory ='C:\'
That is, if you
just say "ModText.", the program will assume that are variables in the SPSS
data file with variables named X, Y, and M.
The data file
should be open; if either the causal variable or moderator is dichotomous,
values should be given for both levels of the variable in the SPSS file; and
labels should be given for the causal variable and the moderator.
ModText was
written on SPSS 16 and there is no guarantee that it work on earlier or later
versions of SPSS. It appears that the three tables at the end of the file are
not correct if SPSS 15 or earlier is run.
The program appears to run on SPSS 17.
ModText does
recognize that the Causal Variable and the Moderator are dichotomies and alters
the outcome accordingly. For a
dichotomous variables, predicted means are given for the two levels of that
variable; otherwise predicted means are given for +1 and -1 standard deviation
above the mean.
The macro:
allows for only a single causal variable,
moderator, and outcome (however, if there are either multiple moderators or
causal variables, they could be treated as "covariates" and pairs of causal
variables and moderators could be examined one at a time),
presumes that the moderation is linear and
not non-linear (e.g., quadratic) but ModText does test for nonlinearity
presumes that the outcome variable is
measured on an interval scale, and
uses listwise deletion.
Variables in the
macro:
x = name of the causal variable
in the SPSS data set (do not use quotes)
y =
name of the outcome variable in the SPSS data set
m =
name of the moderating variable in the SPSS data set
xn = name of the causal variable
in the text output (use quotes; spaces are allowed)
yn = name of the outcome
variable in the text output (use quotes; spaces are allowed)
mn = name of the moderating
variable in the text output (use quotes; spaces are allowed)
(For the above three variables, it is advised to use English names and
not SPSS acronyms. Also it is advised to
capitalize the first letter of each word.)
alpha = significance level
(defaults to .05)
ofile = the name of the output
file (use quotes); this is where you go to find the text
clist = the SPSS names of the
covariates separated by spaces
directory = the name of the
directory where temporary files are written (use quotes); this must be a
directory you are allowed to write on; ModText will leave some files on this
directory when it is done; I am working on finding a way to erase them.
It is safest to
give arguments for all macro variables.
Note carefully what terms have quotes and what do not and where the
slashes are where they are not.
There is no
guarantee for accuracy. Examine not only
DataToText output file, but also the SPSS output file. The user needs to
edit the ModText output in research reports.
Please cite ModText if you do use it.
If a non-English
version of SPSS is being used, ModText changes the language to English. It does not currently change the language
back to the original language.
Warnings
ModText provides
8 possible warnings. The user needs to
pay careful attention to them.
1. The outcome variable is dichotomous and
logistic regression, not multiple regression, should be used. The output from ModText in this case is
wrong! One might consider the Andrew
Hayes macro ModProbe.
2. Because zero is not a possible value for the
causal variable, grand-mean centering that variable should be considered.
3. Because zero is not a possible value for the
moderator, grand-mean centering that variable should be considered.
4. One standard deviation below (above) the mean
for the causal variable is below (above) its minimum (maximum) value. This occurs for the example (see below). The lowest possible and observed score is
zero, but minus 1 sd is a negative value.
5. One or more of the predicted means is either
lower than its minimum value or larger than its maximum value. If there are covariates make sure they are
centered. There might be inappropriate
assumption about the level of measurement of the outcome or a floor or ceiling
effect for that measure.
6. There are
outliers in the dataset. Examine the
output to see what cases are considered to be outliers. ModText uses an the SPSS definition of plus
or minus three standard deviations to determine if a case is an outlier. It should be noted that this procedure is
very conservative and not a very robust way of determining outliers.
7. The causal variable and the moderator are
highly correlated and this colinearity reduces the precision in the estimation
of moderation parameters. ModText use .5 as the cutoff for high colinearity.
8. There is evidence that the effect of the
moderator or the causal variable is nonlinear and either a data transformation
or a nonlinear term might be advisable.
Again the user
needs to pay special attention to these warning and make the necessary
modification.
Details on the
Output
Some of the
output might not be clear. If so, the
user should consult Aiken and West and other sources cited at the end of the
macro.
Effect sizes: For
the interaction, unless both variables are dichotomous, ModText uses f
squared. It represents the proportion of
variance explained by the interaction not explained by other variables in the
model. Almost certainly, the standards
that Cohen gave for small, medium, and large effects are way too optimistic for
test of interactions.
For main effects,
the partial correlation coefficient is used unless the variable is a dichotomy
and then d is used. If both the causal
variable and the moderator are dichotomous, d is used as the effect size for
the moderator effect.
Power analysis:
ModText takes the sample size and the number of covariates and does a power
analysis for a small and a medium effect size.
Tests of
non-linearity: ModText does not report the
quadratic main effects. The user would
need to examine the output. Certainly,
sometimes the finding of nonlinearity may just be a Type I error.
Regions of
significance: Most readers will be
unfamiliar with these procedures.
Consult Aiken and West and other sources for more detail.
Links
My Moderation Page (needs
updating!)
Andrew
Hayes Macro ModProbe (easier to use and allow for a dichotomous outcome)
Macro Output
If Notepad is
used make sure you use the wordwrap option in formal. Also for the tables to align use Courier
font.
The output using
sample data:
WARNING: 1. One
standard deviation below the mean for Housing Contacts or -.095 is below its
minimum value of .000.
MODERATION MODEL
The causal variable is Treatment, a
dichotomy, 42.2% Controls and 57.8% Experimentals. the outcome variable is Days
Housed, and the moderator variable is Housing Contacts. The causal model is as follows: The variable
Treatment is presumed to cause Days Housed linearly whose causal effect is
presumed to be altered linearly by Housing Contacts.
RESULTS
Descriptives
There are a total of 109 cases. The power of the test of moderation assuming
that f squared is .02 (a small effect size, but optimistic according to Aguinis
(2004)) is .11, and the power of the test of moderation assuming that f squared
is .15 (a moderate effect size) is .52.
The means and standard deviations are presented in Table 1. The unexplained standard deviation in Days
Housed is equal to 11.711, and the multiple correlation for the regression
equation is .473.
Main Effects
The results of the moderated regression
analysis are summarized in Table 2. The
overall effect of Treatment on Days Housed, when Housing Contacts is equal to
zero, is 2.482 (p = .441), with a small effect size (d = .212). The overall
effect of Housing Contacts on Days Housed, when Treatment is equal to zero, is
4.792 (p = .005), with a medium effect size (r = .269). The mean of Days Housed
for the Controls is equal to 9.563 and the mean of Days Housed for the
Experimentals is equal to 12.045.
Interaction
Effects
The interaction between Treatment and
Housing Contacts is equal to 1.666 and is not statistically significant (p =
.492), with a less than small effect size (f squared = .0045). As the Housing Contacts increases, the causal
effect of Treatment, though not statistically significant, is amplified or
strengthened. The effect of Treatment
for persons who are one standard deviation below the mean on Housing Contacts
(-.095) is equal to 2.323 (p = .492) with a less than small effect size (d =
.198); the effect of Treatment for persons who are one standard deviation above
the mean on Housing Contacts (1.826) is equal to 5.524 (p = .089), with a small
effect size (d = .472). (See Table 3 and
the graph or table as the end of the SPSS output.)
Test of
Nonlinearity
The test of nonlinearity is as
follows: The quadratic interaction
effect of Housing Contacts with Treatment is -3.041 and is not statistically
significant (p = .084).
Regions of
Significance
The effect of Treatment is not
statistically significant at all in the range of possible values of Housing
Contacts.
Table 1: Descriptive
Statistics
Variable Mean Standard Deviation
--------------------------------------------------------
Treatment .422 .496
Housing
Contacts .865 .961
Days Housed 15.552 13.107
Table 2: Moderated Regression
Coefficients
Predictor Estimate Effect Size p
-------------------------------------------------------------------
Intercept 9.563 <.001
Treatment 2.482 .212 .441
Housing
Contacts 4.792 .269 .005
Treatment x
Housing Contacts 1.666 .0045 .492
(Note that the
effect size measure in Table 2 is d for Treatment, r for Housing Contacts, and
f squared for the interaction.)
Table 3: Predicted
Means for the Causal Variable and the Moderator (+1 and -1 sd)
Housing Contacts
Treatment -.095 1.826
------------------------------------------------
Controls 9.106 18.314
Experimentals 11.428 23.839
References
Aguinis, H. (2004). Moderated regression.
Aiken, L. S., & West, S. G. (1991).
Multiple regression: Testing and interpreting interactions.
Baron, R. M., & Kenny, D. A.
(1986). The moderator-mediator variable
distinction in social psychological research: Conceptual, strategic and
statistical considerations. Journal of Personality and Social Psychology, 51,
1173-1182.
The bar graph from
the SPSS output:
Line graph from
the SPSS output:
