**David A. Kenny**

**December 6, 2010**

** **

**Moderation Macro **

**This
moderation macro, called ModText, was written by David A. Kenny, Department of
Psychology, University of Connecticut (please ****email me).
This is Version 1c, completed on December 5, 2010. This
marco almost certainly contains errors and will certainly be revised, and so it
is advisable to return for updates. Because of these errors, you should
carefully check your output. **

**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 = stable_hous/m = hous_conts**

**/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 18, 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 incorrect if SPSS 15 or earlier is run. **

**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.
For dichotomies, the output is clearer if there are meaningful labels in
the data file.**

** **

**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. Avoid using more than 15 characters.)**

**
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 may
leave some files on this directory when it is done.**

** **

**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 this ModText webpage if you do use it. Moreover, you need a footnote
that says: “Some of the material here was produced by the macro ModText (Kenny,
2010).” It is also strongly encouraged that if you use essentially the same material as generated by Modtext,
that you put such material in quotations.**

** **

**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 and one
half 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 warnings 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 **

** **

** **

**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. **

**Effects of
Treatment and Housing Contacts **

** 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 small 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
Statistical Significance
**

** Considered here are regions of Housing
Contacts in which the effect of Treatment on Days Housed are statistically
significant (Aiken & West, 1991).
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.
New York: **

** 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.**

** **

**Bar graph from the SPSS output:**

**Line graph from the SPSS output:**

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** **