David A. Kenny
April 19, 2013
This
mediation macro, called MedText, was written by David A. Kenny, Department of
Psychology, University of Connecticut.
This is Version 1h, completed on September 25, 2011. This macro has not been
extensively tested and will almost certainly be revised, and so it is advisable
to return for updates. SMALL BUT IMPORTANT CHANGES WERE MADE IN APRIL 2013 AND THIS NEW VERSION, NOT ANY OLDER ONE SHOULD NOW BE USED.
In January of 2013, an R version of MedText was released. Go to the MedText.R page.
Thank You!
I
thank Andrew Hayes and Kris Preacher for allowing me to adapt their
bootstrapping macro into MedText. I also thank Dave MacKinnon, Shengquan Ye, Betsy McCoach,
Tamar Saguy, Eileen Pitpitan,
Stefano Livi, Sylwia Bedyńska, and Amanda Snook for suggestions.
Finally, I thank my good friend the late Bob Calsyn for the
sample data. I am very open to
suggestions and advice from users of this program. However, the priorities of changes will be for MedTextR, the R version of the macro.
I have
created a Frequently Asked Questions page. If you have questions click here.
Download:
MedText.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
please be patient. Make sure to backup
the raw data file, as sometimes an error in the macro can alter the data file.
Note that the output (the text file) cannot be viewed in SPSS. It need to be opened using NotePad or Word.
The Macro Call
This is the
statement for the sample data:
Medtext x = Treatment/y = stable_housing/
xn='Treatment'yn='Days Housed' mn='Housing Contacts'
xm='yes' ofile='c:\medtext.txt' directory ='c:\'.
Please
note the slashes after the entry for x, y, and m. Between all other entries, just use
spaces. Make sure to end the macro with
a period. Carefully use single quotes. The marco is very finicky!
The defaults are
as follows:
x = X
y = Y
m = M
xn ='Causal
Variable'
yn ='Outcome'
mn ='Mediator'
alpha =.05
xm='no'
ofile ='medtext.txt'
trials = 5000
directory = 'C:\'
ncov = 0
clist =
That is, if you
just say "MedText.", the program will assume that are variables in
the SPSS data file with variables named X, Y, and M.
MedText was
written on SPSS 16 and 18; there is no guarantee that it work on earlier or
later versions of SPSS. It appears that the two tables at the end of the file
are not correct if the macro is run in version SPSS earlier than 16.
The macro:
allows for only a single causal variable,
mediator, and outcome (however, if you have a multiple causal variables you can
treat all but one of them as a "covariate"; also, separate runs can
be conducted for each outcomes; multiple mediators are problematic),
presumes that the mediator and the outcome
are measured on an interval scale,
uses listwise
deletion, and
does not do a moderator analysis (though a another
macro has been released).
Variables in the
macro:
x = name of the causal variable
in the SPSS data set (do not use quotes). If a dichotomy, then assign labels in "values" in the SPSS datafile for this variable.
y =
name of the outcome variable in the SPSS data set
m =
name of the mediating 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 mediating 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 use
capitals.
alpha = significance level
(defaults to .05)
xm =
whether the causal variable is manipulated (yes) or not (no) (use quotes and
all lower case)
ofile
= the name of the output file (use quotes); this is where you go to find the
text
directory = the name of the directory where temporary files are
written (use quotes); this must be a directory you are allowed to write on;
MedText will leave some files on this directory when it is done; I am working
on finding a way to erase them.
trials = the number of trials for bootstrapping in multiples of
1000. Do not set to zero! However, if you want a quick run performed,
set it to 1000.)
ncov =
the number of covariates
clist
= the SPSS names of the covariates separated by spaces (make sure the number of
names is equal the number of covariates).
Note carefully
which terms have quotes and which do not and where the slashes are where they are
not.
If a non-English
version of SPSS is being used, MedText changes the
language to English. It does not
currently change the language back to the original language.
Using DataToText
There is no guarantee
for accuracy. Examine not only DataToText output file, but also the SPSS output
file. The user needs to carefully edit the MedText output in research
reports. Please
cite this MedText webpage if you do use it.
Moreover, you need a footnote that says: “Some of the material here was
produced by the SPSS macro MedText (Kenny, 2011).” It is also strongly encouraged that if you
use essentially the same material as generated by Medtext,
that you put such material in quotations.
Warnings
MedText provides eleven possible warnings. The user needs to pay careful attention to
them. Note that the example below
produces two warnings.
1. The outcome variable is dichotomous and
logistic regression, not multiple regression, should be used. The output from MedText in this case is
wrong!
2. The mediator is dichotomous and logistic
regression, not multiple regression, should be used. The output from MedText in this case is
wrong!
3. Given the large sample size, you might want
to consider lowering alpha.
4. The small sample size might preclude a mediational analysis.
5. As zero does not appear to be meaningful
value for mediator, you might consider grand mean centering the mediator.
6. As zero does not appear to be meaningful
value for causal variable, you might consider grand mean centering the causal
variable.
7. There are
outliers in the dataset. Examine the
output to see what cases are considered to be outliers. (MedText uses 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.)
8. There is evidence that the effect of the
mediator or the causal variable is nonlinear and either a data transformation
or a nonlinear term might be advisable.
9. The causal and mediator variables explain
less than 1 percent of the variance of outcome variable.
10. There are sufficient missing data so as to
make the use of listwise missing data option less
than optimal. Better strategies for
missing data (e.g., multiple imputation or full information maximum likelihood).
11. The causal variable and mediator interact to explain the outcome variable and needs to be added to the model.
12. No "values" were given causal variable which is a dichtomy, and so "One" and "Two" have been assigned.
Again the user
needs to pay special attention to these warnings and make the necessary
modifications. For instance for the
example below, the mediator was transformed using a square root
transformation. Warnings are planned for
non-normality and heterogeneity of variance.
Details about the
Output
Some of the
output might not be clear. If so, the
user should consult relevant references.
Power analysis:
MedText takes the sample size and the number of covariates and does a power
analysis for a “medium” effect size, r = .3.
However, for the test of Step 1, it presumes complete mediation and r =
.09 (.3*.3) as the effect size measure.
Tests of
non-linearity: MedText reports the
quadratic effects of the mediator and
the causal variable. The user needs to
examine the output. Sometimes the
finding of nonlinearity may just be a Type I error.
Macro Output
If the X variable
is dichotomous, then you need to have labels for that variable which DataToText will use.
It is advisable to use singular labels (e.g., Man and Woman).
WARNINGS: 1.
There is one outlier for the variable Housing Contacts. Examine the output to see what observations
are considered to be outliers. 2. There is evidence that the effect of Housing
Contacts on Days Housed is nonlinear and either a data transformation or a
nonlinear term might be advisable. MEDIATIONAL MODEL The causal variable or X is Treatment,
a manipulated variable, and is a dichotomy with 42.2% Controls and 57.8% Treateds, the outcome variable or Y variable is Days
Housed, and the mediator or M is Housing Contacts. The causal mediational
model is as follows: The variable Treatment is presumed to cause Housing
Contacts, which in turn is presumed to cause Days Housed. If there were complete mediation, then the
causal effect of Treatment on Days Housed controlling for Housing Contacts
would be zero. For the estimates below
to be valid, it must be assumed that there is no measurement error in Housing
Contacts. Additionally, it must be
assumed that there are no unmeasured common causes of Housing Contacts and Days
Housed. Finally, it must be assumed that
Days Housed does not cause Housing Contacts. RESULTS Descriptive
Statistics There are a total of 109 observations. The means and standard deviations are
presented in Table 1. The unexplained
variance in Housing Contacts is equal to 14.077 (sd =
3.752) controlling for Treatment, with a multiple correlation for the
regression equation of .236. The
unexplained variance in Days Housed is equal to 136.467 (sd
= 11.682) controlling for Treatment and Housing Contacts, with a multiple
correlation for the regression equation of .469. Power In this section, theoretical power
analyses are computed using the study's sample size 109 with an alpha of
.05. Baron and Kenny (1986) terminology
is used. (The power of the test for
Steps 1 and 2 does not take into account that Treatment is a dichotomy.) The power of the Step 1 test is .15, assuming
that direct effect (path c') is zero and that all other paths have a moderate
effect size (r = .3). The power of the
Step 1 test, if a moderate effect size is assumed, would be the same as the
Step 2 test below. The power of the Step
2 test or a is .89, assuming that effect size is moderate (r = .3). The power of the Step 3 (path b) and Step 4
(path c') tests is .87, assuming that the tested path has a moderate effect
size (r = .3) and the other path is zero, and the correlation between Treatment
and Housing Contacts is .236 (the actual correlation between those
variables). A conservative estimate of
power of the test of the indirect effect is .61 assuming that a and b have
moderate effect sizes and that the direct effect is zero. Again, all of these power calculations are
hypothetical. The Four Steps The results of the four Baron and Kenny
(1986) steps, which are summarized in Table 2, are as follows. The effect of
Treatment on Days Housed or path c is equal to 6.558 (p = .009), with a 95%
confidence interval of 1.654 to 11.462 and a medium effect size (d = .514). The
mean for Treateds is equal to 12.784 and the mean for
Controls is equal to 19.342. Step 1 has
been passed. The effect of Treatment on
Housing Contacts or path a is equal to 1.831 (p = .013), with a 95% confidence
interval of .389 to 3.274 and a small effect size (d = .488). The mean for
Controls is equal to 2.689 and the mean for Treateds
is equal to 4.520. Step 2 has been
passed. The effect of Housing Contacts
on Days Housed controlling for Treatment or path b is equal to 1.398 (p <
.001), with a 95% confidence interval of .801 to 1.995 and a medium effect size
(r = .411). Step 3 has been passed. The effect of Treatment on Days Housed
controlling for Housing Contacts or path c' is equal to 3.998 (p = .089), with
a 95% confidence interval of -.625 to 8.621 and a small effect size (d = .342).
The least squares mean for Treatment Controls is equal to 12.784 and the least
squares mean for Treatment Treateds is equal to 16.782. Step 4 has been passed. A mediational
diagram for unstandardized estimates is contained in Figure 1 and for
standardized estimates is contained in Figure 2. (In contemporary analyses, Baron and Kenny
(1986) are no longer reported, but rather total, direct, and indirect effects
are reported and tested.) Indirect Effects The indirect effect of Treatment on
Days Housed or ab is equal to 2.560, with a smaller
than small effect size (d*r = .211; see note at the bottom for an explanation
of effect size of an indirect effect), and the direct effect is equal to 3.998.
The percentage of the total effect or c' + ab that is
mediated is equal to 39.04 percent. The
mediator is said to be "distal" (Hoyle & Kenny, 1999) in that
standardized path b is greater than standardized path a. Thus, Housing Contacts is "closer"
to Days Housed than to Treatment. The Sobel standard error is equal to 1.157, which makes the Z
test of the indirect effect equal to 2.213 (p = .027). Because the Sobel
test is statistically significant, it is concluded that the indirect effect is
significantly different from zero. The bootstrap estimated indirect effect is
2.634 (p = .010) with a standard error of 1.129 (Preacher & Hayes,
2008). The 95 percent bias corrected
bootstrap confidence interval (5000 trials) is from .522 to 4.930, and because
zero is not in the confidence interval, it is concluded that the indirect
effect is different from zero. (In
contemporary analyses, the bootstrapped test, and not the Sobel
test, is reported.) Tests of
Nonlinearity and Interaction The tests of nonlinearity are as
follows: Because Treatment is a
dichotomy, its quadratic effects cannot be measured. The quadratic effect of Housing Contacts
squared on Days Housed is -.106 and is statistically significant (p =
.034). There are concerns about
nonlinear effects and either a data transformation or a nonlinear term might be
advisable. The interactive effect of Treatment and Housing Contacts is not statistically significant (p = .492). OVERALL SUMMARY Here is an attempt to summarize the
results, but they need to be carefully verified by the investigator. The direct effect from Treatment to Days
Housed equals 3.998 and is not statistically significant (p = .089). The predicted mean difference between the Treateds and Controls groups on Days Housed equals
3.998. The indirect effect from
Treatment to Days Housed equals 2.560 and is statistically significant (p =
.010). For the indirect effect, the
predicted mean difference indirectly via Housing Contacts between the Treateds and Controls groups on Days Housed equals
2.560. There is evidence of partial
mediation of the effect of Treatment on Days Housed given that the indirect
effect is statistically significant but the percentage of the total effect
mediated is less than 80 percent. Table 1: Descriptive
Statistics Variable Mean Standard Deviation -------------------------------------------------------- Treatment .422 .496 Days Housed 15.552 13.107 Housing
Contacts 3.462 3.843 Table 2: Baron &
Kenny Steps Step
Path Estimate 95% CI Beta p ------------------------------------------------------------------ 1
c 6.558 1.654 to 11.462 .248
.009 2
a 1.831 .389 to 3.274 .236
.013 3
b 1.398 .801 to 1.995 .410
<.001 4
c' 3.998 -.625 to 8.621 .151
.089 Note: Effect sizes
are partial correlations (r) unless the predictor is a dichotomy where it is
Cohen's d. Because an indirect effect is
the product of two effect sizes, the effect size is the product of partial
correlations (r*r) or Cohen's d times the partial correlation (d*r). If the causal variable is a dichotomy, all
predicted means presume that the mediator and covariates equal zero. Figure 1 Mediation Diagram
with Unstandardized Coefficients Housing
Contacts /\ \ / \ / \ / \ 1.831* / \ 1.398* / \ / \ / \ / \/ Treatment ______________________________> Days Housed 3.998 (6.558*) * p < .05 Figure 2 Mediation Diagram
with Standardized Coefficients Housing Contacts /\ \ / \ / \ / \ .236* / \ .410* / \ / \ / \ / \/ Treatment ______________________________> Days
Housed .151 (.248*) * p < .05 References 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. Hoyle, R. H., & Kenny, D. A. (1999).
Sample size, reliability, and tests of statistical mediation. In R. H. Hoyle (Ed.), Statistical strategies
for small sample research (pp. 195-222).
MacKinnon, D. P., Fairchild, A. J., &
Fritz, M. S. (2007). Mediation analysis.
Annual Review of Psychology, 58, 593-614. Preacher, K. J., & Hayes, A. F.
(2008). Asymptotic and resampling strategies
for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879-891.