David A. Kenny
December 1, 2009
This
mediation macro, called MedText, was written by David A. Kenny, Department of
Psychology,
Thank You!
I
thank Andrew Hayes and Kris Preacher for allowing me to adapt their
bootstrapping macro into MedText. I also thank Dave MacKinnon, Tamar
Saguy, and Amanda Snook for suggestions. Finally, I thank my good friend
Bob Calsyn for the sample data.
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 be patient. Make sure to backup the raw data file, as
sometimes an error in the macro can alter the data file. Note the output (the
text file) cannot be viewed in SPSS.
The Macro Call
This is the
statement for the sample data:
MedText x = Treatment/y = Housing/m = sq_hous
/xn ='Treatment' yn ='Days Housed'
mn='Housing Contacts' xm
='yes'
ofile= 'Medtext.txt' directory='C:\'.
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'
ncov = 0
clist =
trials = 5000
directory = 'C:\'
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 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 SPSS 14 or 15 is run. The macro appears to work with SPSS 17.
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 new
macro has been released).
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 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
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).
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 (Do not set
to zero!)
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
carefully edit the MedText output in research reports. Please cite MedText 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 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 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.
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.
Again the user
needs to pay special attention to these warnings and make the necessary
modification. For instance, based on a
prior analysis of the data and warnings obtained, the mediator was transformed
using a square root transformation.
Details on 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.
Tests of
non-linearity: MedText reports the
quadratic main effects of the mediator and the causal variable. The user needs to examine the output. Certainly, sometimes the finding of
nonlinearity may just be a Type I error.
Macro Output
If Notepad is
used make sure you use the wordwrap option in formal. Also for the tables to
align use Courier font.
MEDIATION MODEL
The causal variable or X is Treatment,
a dichotomy and is a manipulated variable, 42.2% Controls and 57.8%
Experimentals, the outcome variable or Y variable is Days Housed, and the
mediator variable or M is Housing Contacts.
The causal 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 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
Descriptives
There are a total of 109 cases. The means and standard deviations are
presented in Table 1. The unexplained
standard deviation in Treatment is equal to .554, and the multiple correlation for the regression equation is .251. The unexplained standard deviation in Days
Housed is equal to 11.345, and the multiple correlation for the regression
equation is .514. The power of the Step
1 test assuming that path c' is zero and that paths a and b have a moderate
effect size (r = .3) is .15, the power of the Step 2 test assuming that effect
size is moderate (r = .3) is .89, and the power of the Step 3 and Step 4 tests
assuming that paths a, b, and c' have a moderate effect size (r = .3) is .86.
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 Experimentals 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 .289 (p = .008), with a 95% confidence interval of .076 to .502 and a
medium effect size (d = .521). The mean for Controls is equal to .616 and the
mean for Experimentals is equal to .904.
Step 2 has been passed. The
effect of Housing Contacts on Days Housed controlling for Treatment or path b
is equal to 10.710 (p < .001), with a 95% confidence interval of 6.785 to
14.635 and a medium effect size (r = .465). Step 3 has been passed. The effect of Treatment on Days Housed
controlling for Housing Contacts or path c' is equal to 3.468 (p = .130), with
a 95% confidence interval of -1.039 to 7.974 and a small effect size (d =
.306). The least squares mean for Treatment Controls is equal to 12.784 and the
least squares mean for Treatment Experimentals is equal to 16.252. Step 4 has
been passed. A mediational diagram is
contained in Figure 1.
Indirect Effects
The indirect effect is equal to 3.091,
with a medium effect size (d*r = .239), and the direct effect is equal to
6.558. The percentage of the total effect that is mediated is equal to 47.13. 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 1.285,
which makes the Z test of the indirect effect equal to 2.406 (p = .016).
Because the Sobel test is statistically significant, we conclude that the
indirect effect is significantly different from zero. The bootstrap estimated
indirect effect is 3.067 (p = .008) with a standard error of 1.233 (Preacher
& Hayes, 2008). The 95 percent bootstrap confidence interval (5000 trials)
is from .932 to 5.825, and because zero is not in the confidence interval, it
is concluded that the indirect effect is different from zero.
Tests of
Nonlinearity
The tests of nonlinearity are as
follows: The quadratic effect of Housing
Contacts is -1.765 and is not statistically significant (p = .568).
Table 1: Descriptive
Statistics
Variable Mean Standard Deviation
--------------------------------------------------------
Treatment .422 .496
Days Housed 15.552 13.107
Housing
Contacts .737 .570
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 .289 .076 to .502 .251
.008
3
b 10.710 6.785 to 14.635 .466
<.001
4
c' 3.468 -1.039 to 7.974 .131
.130
Figure 1
Mediation Diagram
Housing Contacts
/\ \
/ \
/ \
/ \
.289* / \ 10.710*
/ \
/ \
/ \
/ \/
Treatment ______________________________>
Days Housed
3.468 (6.558*)
* p
< .050
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).
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.
Note: Effect sizes
are partial correlations (r) unless the predictor is a dichotomy and then it is
Cohen's d. Because an indirect effect is
the product of two effect size, 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 are for the mediator and covariates equaling zero.