keywords Mediation, simple mediation
This example shows how to estimate a simple mediation model with three variables in jAMM. Data come from University of Virginia Research Data Service and contain variables related to school achievement in a sample of students. There are three variables, school grades
, self-esteem
, and happiness
, measured on quantitative scales (I renamed the variables to make the data more intuitive, with X=grades
, M=selfesteem
and Y=happiness
. We also defined the variables as continuous in the data tab). The mediation model, explained here, is a classical simple mediation, as shown in the Figure.
First, we launch the module under linear models
menu. You can see in the results panel (right) that a simple mediation model path diagram is ready to be filled by selecting variables (left).
In case of simple mediation, we simply need to define the role of the variables. So, we put happiness
in the Dependent Variable
field, selfesteem
in the Mediators
field, and grades
in the Covariates
(continuous independent variables) field.
When you define the variables role, the module understands the mediation model and updates the path diagram.
In case of simple mediation, the module understands the intended statistical model, that can be checked in the Mediators models
and Full model
tabs.
The tabs simply indicate that the mediation model is composed by a linear regression with selfesteem
as dependent and grades
as independent, and one regression with happiness
as dependent and selfesteem
and grades
as independent variables. These two models are also reported in the Model info
result table.
In the Model info
table you can also see how the module deduced what is the mediated effect to be computed, in our example grades -> selfesteem -> happiness
.
In the mediation literature notation, these models are usually referred to as:
\[ M =k_1 + a \cdot X \]
\[ Y =k_2+ b \cdot M + c^\prime \cdot X\] (\(k_i\) are intercepts)
Results report indirect (mediated), direct (unmediated) and total effects, under the Mediation
section, in the Indirect and direct effects
.
The Indirect
row reports the mediated effect. Thus, this is the classical \(a \cdot b\) mediation effect, where \(a\) is the coefficient from grades
to selfesteem
and \(b\) is the coefficient from selfesteem
to happiness
, keeping constant grades
. Coefficients \(a\) and \(b\) are the components of the mediated effect, and you can see them in the table in the Component
rows. As expected, \(a \cdot b= .5610 \cdot .6355 = .3565\).
The z
test associated with the mediated effect is the large sample z test of the mediated effect, which is a slightly more accurate version of the Sobel test. The confidence intervals are also computed using large sample approximation, but the bootstrap version of confidence intervals can be asked in the Mediation options
tab (see below).
The Direct
row shows the effect of the independent variable not mediated by selfesteem
, the coefficient usually denoted by \(c^\prime\) in the mediation jargon. The Total
effect is the overall effect of grades
on hapiness
, that is \(c=a \cdot b + c^\prime\). All the z
tests associated with these coefficients test the null-hypothesis that the corresponding coefficient is zero. Confidence intervals are computed with the same method used for the indirect effect.
Finally, the \(\beta\) column shows the standardized solution coefficients.
By default, the jAMM computes the confidence intervals using the large sample delta method, that is using the z test as the starting point of computation. However, often users prefer to use a bootstrap method. That can be done in the Mediation options
tab.
Several bootstrap methods can be selected. One of the most used in mediation analysis is the precentile method, which is jAMM is called bootstrap (Percent)
. See GLM mediation models for help on the other options. Please note that the bootstrap method can be very time-consuming and slow.
To recap, to estimate a simple mediation model, simply select the dependent, the independent, and the mediator variable, and the results will be shown in the results table.
If you are interested in checking the convergence of jAMM results with other software results, please visit the rosetta store Rosetta store: conditional mediation
Got comments, issues or spotted a bug? Please open an issue on GAMLj at github“ or send me an email