Given a data frame, a predictor (IV
), an outcome
(DV
), a mediator (M
), and a grouping variable (group
)
conducts a jointsignificant test for withinparticipant mediation (see
Yzerbyt, Muller, Batailler, & Judd, 2018).
mdt_within(data, IV, DV, M, grouping, default_coding = TRUE)
data  a data frame containing the variables in the model. 

IV  an unquoted variable in the data frame which will be used as the independent variable. 
DV  an unquoted variable in the data frame which will be used as the dependent variable. 
M  an unquoted variable in the data frame which will be used as the mediator. 
grouping  an unquoted variable in the data frame which will be used as the grouping variable. 
default_coding  should the variable coding be the default? Defaults to

Returns an object of class "mediation_model
".
An object of class "mediation_model
" is a list containing at least
the components:
A character string containing the type of model that has been
conducted (e.g., "simple mediation"
).
A character string containing the approach that has been
used to conduct the mediation analysis (usually
"joint significance"
).
A named list of character strings describing the variables used in the model.
A named list containing information on each relevant path of the mediation model.
A boolean indicating whether an indirect effect index
has been computed or not. Defaults to FALSE
. See
add_index
to compute mediation index.
(Optional) An object of class
"indirect_index"
. Appears when one applies add_index
to an object of class "mediation_model"
.
A list of objects of class "lm"
. Contains every
model relevant to jointsignificance testing.
The original data frame that has been passed through
data
argument.
With withinparticipant mediation analysis, one tests whether the effect of \(X\) on \(Y\) goes through a third variable \(M\). The specificity of withinparticipant mediation analysis lies in the repeated measures design it relies on. With such a design, each sampled unit (e.g., participant) is measured on the dependent variable \(Y\) and the mediator \(M\) in the two conditions of \(X\). The hypothesis behind this test is that \(X\) has an effect on \(M\) (\(a\)) which has an effect on \(Y\) (\(b\)), meaning that \(X\) has an indirect effect on \(Y\) through \(M\).
As with simple mediation, the total effect of \(X\) on \(Y\) can be conceptually described as follows:
$$c = c' + ab$$
with \(c\) the total effect of \(X\) on \(Y\), \(c'\) the direct of \(X\) on \(Y\), and \(ab\) the indirect effect of \(X\) on \(Y\) through M (see Models section).
To assess whether the indirect effect is different from the null, one has to assess the significance against the null for both \(a\) (the effect of \(X\) on \(M\)) and \(b\) (effect of \(M\) on \(Y\) controlling for the effect of \(X\)). Both \(a\) and \(b\) need to be simultaneously significant for an indirect effect to be claimed (Judd, Kenny, & McClelland, 2001; Montoya & Hayes, 2011).
For withinparticipant mediation, three models will be fitted:
\(Y_{2i}  Y_{1i} = c_{11}\)
\(M_{2i}  M_{1i} = a_{21}\)
\(Y_{2i}  Y_{1i} = c'_{31} + b_{32}(M_{2i}  M_{1i}) + d_{33}[0.5(M_{1i} + M_{2i})  0.5(\overline{M_{1} + M_{2}})]\)
with \(Y_{2i}  Y_{1i}\) the difference score between DV conditions for the outcome variable for the ith observation, \(M_{2i}  M_{1i}\) the difference score between DV conditions for the mediator variable for the ith observation, \(M_{1i} + M_{2i}\) the sum of mediator variables values for DV conditions for the ith observation, and \(\overline{M_{1} + M_{2}}\) the mean sum of mediator variables values for DV conditions across observations (see Montoya & Hayes, 2011).
Coefficients associated with \(a\), \(b\), \(c\), and \(c'\) paths are respectively \(a_{21}\), \(b_{32}\), \(c_{11}\), and \(c'_{31}\).
To be consistent with other mdt_*
family
functions, mdt_within
takes a longformat data frame as data
argument. With this kind of format, each sampled unit has two rows, one for
the first withinparticipant condition and one for the second
withinparticipant condition. In addition, each row has one observation for
the outcome and one observation for the mediator (see
dohle_siegrist
for an example.
Because such formatting is not the most common among social scientists
interested in withinparticipant mediation, JSmediation contains the
mdt_within_wide
function which handles wideformatted data
input (but is syntaxinconsistent with other mdt_*
family
functions).
Models underlying withinparticipant mediation use
difference scores as DV (see Models section). Because the function input
does not allow the user to specify how the difference scores should be
computed, mdt_within
has a default coding.
mdt_within
's default behavior is to compute the difference score so
the total effect (the effect of \(X\) on \(Y\)) will be positive and
compute the other difference scores accordingly. That is, if
mdt_within
has to use \(Y_{2i}  Y_{1i}\) (instead of \(Y_{1i}
 Y_{2i}\)) so that \(c_{11}\) is positive, it will use \(M_{2i} 
M_{1i}\) (instead of \(M_{1i}  M_{2i}\) in the other models.
User can choose to have a negative total effect by using the
default_coding
argument.
Note that DV
and M
have to be numeric.
Judd, C. M., Kenny, D. A., & McClelland, G. H. (2001). Estimating and testing mediation and moderation in withinsubject designs. Psychological Methods, 6(2), 115134. doi: 10.1037//1082989X.6.2.115
Montoya, A. K., & Hayes, A. F. (2017). Twocondition withinparticipant statistical mediation analysis: A pathanalytic framework. Psychological Methods, 22(1), 627. doi: 10.1037/met0000086
Yzerbyt, V., Muller, D., Batailler, C., & Judd, C. M. (2018). New recommendations for testing indirect effects in mediational models: The need to report and test component paths. Journal of Personality and Social Psychology, 115(6), 929–943. doi: 10.1037/pspa0000132
Other mediation models:
mdt_moderated()
,
mdt_simple()