Given a data frame, a predictor (`IV`

), an outcome
(`DV`

), a mediator (`M`

), and a grouping variable (`group`

)
conducts a joint-significant test for within-participant 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

`TRUE`

.

Returns an object of class "`mediation_model`

".

An object of class "`mediation_model`

" is a list containing at least
the components:

- type
A character string containing the type of model that has been conducted (e.g.,

`"simple mediation"`

).- method
A character string containing the approach that has been used to conduct the mediation analysis (usually

`"joint significance"`

).- params
A named list of character strings describing the variables used in the model.

- paths
A named list containing information on each relevant path of the mediation model.

- indirect_index
A boolean indicating whether an indirect effect index has been computed or not. Defaults to

`FALSE`

. See`add_index`

to compute mediation index.- indirect_index_infos
(Optional) An object of class

`"indirect_index"`

. Appears when one applies`add_index`

to an object of class`"mediation_model"`

.- js_models
A list of objects of class

`"lm"`

. Contains every model relevant to joint-significance testing.- data
The original data frame that has been passed through

`data`

argument.

With within-participant mediation analysis, one tests whether the effect of \(X\) on \(Y\) goes through a third variable \(M\). The specificity of within-participant 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 within-participant 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 *i*th observation,
\(M_{2i} - M_{1i}\) the difference score between DV conditions
for the mediator variable for the *i*th observation, \(M_{1i} +
M_{2i}\) the sum of mediator variables values for DV conditions
for the *i*th 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 long-format data frame as `data`

argument. With this kind of format, each sampled unit has two rows, one for
the first within-participant condition and one for the second
within-participant 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 within-participant mediation, JSmediation contains the
`mdt_within_wide`

function which handles wide-formatted data
input (but is syntax-inconsistent with other `mdt_*`

family
functions).

Models underlying within-participant 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 within-subject designs.
*Psychological Methods*, *6*(2), 115-134. doi:
10.1037//1082-989X.6.2.115

Montoya, A. K., & Hayes, A. F. (2017). Two-condition within-participant
statistical mediation analysis: A path-analytic framework.
*Psychological Methods*, *22*(1), 6-27. 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()`