Joint-significance test for within-participant mediation

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)

Arguments

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.

Value

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.

Details

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).

Models

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 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 $c'_{31}$.

Data formatting

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).

Variable coding

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.

References

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