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_wide(data, DV_A, DV_B, M_A, M_B)

## Arguments

data a data frame containing the variables in the model. an unquoted numeric variable in the data frame which will be used as the dependent variable value for the "A" independent variable condition. an unquoted numeric variable in the data frame which will be used as the dependent variable value for the "B" independent variable condition. an unquoted numeric variable in the data frame which will be used as the mediatior variable value for the "A" independent variable condition. an unquoted numeric variable in the data frame which will be used as the mediatior variable value for the "b" independent variable condition.

## 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).

## 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). mdt_within_wide uses M_A $$-$$ M_B and DV_A $$-$$ DV_B in these models.

## 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 $$c'_{31}$$.

## 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