Given a data frame, a predictor (IV), an outcome (DV), a mediator (M), and a moderator (Mod) conducts a joint-significant test for moderated mediation (see Yzerbyt, Muller, Batailler, & Judd, 2018).You can learn about moderated mediation in vignette("moderated-mediation")

add_index.moderated_mediation computes the moderated mediation index. compute_indirect_effect_for is used to compute the indirect effect index for a specific value of the moderator.

mdt_moderated(data, IV, DV, M, Mod)

## Arguments

data A data frame containing the variables in the model. An unquoted variable in the data frame which will be used as the independent variable. An unquoted variable in the data frame which will be used as the dependent variable. An unquoted variable in the data frame which will be used as the mediator. An unquoted variable in the data frame which will be used as the moderator.

## 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 moderated mediation analysis, one tests whether the indirect effect of $$X$$ on $$Y$$ through $$M$$ is moderated by $$Mod$$. 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 $$M$$.

Total moderation of the indirect effect of $$X$$ on $$Y$$ can be described as follows:

$$c * Mod = c' * Mod + (a * Mod) * b + a * (b * Mod)$$

with $$c * Mod$$ the total moderation of the indirect effect, $$c' * Mod$$ the moderation of the direct effect, $$(a * Mod) * b$$, the moderation of the indirect effect passing by the moderation of $$a$$, and $$a * (b * Mod)$$, the moderation of the indirect effect passing by the moderation of $$b$$ (see Models section; Muller et al., 2005).

Either both $$a * Mod$$ and $$b$$ or both $$a$$ and $$b * Mod$$ need to be simultaneously significant for a moderation of the indirect effect to be claimed (Muller et al., 2005).

## Models

In a moderated mediation model, three models will be used:

• $$Y_i = b_{40} + \mathbf{b_{41}} X_i + b_{42} Mo_i + \mathbf{b_{43}} XMo_i$$

• $$M_i = b_{50} + \mathbf{b_{51}} X_i + b_{52} Mo_i + \mathbf{b_{53} XMo_i}$$

• $$Y_i = b_{60} + \mathbf{c'_{61}} X_i + b_{62} Mo_i + \mathbf{b_{63} Xmo_i} + \mathbf{b_{64} Me_i} + \mathbf{b_{65} MeMo_i}$$

with $$Y_i$$, the outcome value for the ith observation, $$X_i$$, the predictor value for the ith observation, $$Mo_i$$, the moderator value for the ith observation, and $$M_i$$, the mediator value for the ith observation.

Coefficients associated with $$a$$, $$a \times Mod$$, $$b$$, $$b \times Mod$$, $$c$$, $$c \times Mod$$, $$c'$$, and $$c' \times Mod$$, paths are respectively $$b_{51}$$, $$b_{53}$$, $$b_{64}$$, $$b_{65}$$, $$b_{41}$$, $$b_{43}$$, $$b_{61}$$, and $$b_{63}$$ (see Muller et al., 2005).

## Variable coding

Because joint-significance tests use linear models behind the scenes, variables involved in the model have to be numeric. mdt_simple will give an error if non-numeric variables are specified in the model.

If you need to convert a dichotomous categorical variable to a numeric one, please refer to the build_contrast function.

Note that variable coding is especially important in models with multiple predictors as is the case in the model used to conduct a joint-significance test of moderated mediation. Muller et al. (2005) recommend using variables that are either contrast-coded or centered. Using mdt_moderated with a DV, a mediator, or a moderator that is neither contrast-coded nor centered will give a warning message.

## References

Muller, D., Judd, C. M., & Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. Journal of Personality and Social Psychology, 89(6), 852-863. doi: 10.1037/0022-3514.89.6.852

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_simple(), mdt_within()