Joint-significance test for simple mediation

Given a data frame, a predictor (IV), an outcome (DV), and a mediator (M), conducts a joint-significant test for simple mediation (see Yzerbyt, Muller, Batailler, & Judd, 2018).

mdt_simple(data, IV, DV, M)

Arguments

data: A data frame containing the variables to be used in the model.
IV: An unquoted numeric variable in the data frame which will be used as independent variable.
DV: An unquoted numeric variable in the data frame which will be used as dependent variable.
M: An unquoted numeric variable in the data frame which will be used as mediator.

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 simple mediation analysis, one is interested in finding if the effect of $X$ on $Y$ goes through a third variable $M$. The hypothesis behind this test is that $X$ has an effect on $M$ ($a$) that has an effect on $Y$ ($b$), meaning that $X$ has an indirect effect on $Y$ through $M$.

The total effect of $X$ on $Y$ can be 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 (Cohen & Cohen, 1983; Yzerbyt, Muller, Batailler, & Judd, 2018).

Models

In a simple mediation model, three models will be fitted:

$Y_i = b_{10} + \mathbf{c_{11}} X_i$
$M_i = b_{20} + \mathbf{a_{21}} X_i$
$Y_i = b_{30} + \mathbf{c'_{31}} X_i + \mathbf{b_{32}} M_i$

with $Y_i$, the outcome value for the ith observation, $X_i$, the predictor value for the ith observation, and $M_i$, the mediator value for the ith observation (Cohen & Cohen, 1983; Yzerbyt, Muller, Batailler, & Judd, 2018).

Coefficients associated with $a$, $b$, $c$, and $c'$ paths are respectively $a_{21}$, $b_{32}$, $c_{11}$, and $c'_{31}$.

Variable coding

Because joint-significance tests uses 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.

To convert a dichotomous categorical variable to a numeric one, please refer to the build_contrast function.

References

Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed). Hillsdale, N.J: L. Erlbaum Associates.

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

Examples

## fit a simple mediation model
data(ho_et_al)
ho_et_al$condition_c <- build_contrast(ho_et_al$condition,
                                       "Low discrimination",
                                       "High discrimination")
mdt_simple(data = ho_et_al,
           IV = condition_c,
           DV = hypodescent,
           M = linkedfate)
#> Test of mediation (simple mediation)
#> ==============================================
#> 
#> Variables:
#> 
#> - IV: condition_c 
#> - DV: hypodescent 
#> - M: linkedfate 
#> 
#> Paths:
#> 
#> ====  ==============  =====  =======================
#> Path  Point estimate     SE  APA                    
#> ====  ==============  =====  =======================
#> a              0.772  0.085  t(822) = 9.10, p < .001
#> b              0.187  0.033  t(821) = 5.75, p < .001
#> c              0.171  0.081  t(822) = 2.13, p = .034
#> c'             0.027  0.083  t(821) = 0.33, p = .742
#> ====  ==============  =====  =======================
#> 
#> Indirect effect index:
#> 
#> Indirect effect index is not computed by default.
#> Please use add_index() to compute it.
#> 
#> Fitted models:
#> 
#> - X -> Y 
#> - X -> M 
#> - X + M -> Y