knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
The JSmediation package was designed to help intuitively typing the code to test mediations. In this vignette, we will use it to assess a simple mediation.
Simple mediation analysis refers to the analysis testing whether the effect of
an independent variable on a dependent variable goes through a third variable
(the mediator). The ho_et_al
data set, shipped with the JSmediation package,
contains data illustrating a case of simple mediation. This data set contains
the data collected by Ho et al. in a paper focusing on hypodescent
[-@ho_youre_2017], a rule sometimes use when people have to perform multiracial
categorization and where a perceivers associate a biracial person more easily to
their lowest status group.
In this experiment, Ho et al. [-@ho_youre_2017] made the hypothesis that a Black American participants exposed to the discrimination of Black-White biracials would be more likely to associate Black-White biracials with Black Americans rather than with White Americans. In other words, participants of their experiment would be more likely to use the hypodescent rule when exposed to high discrimination content compared to low discrimination content. In the experiment that we will investigate, the authors went further and tested whether the effect of the discrimination condition on the use of hypodescent was mediated by a feeling of linked fate between the participants (Black Americans) and Black-White biracials [@ho_youre_2017].
In this vignette, we will use the ho_et_al
data set to test whether feeling
of linked fate mediates the relationship between the exposition to a high
discrimination content and the use of hypodescent among Black Africans.
Simple mediation is often times summarized with one equation [@baron_moderator-mediator_1986;@cohen_applied_1983]:
$$ c = c' + a \times b $$
with $c$ the total effect of the independent variable ($X$) on the dependent
variable ($Y$), $c'$ the direct of $X$ on $Y$, and $a \times b$ the indirect
effect of $X$ on $Y$ through the mediator variable ($M$; see Models section of
the mdt_simple
help page).
To assess whether the indirect effect is different from the null, one has to assess the significance against of 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 [@yzerbyt_new_2018].
Because we want to test whether the feeling of linked fate is mediating the effect of the discrimination condition on the use of hypodescent, we must test whether the discrimination condition predicts the feeling of linked fate and whether feeling of link fate predicts the use of hypodescent (when controlling for the effect of the discrimination condition). The JSmediation package will help us in that regard.
Our first step will be to attach the JSmediation package to our environment. This will allow us to use the functions and data sets shipped with the package.
library(JSmediation)
To begin with the analysis, we will take a look at the ho_et_al
data set.
data(ho_et_al) head(ho_et_al)
This data set contains 5 columns:
ìd
: a unique identifier for each participant,
condition
: the discrimination condition of the participants (either "Low
discrimination" or "High discrimination"),
sdo
: a measure of Social Dominance Orientation (SDO) of the participant
which is extensively used in our example of [moderated
mediation]((moderated_mediation_analysis.html),
linkedfate
: the feeling of linked fate between the participants and
Black-White biracials,
* hypodescent
: the tendency to use the hypodescent rules in multiracial
categorization (see, Ho et al. 2017).
This data set is almost ready for our analysis. The only thing that we need is a
data frame (or a tibble
) with the value of our different variables for each
participant (i.e., the independent variable, the dependent variable, and the
mediator). Our data, however, must be properly formatted for the analysis. In
particular, every variable must be coded as a numeric variable.
Because the condition
variable is coded as a character (and not as a
numeric)—a format which is not supported by JSmediation, we will need to
pre-process our data set. Thanks to the build_contrast
function, we will
create a new variable in ho_et_al
(condition_c
) representing the
discrimination condition as a numeric variable.
ho_et_al$condition_c <- build_contrast(ho_et_al$condition, "Low discrimination", "High discrimination") head(ho_et_al)
mdt_fit
Now that we have a data frame ready for analysis, we will use the mdt_simple
function to fit a simple mediation model. Any mediation model supported by
JSmediation comes with a mdt_*
function. These functions need the users to
indicate the data set used for the analysis as well as the variable relevant for
the analysis thanks to the function argument. Once done, it will run the
relevant linear regression in order to test the conditions necessary for
mediation.
mediation_fit <- mdt_simple(ho_et_al, IV = condition_c, DV = hypodescent, M = linkedfate)
The mediation_fit
model that we just created contains every bit of information
necessary to use a joint-significance approach to assess simple mediation
[@yzerbyt_new_2018].
mediation_model
ObjectsBefore diving into the results, because the joint-significance approach runs
linear regression under the hood, we will test the assumptions of ordinary least
square for each of the regression used by mdt_simple
[@judd_data_2017]. To do
so, we will use the check_model
from the performance package function which
prints several diagnostic plots [@ludecke_performance_2021]^[Recent versions of
JSmediation offers the check_assumptions
and plot_assumptions
to help you
check the OLS assumptions of the fitted model.].
We will first extract the models used by mdt_simple
, and then run the
check_model
function. The extract_model
function will be helpful to that
regard. This function uses a mediation model as a first argument, and the model
name (or model index) as a second argument. It then returns a linear model
object (i.e., an lm
object).
first_model <- extract_model(mediation_fit, step = "X -> M") performance::check_model(first_model)
We will do the same thing for the two other models mdt_simple has fitted.
second_model <- extract_model(mediation_fit, step = 2) performance::check_model(second_model)
third_model <- extract_model(mediation_fit, step = 3) performance::check_model(third_model)
Thanks to these plots, we can now interpret the results of the mediation knowing whether their data suffer from any violation [@judd_data_2017].
Now that we check for our assumptions, we can interpret our model. To do
so, we simply have to call model_fit
.
mediation_fit
In this summary, we can see that both $a$ and $b$ paths are significant, and we can therefore conclude that the indirect effect of the discrimination condition on hypodescent used passing through the feeling of linked fate is significant [@yzerbyt_new_2018].
Thanks to the mdt_simple
function, we almost have every information to report
our joint-significance test [@yzerbyt_new_2018]. Besides reporting the
significance of $a$ and $b$, it is sometimes recommended to report the index of
indirect effect, a single value accounting for $a \times b$. Wa can compute this
index thanks to Monte Carlo methods thanks to the add_index
function. This
functions adds the indirect effect to the model summary object.
model_fit_with_index <- add_index(mediation_fit) model_fit_with_index
The only thing left to do is to report the mediation analysis:
First, we examined the effect of the discrimination condition (low vs. high) on hypodescent use. This analysis revealed a significant effect, t(822) = 2.13, p = .034. > > We then tested our hypothesis of interest, namely, we tested whether the sentiment of linked fate between Black Americans and Black-White biracials mediated the effect of the discrimination condition on hypodescent. To do so, we conducted a joint significant test [@yzerbyt_new_2018]. This analysis revealed a significant effect of discrimination condition on linked fate, t(822) = 9.10, p < .001, and a significant effect of linked fate on hypodescent, controlling for the discrimination condition, t(821) = 5.75, p < .001. The effect of discrimination condition on hypodescent after controlling for the feeling of linked fate was no longer significant, t(821) = 0.33, p = .742. Consistently with this analysis, the Monte Carlo confidence interval for the indirect effect did not contain 0, CI95% [0.0889; 0.208]. This analysis reveals that the feeling of linked fate mediates the effect of the discrimination condition on hypodescent.
JSmediation
makes conducting a mediation analysis easy with the mdt_*
functions, but they are not the only function in the package. Some functions
will help with the linear regression models fitted during the analysis.
check_assumptions
tests every model's OLS assumptions using the
performance package. plot_assumptions
plots plots diagnostic of the models' OLS assumptions using
the performance package.
extract_model
returns one of the model used (as an lm
object).
extract_models
returns a named list of the models used. extract_tidy_models
returns a data frame containing models summary
information à la broom [@robinson_broom_2021].display_models
print a summary of each lm
model.Any scripts or data that you put into this service are public.
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