(Robustly) estimate the effects in a mediation model.
fit_mediation(object, ...)# S3 method for formula
fit_mediation(formula, data, ...)
# S3 method for default
fit_mediation(
object,
x,
y,
m,
covariates = NULL,
method = c("regression", "covariance"),
robust = TRUE,
family = "gaussian",
contrast = FALSE,
fit_yx = TRUE,
control = NULL,
...
)
the first argument will determine the method of the generic function to be dispatched. For the default method, this should be a data frame containing the variables.
additional arguments to be passed down. For the default
method, this can be used to specify tuning parameters directly instead
of via control.
an object of class "formula" (or one that can be coerced to
that class): a symbolic description of the model to be fitted. Hypothesized
mediator variables should be wrapped in a call to m() (see
examples), and any optional control variables should be wrapped in a call to
covariates().
for the formula method, a data frame containing the
variables.
a character, integer or logical vector specifying the columns of
object containing the independent variables.
a character string, an integer or a logical vector specifying the
column of object containing the dependent variable.
a character, integer or logical vector specifying the columns of
object containing the hypothesized mediator variables.
optional; a character, integer or logical vector
specifying the columns of object containing additional covariates to
be used as control variables.
a character string specifying the method of
estimation. Possible values are "regression" (the default)
to estimate the effects via regressions, or "covariance" to
estimate the effects via the covariance matrix. Note that the effects are
always estimated via regressions if more than one independent variable or
hypothesized mediator is specified, or if control variables are supplied.
a logical indicating whether to robustly estimate the effects
(defaults to TRUE). For estimation via regressions
(method = "regression"), this can also be a character string, with
"MM" specifying the MM-estimator of regression, and "median"
specifying median regression.
a character string specifying the error distribution to be
used in maximum likelihood estimation of regression models. Possible values
are "gaussian" for a normal distribution (the default),
skewnormal for a skew-normal distribution, "student" for
Student's t distribution, "skewt" for a skew-t distribution, or
"select" to select among these four distributions via BIC (see
‘Details’). This is only relevant if method = "regression"
and robust = FALSE.
a logical indicating whether to compute pairwise contrasts
of the indirect effects (defaults to FALSE). This can also be a
character string, with "estimates" for computing the pairwise
differences of the indirect effects, and "absolute" for computing the
pairwise differences of the absolute values of the indirect effects. This
is only relevant for models with multiple indirect effects, which are
currently only implemented for estimation via regressions
(method = "regression").
a logical indicating whether to fit the regression model
y ~ x + covariates to estimate the total effect (the default is
TRUE). This is only relevant if method = "regression" and
robust = FALSE.
a list of tuning parameters for the corresponding robust
method. For robust regression (method = "regression", and
robust = TRUE or robust = "MM"), a list of tuning
parameters for lmrob() as generated by
reg_control(). For winsorized covariance matrix estimation
(method = "covariance" and robust = TRUE), a list of tuning
parameters for cov_Huber() as generated by
cov_control(). No tuning parameters are necessary for median
regression (method = "regression" and robust = "median").
An object inheriting from class "fit_mediation" (class
"reg_fit_mediation" if method = "regression" or
"cov_fit_mediation" if method = "covariance") with
the following components:
a numeric vector containing the point estimates of the effects of the independent variables on the proposed mediator variables.
a numeric vector containing the point estimates of the direct effects of the proposed mediator variables on the dependent variable.
a numeric vector containing the point estimates of the direct effects of the independent variables on the dependent variable.
a numeric vector containing the point estimates of the total effects of the independent variables on the dependent variable.
a numeric vector containing the point estimates of the indirect effects.
an object of class "lmrob",
"rq", "lm" or "lmse"
containing the estimation results from the regression of the proposed
mediator variable on the independent variables, or a list of such objects
in case of more than one hypothesized mediator (only
"reg_fit_mediation").
an object of class "lmrob",
"rq", "lm" or "lmse"
containing the estimation results from the regression of the dependent
variable on the proposed mediator and independent variables (only
"reg_fit_mediation").
an object of class "lm" or "lmse"
containing the estimation results from the regression of the dependent
variable on the independent variables (only "reg_fit_mediation"
if arguments robust = FALSE and fit_yx = TRUE were used).
an object of class "cov_Huber" or
"cov_ML" containing the covariance matrix estimates
(only "cov_fit_mediation").
character vectors specifying the respective variables used.
a data frame containing the independent, dependent and proposed mediator variables, as well as covariates.
either a logical indicating whether the effects were estimated
robustly, or one of the character strings "MM" and "median"
specifying the type of robust regressions.
either a logical indicating whether contrasts of the
indirect effects were computed, or one of the character strings
"estimates" and "absolute" specifying the type of contrasts
of the indirect effects (only "reg_fit_mediation").
a list of tuning parameters used (if applicable).
With method = "regression", and robust = TRUE or
robust = "MM", the effects are computed via the robust MM-estimator
of regression from lmrob(). This is the default
behavior.
With method = "regression" and robust = "median", the effects
are estimated via median regressions with rq().
Unlike the robust MM-regressions above, median regressions are not robust
against outliers in the explanatory variables.
With method = "regression", robust = FALSE and
family = "select", the error distribution to be used in maximum
likelihood estimation of the regression models is selected via BIC. The
following error distributions are included in the selection procedure: a
normal distribution, a skew-normal distribution, Student's t distribution,
and a skew-t distribution. Note that the parameters of those distributions
are estimated as well. The skew-normal and skew-t distributions thereby
use a centered parametrization such that the residuals are (approximately)
centered around 0. Moreover, the skew-t distribution is only evaluated in
the selection procedure if both the skew-normal and Student's t distribution
yield an improvement in BIC over the normal distribution. Otherwise the
estimation with a skew-t error distribution can be unstable. Furthermore,
this saves a considerable amount of computation time in a bootstrap test,
as estimation with those error distributions is orders of magnitude slower
than any other estimation procedure in package robmed.
With method = "covariance" and robust = TRUE, the effects are
estimated based on a Huber M-estimator of location and scatter. Note that
this covariance-based approach is less robust than the approach based on
robust MM-regressions described above.
Alfons, A., Ates, N.Y. and Groenen, P.J.F. (2021) A robust bootstrap test for mediation analysis. Organizational Research Methods, 10.1177/1094428121999096.
Azzalini, A. and Arellano-Valle, R. B. (2013) Maximum penalized likelihood estimation for skew-normal and skew-t distributions. Journal of Statistical Planning and Inference, 143(2), 419--433.
Yuan, Y. and MacKinnon, D.P. (2014) Robust mediation analysis based on median regression. Psychological Methods, 19(1), 1--20.
Zu, J. and Yuan, K.-H. (2010) Local influence and robust procedures for mediation analysis. Multivariate Behavioral Research, 45(1), 1--44.
# NOT RUN {
data("BSG2014")
## The results in Alfons et al. (2021) were obtained with an
## older version of the random number generator. To reproduce
## those results, uncomment the call to RNGversion() below.
# RNGversion("3.5.3")
seed <- 20150601
# formula interface
set.seed(seed)
fit1 <- fit_mediation(TeamCommitment ~ m(TaskConflict) + ValueDiversity,
data = BSG2014)
test1 <- test_mediation(fit1)
summary(test1)
# default method
set.seed(seed)
fit2 <- fit_mediation(BSG2014,
x = "ValueDiversity",
y = "TeamCommitment",
m = "TaskConflict")
test2 <- test_mediation(fit2)
summary(test2)
# }
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