neg.esm {negligible}

Test for Evaluating Substantial Mediation

Description

Function computes the equivalence testing method (total effect) for evaluating substantial mediation and Kenny method for full mediation.

Usage

neg.esm(
  X,
  Y,
  M,
  alpha = 0.05,
  minc = 0.15,
  eil = -0.15,
  eiu = 0.15,
  nboot = 1000L,
  data = NULL,
  plot = TRUE,
  saveplot = FALSE,
  seed = NA
)

## S3 method for class 'neg.esm'
print(x, ...)

Arguments

X

predictor variable

Y

outcome variable

M

mediator variable

alpha

alpha level (default = .05)

minc

minimum correlation between x and Y (default is .15)

eil

lower bound of equivalence interval in standardized units(default is -.15)

eiu

upper bound of equivalence interval in standardized units (default is .15)

nboot

number of bootstraps (default = 500L)

data

optional data argument

plot

logical, plotting the results (default = TRUE)

saveplot

saving plots (default = FALSE)

seed

optional argument to set seed

x

object of class neg.esm

...

extra arguments

Details

This function evaluates whether a negligible direct effect of X on Y exists after controlling for the mediator. Another way to word this is that the indirect effect accounts for a substantial proportion of the variability in X-Y relationship. See Beribisky, Mara, and Cribbie (https://doi.org/10.20982/tqmp.16.4.p424)

The user specifies the IV (X), DV (Y) and mediator (M). The user can also specify the alpha level, the lower/upper bound of the negligible effect interval (eiL, eiU), the number of bootstrap samples (nboot), as well as the minimum correlation between X and Y that is permitted for a valid test of substantial mediation.

The variables X, Y and M can be specified as stand-alone, or a data argument can be used if the data reside in an R dataset.

For the Kenny method see: https://davidakenny.net/cm/mediate.htm

The proportional distance quantifies the proportional distance from 0 to the nearest negligible effect (equivalence) interval (eiL, eiU). As values get farther from 0 the relationship becomes more substantial, with values greater than 1 indicating that the effect falls outside of the negligible effect (equivalence) interval.

Note that the number of bootstrap samples (nboot) are low for the example since the example has a time limit of 5 seconds to pass CRAN testing; we recommend running a much higher number of bootstrap samples for analyses.

Value

A list including the following:

• minc Minimum correlation between X and Y for a valid negligible effect (equivalence) test

• corxy Sample correlation between the IV (X) and DV (Y)

• dir_eff Sample standardized direct effect between the IV (X) and DV (Y) after controlling for the mediator (M)

• eiL Lower bound of the negligible effect (equivalence) interval

• eiU Upper bound of the negligible effect (equivalence) interval

• cil Lower bound of the 1-2*alpha CI for the standardized direct effect of X on Y

• ciu Upper bound of the 1-2*alpha CI for the standardized direct effect of X on Y

• PD Proportional distance (PD)

• cilpd Lower bound of the 1-alpha CI for the PD

• ciupd Upper bound of the 1-alpha CI for the PD

• ab_par Standardized indirect effect

• abdivc_k Proportion mediated: Standardized indirect effect divided by the standardized total effect

• alpha Nominal Type I error rate

Author(s)

Rob Cribbie [e-mail] and Nataly Beribisky [e-mail]

Examples

#equivalence test for substantial mediation
#with an equivalence interval of -.15 to .15
X<-rnorm(100,sd=2)
M<-.5*X + rnorm(100)
Y<-.5*M + rnorm(100)
neg.esm(X,Y,M, eil = -.15, eiu = .15, nboot = 5)