RMediation

Overview

RMediation computes confidence intervals for indirect effects in mediation analysis. It implements statistically rigorous methods that account for the non-normal distribution of the product of regression coefficients—addressing the well-known limitations of normal-theory approaches like the Sobel test.

The package supports:

• Single mediator models (X → M → Y)
• Sequential/serial mediators (X → M₁ → M₂ → Y)
• Parallel mediators with complex indirect effects
• Any product of normal random variables for custom applications

Why RMediation?

Traditional methods (e.g., Sobel test) assume the indirect effect ab follows a normal distribution. This assumption is often violated because the product of two normal variables is not normally distributed—especially when effect sizes are small or sample sizes are modest.

RMediation provides methods that correctly handle this non-normality:

Method	Best For	Speed
DOP (Distribution of Product)	Two-variable products; publication-quality results	Fast
Monte Carlo	Complex models; 3+ variable products	Moderate
MBCO (Model-Based Constrained Optimization)	Hypothesis testing; bootstrap inference	Slower

Installation

From CRAN (Stable)

install.packages("RMediation")

From GitHub (Development)

# Using pak (recommended)
pak::pak("Data-Wise/rmediation@develop")

# Or using remotes
remotes::install_github("Data-Wise/rmediation", ref = "develop")

Usage

Basic Example: Single Mediator

When you have coefficient estimates and standard errors (e.g., from a published study):

library(RMediation)

# Path coefficients: a = 0.5 (SE = 0.08), b = 0.6 (SE = 0.04)
# Compute 95% CI for the indirect effect ab
medci(mu.x = 0.5, mu.y = 0.6,
      se.x = 0.08, se.y = 0.04,
      rho = 0, type = "dop")

#> 95% CI for ab: [0.178, 0.422]
#> Estimate: 0.300, SE: 0.062

Sequential Mediators (3+ Variables)

For models with multiple sequential mediators (X → M₁ → M₂ → Y), use the ci() function with a formula:

# Four-path indirect effect: b1 * b2 * b3 * b4
ci(mu = c(b1 = 1.0, b2 = 0.7, b3 = 0.6, b4 = 0.45),
   Sigma = c(0.05, 0, 0, 0,    # Covariance matrix (lower triangle)
             0.05, 0, 0,
             0.03, 0,
             0.03),
   quant = ~ b1 * b2 * b3 * b4,
   type = "MC",
   n.mc = 1e5)

With lavaan Models

RMediation integrates directly with lavaan SEM models:

library(lavaan)
library(RMediation)

# Define mediation model with labeled paths
model <- '
  m ~ a*x
  y ~ b*m + c*x

  # Define indirect effect
  ab := a*b
'

fit <- sem(model, data = mydata)

# Compute CI for indirect effect (auto-detects 'ab := a*b')
ci(fit, type = "dop")

Using the S7 ProductNormal Class

For programmatic use, create ProductNormal objects directly:

# Define distribution of two correlated normal variables
pn <- ProductNormal(
  mu = c(0.5, 0.3),
  Sigma = matrix(c(0.01, 0.002,
                   0.002, 0.01), 2, 2)
)

# Compute confidence interval
ci(pn, level = 0.95, type = "dop")

# Get CDF and quantiles
cdf(pn, q = 0.15)
dist_quantile(pn, p = 0.975)

# View summary
summary(pn)

Hypothesis Testing with MBCO

For formal hypothesis testing of indirect effects using bootstrap:

# Requires OpenMx model
library(OpenMx)

# ... define your OpenMx mediation model ...

# Run MBCO test (H0: indirect effect = 0)
mbco(model, effect = "ab", n.boot = 1000, type = "parametric")

Key Functions

Function	Purpose
medci()	CI for product of two normal variables
ci()	CI for any function of parameters (formulas, lavaan, ProductNormal)
mbco()	Bootstrap hypothesis tests via MBCO
pprodnormal()	CDF of product of two normals
qprodnormal()	Quantiles of product of two normals
ProductNormal()	S7 class for product distributions

Part of the Mediationverse

RMediation is part of the mediationverse—a suite of R packages for comprehensive mediation analysis:

Package	Purpose
mediationverse	Meta-package: install and load all packages
medfit	Model fitting and coefficient extraction
probmed	Probabilistic effect size (P_med)
RMediation	Confidence intervals (DOP, Monte Carlo, MBCO)
medrobust	Sensitivity analysis
medsim	Simulation infrastructure

Install the entire ecosystem:

pak::pak("Data-Wise/mediationverse")
library(mediationverse)  # Loads all packages

Citation

If you use RMediation in your research, please cite:

Tofighi, D., & MacKinnon, D. P. (2011). RMediation: An R package for mediation
analysis confidence intervals. Behavior Research Methods, 43, 692-700.
https://doi.org/10.3758/s13428-011-0076-x

For Monte Carlo CIs in SEM:

Tofighi, D., & MacKinnon, D. P. (2016). Monte Carlo confidence intervals for
complex functions of indirect effects. Structural Equation Modeling: A
Multidisciplinary Journal, 23, 194-205.
https://doi.org/10.1080/10705511.2015.1057284

For sequential mediation and CI method comparisons:

Tofighi, D., & Kelley, K. (2020). Indirect effects in sequential mediation
models: Evaluating methods for hypothesis testing and confidence interval
formation. Multivariate Behavioral Research, 55(2), 188-210.
https://doi.org/10.1080/00273171.2019.1618545

For MBCO and bootstrap methods:

Tofighi, D., & Kelley, K. (2020). Improved inference in mediation analysis:
Introducing the model-based constrained optimization procedure.
Psychological Methods, 25(4), 496-515. https://doi.org/10.1037/met0000259

Tofighi, D. (2020). Bootstrap model-based constrained optimization tests of
indirect effects. Frontiers in Psychology, 10, 2989.
https://doi.org/10.3389/fpsyg.2019.02989

Getting Help

• Package documentation
• Report issues
• Mediationverse roadmap

License

GPL-3