Bayesian Marginal Effects for 'brms' Models

Calculate Bayesian marginal effects, average marginal effects, and marginal coefficients (also called population averaged coefficients) for models fit using the 'brms' package including fixed effects, mixed effects, and location scale models. These are based on marginal predictions that integrate out random effects if necessary (see for example and ).

Overview

This package has functions to calculate marginal effects from brms models ( http://paul-buerkner.github.io/brms/ ). A central motivator is to calculate average marginal effects (AMEs) for continuous and discrete predictors in fixed effects only and mixed effects regression models including location scale models.

This table shows an overview of currently supported models / features where "X" indicates a specific model / feature is currently supported. The column 'Fixed' means fixed effects only models. The column 'Mixed' means mixed effects models.

*limitted support for relatively simple random effect sturctures. Experimental. In general, any distribution supported by brms that generates one and only one predicted value (e.g., not multinomial logistic regression models) should be supported for fixed effects only models. Also note that currently, only Gaussian random effects are supported. This is not too limiting as even for Bernoulli, Poisson, etc. outcomes, the random effects are commonly assumed to have a Gaussian distribution.

Here is a quick syntax overview of how to use the main function, brmsmargins().

Fixed effects, continuous predictor.

h <- .001
ames <- brmsmargins(
  object = model,
  add = data.frame(x = c(0, h)),
  contrasts = cbind("AME x" = c(-1 / h, 1 / h)),
  effects = "fixedonly")
  
ames$ContrastSummary

Fixed effects, discrete predictor.

ames <- brmsmargins(
  object = model,
  add = data.frame(x = c(0, 1)),
  contrasts = cbind("AME x" = c(-1, 1)),
  effects = "fixedonly")

ames$Summary
ames$ContrastSummary

Mixed effects, continuous predictor.

h <- .001
ames <- brmsmargins(
  object = model,
  add = data.frame(x = c(0, h)),
  contrasts = cbind("AME x" = c(-1 / h, 1 / h)),
  effects = "integrateoutRE")
  
ames$ContrastSummary

Mixed effects, discrete predictor.

ames <- brmsmargins(
  object = model,
  add = data.frame(x = c(0, 1)),
  contrasts = cbind("AME x" = c(-1, 1)),
  effects = "integrateoutRE")

ames$Summary
ames$ContrastSummary

Mixed Effects Location Scale, continuous predictor

h <- .001
ames <- brmsmargins(
  object = model,
  add = data.frame(x = c(0, h)),
  contrasts = cbind("AME x" = c(-1 / h, 1 / h)),
  dpar = "sigma",
  effects = "integrateoutRE")
  
ames$ContrastSummary

Mixed Effects Location Scale, discrete predictor

ames <- brmsmargins(
  object = model,
  at = data.frame(x = c(0, 1)),
  contrasts = cbind("AME x" = c(-1, 1)),
  dpar = "sigma",
  effects = "integrateoutRE")

ames$Summary
ames$ContrastSummary

Note that even on mixed effects models, it is possible to generate predictions and marginal effects from the fixed effects only, just by specifying effects = "fixedonly" but this is probably not a good idea generally so not shown by default.

Also note that for all of these examples ames$Summary would have a summary of the averaged predicted values. These often are useful for discrete predictors. For continuous predictors, if the focus is on marginal effects, they often are not interesting. However, the at argument can be used with continuous predictors to generate interesting averaged predicted values. For example, this would get predicted values integrating out random effects for a range of ages averaging (marginalizing) all other predictors / covariates.

ames <- brmsmargins(
  object = model,
  at = data.frame(age = c(20, 30, 40, 50, 60)),
  effects = "integrateoutRE")

ames$Summary

Installation

You can install the package from CRAN by running this code:

install.packages("brmsmargins")

Alternately, for the latest, development version, run:

remotes::install_github("JWiley/brmsmargins")

Learn More

There are three vignettes that introduce how to use the package for several scenarios.

• Fixed effects only models (also called single level models). This also is the best place to start learning about how to use the package. It includes a brief amount of motivation for why we would want to calculate marginal effects at all.
• Mixed effects models (also called multilevel models). This shows how to calculate marginal effects for mixed effects / multilevel models. There are runnable examples, but not much background.
• Location scale models. Location scale models are models where both the location (e.g., mean) and scale (e.g., variance / residual standard deviation) are explicitly modeled as outcomes. These require use of distributional parameters dpar in brms. This vignette shows how to calculate marginal effects from location scale models for the scale part.