## What?

The marginaleffects package allows R users to compute and plot four principal quantities of interest for a wide variety of models:

• Marginal Effect (Vignette)
• A partial derivative (slope) of the regression equation with respect to a regressor of interest.
• The outcome predicted by a model for some combination of the regressors’ values, such as their means or factor levels (a.k.a. “reference grid”).
• Contrast (Vignette)
• The difference between two adjusted predictions, calculated for meaningfully different regressor values (e.g., College graduates vs. Others).
• Marginal Mean (Vignette)
• Adjusted predictions of a model, averaged across a “reference grid” of categorical predictors.

## Why?

To calculate marginal effects we need to take derivatives of the regression equation. This can be challenging to do manually, especially when our models are non-linear, or when regressors are transformed or interacted. Computing the variance of a marginal effect is even more difficult.

The marginaleffects package hopes to do most of this hard work for you.

Many R packages advertise their ability to compute “marginal effects.” However, most of them do not actually compute marginal effects as defined above. Instead, they compute “adjusted predictions” for different regressor values, or differences in adjusted predictions (i.e., “contrasts”). The rare packages that actually compute marginal effects are typically limited in the model types they support, and in the range of transformations they allow (interactions, polynomials, etc.).

The main packages in the R ecosystem to compute marginal effects are the trailblazing and powerful margins by Thomas J. Leeper, and emmeans by Russell V. Lenth and contributors. The marginaleffects package is essentially a clone of margins, with some additional features from emmeans.

So why did I write a clone?

• Powerful: Marginal effects and contrasts can be computed for about 40 different kinds of models. Adjusted predictions and marginal means can be computed for about 100 model types.
• Extensible: Adding support for new models is very easy, often requiring less than 10 lines of new code. Please submit feature requests on Github.
• Fast: In one benchmark, computing unit-level standard errors is over 400x faster with marginaleffects (minutes vs. milliseconds).
• Efficient: Smaller memory footprint (1.8GB vs 52MB in the same example).
• Valid: When possible, numerical results are checked against alternative software like Stata, or other R packages.
• Beautiful: ggplot2 support for plotting (conditional) marginal effects and adjusted predictions.
• Tidy: The results produced by marginaleffects follow “tidy” principles. They are easy to program with and feed to other packages like modelsummary.
• Simple: All functions share a simple, unified, and well-documented interface.
• Thin: The package requires few dependencies.
• Safe: User input is checked extensively before computation. When needed, functions fail gracefully with informative error messages.
• Active development

Downsides of marginaleffects include:

• Functions to estimate contrasts and marginal means are considerably less flexible than emmeans.
• Simulation-based inference is not supported.

## How?

By using the numDeriv package to compute gradients and jacobians, and the insight package to extract information from model objects. That’s it. That’s the secret sauce.

## Supported models

#### Adjusted predictions and marginal means

Under the hood, marginaleffects’s predictions function uses the insight package to retrieve adjusted predictions from a wide variety of models. Currently, insight supports over 100 model types, and many should work out-of-the-box with the predictions function. If you run into problems, do not hesitate to report them on Github or via email.

#### Marginal effects and contrasts

This table shows the list of models supported by the marginaleffects function, and shows which numerical results – marginal effects (dY/dX) or standard errors (Std. Error) – have been checked against alternative software packages: Stata’s margins command and R’s margins package. Empty cells mean that the results of a model have not yet been validated against external software. Green cells indicate that the results of at least one model from the test suite match to a reasonable tolerance. Red cells mean that marginaleffects results do not match those produced by alternative software packages. Obviously, caution is especially warranted when working with estimates from red cells.

I am very eager to add support for new models. Feel free to file a request on Github or – even better – submit some code.

Warning: When using marginaleffects with different models, you will probably have to adjust the type argument. Refer to the documentation of your modeling package to see what type argument is allowed in the predict function.

## Installation

You can install the released version of marginaleffects from CRAN:

install.packages("marginaleffects")

You can install the development version of marginaleffects from Github:

remotes::install_github("vincentarelbundock/marginaleffects")

## Getting started

First, we estimate a linear regression model with multiplicative interactions:

library(marginaleffects)

mod <- lm(mpg ~ hp * wt * am, data = mtcars)

#### Marginal effects

A “marginal effect” is a unit-specific measure of association between a change in a regressor and a change in the regressand. The marginaleffects function thus computes a distinct estimate of the marginal effect and of the standard error for each regressor (“term”), for each unit of observation (“rowid”). You can view and manipulate the full results with functions like head, as you would with any other data.frame:

mfx <- marginaleffects(mod)

#>   rowid     type term       dydx std.error  mpg  hp    wt am predicted
#> 1     1 response   am  0.3251736  1.682202 21.0 110 2.620  1  22.48857
#> 2     2 response   am -0.5438639  1.568211 21.0 110 2.875  1  20.80186
#> 3     3 response   am  1.2007132  2.347558 22.8  93 2.320  1  25.26465
#> 4     4 response   am -1.7025805  1.867130 21.4 110 3.215  0  20.25549

The function summary calculates the “Average Marginal Effect,” that is, the average of all unit-specific marginal effects:

summary(mfx)
#> Average marginal effects
#>       type Term   Effect Std. Error  z value   Pr(>|z|)    2.5 %   97.5 %
#> 1 response   am -0.04811    1.85260 -0.02597 0.97928233 -3.67913  3.58291
#> 2 response   hp -0.03807    0.01279 -2.97717 0.00290923 -0.06314 -0.01301
#> 3 response   wt -3.93909    1.08596 -3.62728 0.00028642 -6.06754 -1.81065
#>
#> Model type:  lm
#> Prediction type:  response

The plot_cme plots “Conditional Marginal Effects,” that is, the marginal effects estimated at different values of a regressor (often an interaction):

plot_cme(mod, effect = "hp", condition = c("wt", "am"))

Beyond marginal effects, we can also use the predictions function to estimate – you guessed it – adjusted predicted values. We use the variables argument to select the categorical variables that will form a “grid” of predictor values over which to compute means/predictions:

predictions(mod, variables = c("am", "wt"))
#>        type predicted std.error  conf.low conf.high       hp am     wt
#> 1  response 23.259500 2.7059342 17.674726  28.84427 146.6875  0 1.5130
#> 2  response 27.148334 2.8518051 21.262498  33.03417 146.6875  1 1.5130
#> 3  response 20.504387 1.3244556 17.770845  23.23793 146.6875  0 2.5425
#> 4  response 21.555612 1.0723852 19.342318  23.76891 146.6875  1 2.5425
#> 5  response 18.410286 0.6151016 17.140779  19.67979 146.6875  0 3.3250
#> 6  response 17.304709 1.5528055 14.099876  20.50954 146.6875  1 3.3250
#> 7  response 17.540532 0.7293676 16.035192  19.04587 146.6875  0 3.6500
#> 8  response 15.539158 2.1453449 11.111383  19.96693 146.6875  1 3.6500
#> 9  response 12.793013 2.9784942  6.645703  18.94032 146.6875  0 5.4240
#> 10 response  5.901966 5.8149853 -6.099574  17.90351 146.6875  1 5.4240

The typical function gives us an even more powerful way to customize the grid:

predictions(mod, newdata = typical(am = 0, wt = c(2, 4)))
#>       type predicted std.error conf.low conf.high       hp am wt
#> 1 response  21.95621  2.038630 17.74868  26.16373 146.6875  0  2
#> 2 response  16.60387  1.083201 14.36826  18.83949 146.6875  0  4

We can plot the adjusted predictions with the plot_cap function:

plot_cap(mod, condition = c("hp", "wt"))

Or you can work with the output of the predictions or marginaleffects directly to create your own plots. For example:

library(tidyverse)

predictions(mod,
newdata = typical(am = 0:1,
wt = fivenum(mtcars$wt), hp = seq(100, 300, 10))) %>% ggplot(aes(x = hp, y = predicted, ymin = conf.low, ymax = conf.high)) + geom_ribbon(aes(fill = factor(wt)), alpha = .2) + geom_line(aes(color = factor(wt))) + facet_wrap(~am) And of course, categorical variables work too: mod <- lm(mpg ~ factor(cyl), data = mtcars) plot_cap(mod, condition = "cyl") #### Marginal means To compute marginal means, we first need to make sure that the categorical variables of our model are coded as such in the dataset: dat <- mtcars dat$am <- as.logical(dat$am) dat$cyl <- as.factor(dat\$cyl)

Then, we estimate the model and call the marginalmeans function:

mod <- lm(mpg ~ am + cyl + hp, data = dat)
mm <- marginalmeans(mod)
summary(mm)
#> Estimated marginal means
#>   Term Group  Mean Std. Error z value   Pr(>|z|) 2.5 % 97.5 %
#> 1   am FALSE 18.32     0.7854   23.33 < 2.22e-16 16.78  19.86
#> 2   am  TRUE 22.48     0.8343   26.94 < 2.22e-16 20.84  24.11
#> 3  cyl     4 22.88     1.3566   16.87 < 2.22e-16 20.23  25.54
#> 4  cyl     6 18.96     1.0729   17.67 < 2.22e-16 16.86  21.06
#> 5  cyl     8 19.35     1.3771   14.05 < 2.22e-16 16.65  22.05
#>
#> Model type:  lm
#> Prediction type:  response

#### More

There is much more you can do with marginaleffects. Please read the other articles on this website to learn how to report marginal effects and means in nice tables with the modelsummary package, how to define your own prediction “grid”, and more: