`marginaleffects`

package for `R`

The `marginaleffects`

package allows `R`

users to compute and plot four principal quantities of interest for a very wide variety of models:

*Marginal Effect*(Vignette)- A partial derivative (slope) of the regression equation with respect to a regressor of interest.

*Adjusted Prediction*(Vignette)- 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.

The rest of this page includes a “Getting Started” tutorial with simple examples. To go beyond these simple examples, please read the vignettes linked above, for each of the four quantities. In addition, you can consult these pages:

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.
- Newer package with a smaller (read: nonexistent) user base.

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.

You can install the released version of `marginaleffects`

from CRAN:

You can install the development version of `marginaleffects`

from Github:

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

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)
head(mfx, 4)
#> rowid type term dydx std.error mpg hp wt am
#> 1 1 response hp -0.03690556 0.01850168 21.0 110 2.620 1
#> 2 2 response hp -0.02868936 0.01562768 21.0 110 2.875 1
#> 3 3 response hp -0.04657166 0.02259121 22.8 93 2.320 1
#> 4 4 response hp -0.04227128 0.01328275 21.4 110 3.215 0
```

The function `summary`

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

```
summary(mfx)
#> Average marginal effects
#> Term Effect Std. Error z value Pr(>|z|) 2.5 % 97.5 %
#> 1 am -0.04811 1.85260 -0.02597 0.97928233 -3.67913 3.58291
#> 2 hp -0.03807 0.01279 -2.97717 0.00290923 -0.06314 -0.01301
#> 3 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):

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 `datagrid`

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

```
predictions(mod, newdata = datagrid(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:

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 = datagrid(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:

To compute marginal means, we first need to make sure that the categorical variables of our model are coded as such in the dataset:

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 Value 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
```

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: