The parameters of a statistical model can sometimes be difficult to interpret substantively, especially when that model includes non-linear components, interactions, or transformations. Analysts who fit such complex models often seek to transform raw parameter estimates into quantities that are easier for domain experts and stakeholders to understand, such as predictions, contrasts, risk differences, ratios, odds, lift, slopes, and so on.

Unfortunately, computing these quantities—along with associated
standard errors—can be a tedious and error-prone task. This problem is
compounded by the fact that modeling packages in `R`

and
`Python`

produce objects with varied structures, which hold
different information. This means that end-users often have to write
customized code to interpret the estimates obtained by fitting Linear,
GLM, GAM, Bayesian, Mixed Effects, and other model types. This can lead
to wasted effort, confusion, and mistakes, and it can hinder the
implementation of best practices.

This free online book
introduces a conceptual framework to clearly define statistical
quantities of interest, and shows how to estimate those quantities using
the `marginaleffects`

package for `R`

and
`Python`

. The techniques introduced herein can enhance the
interpretability of over
100 classes of statistical and machine learning models, including
linear, GLM, GAM, mixed-effects, bayesian, categorical outcomes,
XGBoost, and more. With a single unified interface, users can compute
and plot many estimands, including:

- Predictions (aka fitted values or adjusted predictions)
- Comparisons such as contrasts, risk differences, risk ratios, odds, etc.
- Slopes (aka marginal effects or partial derivatives)
- Marginal means
- Linear and non-linear hypothesis tests
- Equivalence tests
- Uncertainty estimates using the delta method, bootstrapping, simulation, or conformal inference.
- Much more!

The Marginal Effects Zoo
book includes over 30 chapters of tutorials, case studies, and technical
notes. It covers a wide range of topics, including how the
`marginaleffects`

package can facilitate the analysis of:

- Experiments
- Observational data
- Causal inference with G-Computation
- Machine learning models
- Bayesian modeling
- Multilevel regression with post-stratification (MRP)
- Missing data
- Matching
- Inverse probability weighting
- Conformal prediction

Our article on `marginaleffects`

is provisionally accepted
for publication by the *Journal of Statistical Software*. You can
read the
preprint here.

To cite `marginaleffects`

in publications please use:

Arel-Bundock V, Greifer N, Heiss A (Forthcoming). “How to Interpret
Statistical Models Using marginaleffects in R and Python.” *Journal
of Statistical Software*.

A BibTeX entry for LaTeX users is:

```
@Article{,
title = {How to Interpret Statistical Models Using {marginaleffects} in {R} and {Python}},
author = {Vincent Arel-Bundock and Noah Greifer and Andrew Heiss},
year = {Forthcoming},
journal = {Journal of Statistical Software},
}
```

The `marginaleffects`

package for `R`

and
`Python`

offers a single point of entry to easily interpret
the results of over
100 classes of models, using a simple and consistent user interface.
Its benefits include:

*Powerful:*It can compute and plot predictions; comparisons (contrasts, risk ratios, etc.); slopes; and conduct hypothesis and equivalence tests for over 100 different classes of models in`R`

.*Simple:*All functions share a simple and unified interface.*Documented*: Each function is thoroughly documented with abundant examples. The Marginal Effects Zoo website includes 20,000+ words of vignettes and case studies.*Efficient:*Some operations can be up to 1000 times faster and use 30 times less memory than with the`margins`

package.

*Valid:*When possible, numerical results are checked against alternative software like`Stata`

or other`R`

packages.*Thin:*The`R`

package requires relatively few dependencies.*Standards-compliant:*`marginaleffects`

follows “tidy” principles and returns simple data frames that work with all standard`R`

functions. The outputs are easy to program with and feed to other packages like`ggplot2`

or`modelsummary`

.*Extensible:*Adding support for new models is very easy, often requiring less than 10 lines of new code. Please submit feature requests on Github.*Active development*: Bugs are fixed promptly.