formulaic

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Formulaic is a high-performance implementation of Wilkinson formulas for Python.

Documentation: https://matthewwardrop.github.io/formulaic
Source Code: https://github.com/matthewwardrop/formulaic
Issue tracker: https://github.com/matthewwardrop/formulaic/issues

It provides:

high-performance dataframe to model-matrix conversions.
support for reusing the encoding choices made during conversion of one data-set on other datasets.
extensible formula parsing.
extensible data input/output plugins, with implementations for:
- input:
  - pandas.DataFrame
  - Any dataframe representation supported by narwhals including
    - pyarrow.Table
    - polars.DataFrame
    - ...
- output:
  - pandas.DataFrame
  - numpy.ndarray
  - scipy.sparse.CSCMatrix
  - narwhals dataframe passthrough when using narwhals dataframes.
support for symbolic differentiation of formulas (and hence model matrices).
and much more.

Example code

import pandas
from formulaic import Formula

df = pandas.DataFrame({
    'y': [0, 1, 2],
    'x': ['A', 'B', 'C'],
    'z': [0.3, 0.1, 0.2],
})

y, X = Formula('y ~ x + z').get_model_matrix(df)

y =

	y
0	0
1	1
2	2

X =

	Intercept	x[T.B]	x[T.C]	z
0	1.0	0	0	0.3
1	1.0	1	0	0.1
2	1.0	0	1	0.2

Note that the above can be short-handed to:

from formulaic import model_matrix
model_matrix('y ~ x + z', df)

Benchmarks

Formulaic typically outperforms R for both dense and sparse model matrices, and vastly outperforms patsy (the existing implementation for Python) for dense matrices (patsy does not support sparse model matrix output).

Benchmarks

For more details, see here.

Patsy: a prior implementation of Wilkinson formulas for Python, which is widely used (e.g. in statsmodels). It has fantastic documentation (which helped bootstrap this project), and a rich array of features.
StatsModels.jl @formula: The implementation of Wilkinson formulas for Julia.
R Formulas: The implementation of Wilkinson formulas for R, which is thoroughly introduced here. [R itself is an implementation of S, in which formulas were first made popular].
The work that started it all: Wilkinson, G. N., and C. E. Rogers. Symbolic description of factorial models for analysis of variance. J. Royal Statistics Society 22, pp. 392–399, 1973.

Used by

Below are some of the projects that use Formulaic:

Glum: High performance Python GLM's with all the features.
Lifelines: Survival analysis in Python.
Linearmodels: Additional linear models including instrumental variable and panel data models that are missing from statsmodels.
Pyfixest: Fast High-Dimensional Fixed Effects Regression in Python following fixest-syntax.
Tabmat: Efficient matrix representations for working with tabular data.
Add your project here!

Metadata

Release files for formulaic 1.2.2

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for formulaic 1.2.2
File	Size	Uploaded
formulaic-1.2.2.tar.gz	657.5 kB	Jun 2, 2026	Details

Built distribution (wheel)

Table of built distributions (wheels) for formulaic 1.2.2
File	Interpreter	ABI	Platform	Reset
formulaic-1.2.2-py3-none-any.whl 118.9 kB Jun 2, 2026	Python 3	none	any	Details

Total release size: 776.5 kB

Release files / formulaic-1.2.2.tar.gz

Download URL	formulaic-1.2.2.tar.gz
Size	657.5 kB
Tags	Source
SHA-256 checksum How to use checksums	`c99e8f11ff7d327eaecaf63855ca69b7fa0da100ad6c0041ef80912fbac667e6`
BLAKE2b-256 checksum How to use checksums	`f187e7b9b39d218793f159d7425e264c0ac196da07f1decc333001502fac02fb`
Upload date	Jun 2, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	No
Uploaded via	`Hatch/1.17.0 {"ci":true,"cpu":"x86_64","distro":{"id":"noble","libc":{"lib":"glibc","version":"2.39"},"name":"Ubuntu","version":"24.04"},"implementation":{"name":"CPython","version":"3.14.5"},"installer":{"name":"hatch","version":"1.17.0"},"openssl_version":"OpenSSL 3.0.13 30 Jan 2024","python":"3.14.5","system":{"name":"Linux","release":"6.17.0-1015-azure"}} HTTPX2/2.3.0`

Release files / formulaic-1.2.2-py3-none-any.whl

Download URL	formulaic-1.2.2-py3-none-any.whl
Size	118.9 kB
Tags	Python 3
SHA-256 checksum How to use checksums	`0f84ff49e3fc9dc0e68ab08a0a9427874021aa6c558e66b44dc634a35739b09b`
BLAKE2b-256 checksum How to use checksums	`fc750576b03f7889ad25b5385b4f6c69e0543713425a6f193b056c9b0a2e65ce`
Upload date	Jun 2, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	No
Uploaded via	`Hatch/1.17.0 {"ci":true,"cpu":"x86_64","distro":{"id":"noble","libc":{"lib":"glibc","version":"2.39"},"name":"Ubuntu","version":"24.04"},"implementation":{"name":"CPython","version":"3.14.5"},"installer":{"name":"hatch","version":"1.17.0"},"openssl_version":"OpenSSL 3.0.13 30 Jan 2024","python":"3.14.5","system":{"name":"Linux","release":"6.17.0-1015-azure"}} HTTPX2/2.3.0`