formulaic

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).

For more details, see here.

Related projects and prior art

• 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!