Linear Models

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Linear (regression) models for Python. Extends statsmodels with Panel regression, instrumental variable estimators, system estimators and models for estimating asset prices:

• Panel models:

• High-dimensional Regression:

• Instrumental Variable estimators

• Factor Asset Pricing Models:

• System Regression:

Designed to work equally well with NumPy, Pandas or xarray data.

Panel models

Like statsmodels to include, supports formulas for specifying models. For example, the classic Grunfeld regression can be specified

import numpy as np
from statsmodels.datasets import grunfeld
data = grunfeld.load_pandas().data
data.year = data.year.astype(np.int64)
MultiIndex, entity - time
data = data.set_index(['firm','year'])
from linearmodels import PanelOLS
mod = PanelOLS(data.invest, data[['value','capital']], entity_effects=True)
res = mod.fit(cov_type='clustered', cluster_entity=True)

Models can also be specified using the formula interface.

from linearmodels import PanelOLS
mod = PanelOLS.from_formula('invest ~ value + capital + EntityEffects', data)
res = mod.fit(cov_type='clustered', cluster_entity=True)

The formula interface for PanelOLS supports the special values EntityEffects and TimeEffects which add entity (fixed) and time effects, respectively.

Formula support comes from the formulaic package which is a replacement for patsy.

Instrumental Variable Models

IV regression models can be similarly specified.

import numpy as np
from linearmodels.iv import IV2SLS
from linearmodels.datasets import mroz
data = mroz.load()
mod = IV2SLS.from_formula('np.log(wage) ~ 1 + exper + exper ** 2 + [educ ~ motheduc + fatheduc]', data)

The expressions in the [ ] indicate endogenous regressors (before ~) and the instruments.

Installation

The latest release can be installed using pip

pip install linearmodels

Binary wheels are available for Windows, macOS and Linux. Without a wheel, pip builds linearmodels from source, which requires a C compiler.

The main branch can be installed by cloning the repo and building it with pip. The build uses meson-python, and pip installs the other build requirements (Cython, NumPy and setuptools_scm) automatically.

git clone https://github.com/bashtage/linearmodels
cd linearmodels
pip install .

To work on linearmodels, install the requirements and then build an editable install

python -m pip install -r requirements.txt -r requirements-dev.txt
python -m pip install -e . --no-build-isolation

Documentation

Stable Documentation is built by GitHub Actions when a release is published. Development Documentation is built by the same workflow on every push to main.

Plan and status

• Linear Instrumental variable estimation - complete
• Linear Panel model estimation - complete
• Fama-MacBeth regression - complete
• Linear Factor Asset Pricing - complete
• System regression - complete
• Linear IV Panel model estimation - _not started_
• Dynamic Panel model estimation - _not started_

Requirements

**linearmodels 7.1 is the last release that supports Python 3.10 and NumPy 1.x (NumPy < 2).** Later releases will raise the minimum supported versions of Python, NumPy and the other dependencies.

Running

• Python 3.10+
• NumPy (1.23.5+)
• SciPy (1.8+)
• pandas (1.4+)
• statsmodels (0.14.6+)
• formulaic (1.2.1+)
• pyhdfe (0.2.0+)
• mypy_extensions (0.4+)
• packaging
• xarray (0.16+, optional)

Building from source

• A C compiler
• Cython (3.1.0+)
• meson-python
• NumPy (2.0+)
• setuptools_scm (9.2+)

Testing

• pytest (9.0+)

Documentation

• sphinx
• sphinx-immaterial
• nbsphinx
• nbconvert
• nbformat
• ipython
• jupyter