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# 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:

• Fixed effects (maximum two-way)
• First difference regression
• Between estimator for panel data
• Pooled regression for panel data
• Fama-MacBeth estimation of panel models
• High-dimensional Regresssion:

• Absorbing Least Squares
• Instrumental Variable estimators

• Two-stage Least Squares
• Limited Information Maximum Likelihood
• k-class Estimators
• Generalized Method of Moments, also with continuously updating
• Factor Asset Pricing Models:

• 2- and 3-step estimation
• Time-series estimation
• GMM estimation
• System Regression:

• Seemingly Unrelated Regression (SUR/SURE)
• Three-Stage Least Squares (3SLS)
• Generalized Method of Moments (GMM) System Estimation

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

### Panel models

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

``````import numpy as np
from statsmodels.datasets import grunfeld
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.

### Instrumental Variable Models

IV regression models can be similarly specified.

``````import numpy as np
from linearmodels.iv import IV2SLS
from linearmodels.datasets import mroz
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.

## Installing

The latest release can be installed using pip

``````pip install linearmodels
``````

The main branch can be installed by cloning the repo and running setup

``````git clone https://github.com/bashtage/linearmodels
cd linearmodels
python setup.py install
``````

## Documentation

Stable Documentation is built on every tagged version using doctr. Development Documentation is automatically built on every successful build of main.

## Plan and status

Should eventually add some useful linear model estimators such as panel regression. Currently only the single variable IV estimators are polished.

• 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

### Running

With the exception of Python 3 (3.7+ tested), which is a hard requirement, the others are the version that are being used in the test environment. It is possible that older versions work.

• Python 3.7+
• NumPy (1.15+)
• SciPy (1.3+)
• pandas (0.25+)
• statsmodels (0.11+)
• xarray (0.13+, optional)
• Cython (0.29.21+, optional)

• py.test

### Documentation

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

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