linearmodels.system.model.IV3SLS.from_formula¶

Specify a 3SLS using the formula interface

Parameters:¶

formula: str | dict[str, str]¶: Either a string or a dictionary of strings where each value in the dictionary represents a single equation. See Notes for a description of the accepted syntax
data: DataFrame¶: Frame containing named variables
sigma: ndarray | DataArray | DataFrame | Series | None = None¶: Prespecified residual covariance to use in GLS estimation. If not provided, FGLS is implemented based on an estimate of sigma.
weights: Mapping[str, ndarray | DataArray | DataFrame | Series] | None = None¶: Dictionary like object (e.g. a DataFrame) containing variable weights. Each entry must have the same number of observations as data. If an equation label is not a key weights, the weights will be set to unity

Returns:¶

model – Model instance

Return type:¶

linearmodels.system.model.IV3SLS

Notes

Models can be specified in one of two ways. The first uses curly braces to encapsulate equations. The second uses a dictionary where each key is an equation name.

Examples

The simplest format uses standard formulas for each equation in a dictionary. Best practice is to use an Ordered Dictionary

>>> import pandas as pd
>>> import numpy as np
>>> cols = ["y1", "x1_1", "x1_2", "z1", "y2", "x2_1", "x2_2", "z2"]
>>> data = pd.DataFrame(np.random.randn(500, 8), columns=cols)
>>> from linearmodels.system import IV3SLS
>>> formula = {"eq1": "y1 ~ 1 + x1_1 + [x1_2 ~ z1]",
...            "eq2": "y2 ~ 1 + x2_1 + [x2_2 ~ z2]"}
>>> mod = IV3SLS.from_formula(formula, data)

The second format uses curly braces {} to surround distinct equations

>>> formula = "{y1 ~ 1 + x1_1 + [x1_2 ~ z1]} {y2 ~ 1 + x2_1 + [x2_2 ~ z2]}"
>>> mod = IV3SLS.from_formula(formula, data)

It is also possible to include equation labels when using curly braces

>>> formula = "{eq1: y1 ~ x1_1 + [x1_2 ~ z1]} {eq2: y2 ~ 1 + [x2_2 ~ z2]}"
>>> mod = IV3SLS.from_formula(formula, data)