linearmodels.panel.results.PanelResults.wald_test¶
-
PanelResults.wald_test(restriction: ndarray | DataFrame | None =
None
, value: ndarray | Series | None =None
, *, formula: str | list[str] | None =None
) WaldTestStatistic [source]¶ Test linear equality constraints using a Wald test
- Parameters:¶
- restriction: ndarray | DataFrame | None =
None
¶ q by nvar array containing linear weights to apply to parameters when forming the restrictions. It is not possible to use both restriction and formula.
- value: ndarray | Series | None =
None
¶ q element array containing the restricted values.
- formula: str | list[str] | None =
None
¶ formulaic linear constraints. The simplest formats are one of:
A single comma-separated string such as “x1=0, x2+x3=1”
A list of strings where each element is a single constraint such as [“x1=0”, “x2+x3=1”]
A single string without commas to test simple constraints such as “x1=x2=x3=0”
A dictionary where each key is a parameter restriction and the corresponding value is the restriction value, e.g., {“x1”: 0, “x2+x3”: 1}.
It is not possible to use both
restriction
andformula
.
- restriction: ndarray | DataFrame | None =
- Returns:¶
Test statistic for null that restrictions are valid.
- Return type:¶
Notes
Hypothesis test examines whether \(H_0:C\theta=v\) where the matrix C is
restriction
and v isvalue
. The test statistic has a \(\chi^2_q\) distribution where q is the number of rows in C.Examples
>>> from linearmodels.datasets import wage_panel >>> import statsmodels.api as sm >>> import numpy as np >>> import pandas as pd >>> data = wage_panel.load() >>> year = pd.Categorical(data.year) >>> data = data.set_index(["nr", "year"]) >>> data["year"] = year >>> from linearmodels.panel import PanelOLS >>> exog_vars = ["expersq", "union", "married", "year"] >>> exog = sm.add_constant(data[exog_vars])
>>> mod = PanelOLS(data.lwage, exog, entity_effects=True) >>> fe_res = mod.fit()
Test the restriction that union and married have 0 coefficients
>>> restriction = np.zeros((2, 11)) >>> restriction[0, 2] = 1 >>> restriction[1, 3] = 1 >>> value = np.array([0, 0]) >>> wald_res = fe_res.wald_test(restriction, value)
The same test using formulas
>>> formula = "union = married = 0" >>> wald_res = fe_res.wald_test(formula=formula)