Python statsmodels logit wald test input

Question

I have fitted a logisitic regression model to some data, everything is working great. I need to calculate the wald statistic which is a function of the model result.

My problem is that I do not understand, from the documentation, what the wald test requires as input? Specifically what is the R matrix and how is it generated?

I tried simply inputting the data I used to train and test the model as the R matrix, but I do not think this is correct. The documentation suggest examining the examples however none give an example of this test. I also asked the same question on crossvalidated but got shot down.

Kind regards

http://statsmodels.sourceforge.net/0.6.0/generated/statsmodels.discrete.discrete_model.LogitResults.wald_test.html#statsmodels.discrete.discrete_model.LogitResults.wald_test

Answer 1

The Wald test is used to test if a predictor is significant or not, of the form:

W = (beta_hat - beta_0) / SE(beta_hat) ~ N(0,1)

So somehow you'll want to input the predictors into the test. Judging from the example of the t.test and f.test, it may be simpler to input a string or tuple to indicate what you are testing.

Here is their example using a string for the f.test:

from statsmodels.datasets import longley
from statsmodels.formula.api import ols
dta = longley.load_pandas().data
formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
results = ols(formula, dta).fit()
hypotheses = '(GNPDEFL = GNP), (UNEMP = 2), (YEAR/1829 = 1)'
f_test = results.f_test(hypotheses)
print(f_test)

And here is their example using a tuple:

import numpy as np
import statsmodels.api as sm
data = sm.datasets.longley.load()
data.exog = sm.add_constant(data.exog)
results = sm.OLS(data.endog, data.exog).fit()
r = np.zeros_like(results.params)
r[5:] = [1,-1]
T_test = results.t_test(r)

If you're still struggling getting the wald test to work, include your code and I can try to help make it work.