Logit

Binary logistic regression

from _api_doc_utils import *

1 Where it fits

Group: Regression

Logit models a binary outcome through

\[ \Pr(Y_i=1\mid X_i=x_i)=\Lambda(\alpha+x_i'\beta), \]

with optional L2 regularization controlled by alpha. predict(x) returns probabilities for label 1; predict_label(x) returns class labels.

2 Python API

Constructor: cm.Logit

Fit with integer labels using fit(x, y_int32). summary() returns intercept and coefficient estimates. Fisher-information standard errors are available only for the unpenalized fit (alpha=0); penalized fits are explicitly prediction-only. bootstrap() resamples observations and refits the classifier.

print(inspect.signature(cm.Logit))
(alpha=0.0, max_iterations=100, gradient_tolerance=0.0001)
cls = cm.Logit
display(HTML(html_table(["Public method"], public_methods(cls))))
Public method
bootstrap(self, /, n_bootstrap, seed=None)
fit(self, /, x, y)
predict(self, /, x)
predict_label(self, /, x, cutoff=0.5)
predict_lin(self, /, x)
summary(self, /)
wald_test(self, /, r, q=None)

3 Minimal example

rng = np.random.default_rng(5)
x = rng.normal(size=(220, 3))
eta = -0.2 + x @ np.array([0.7, -0.4, 0.9])
p = 1 / (1 + np.exp(-eta))
y = rng.binomial(1, p, size=220).astype(np.int32)
model = cm.Logit(max_iterations=200)
model.fit(x, y)
print(model.summary()['coef'])
print(model.predict(x[:5]))
[ 0.56568906 -0.58550069  0.85818987]
[0.5239276  0.4143503  0.68494357 0.42404209 0.2112137 ]

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

rng = np.random.default_rng(105)
x = rng.normal(size=(90, 3))
p = 1 / (1 + np.exp(-(x @ np.array([0.7, -0.4, 0.9]))))
y = rng.binomial(1, p, size=90).astype(np.int32)
model = cm.Logit(max_iterations=200)
model.fit(x, y)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))
summary() key shape
intercept ()
coef (3,)
penalty ()
inference_available ()
intercept_se ()
coef_se (3,)
vcov (4, 4)