Poisson

Poisson GLM for count outcomes

Code 
from _api_doc_utils import *

1 Where it fits

Group: Regression

Poisson fits

\[ \mathbb E[Y_i\mid X_i=x_i]=\exp(\alpha+x_i'\beta). \]

The alpha constructor argument is an L2 penalty, not the intercept. For alpha=0, summary(vcov='vanilla') reports Fisher-information standard errors and summary(vcov='sandwich') reports robust QMLE-style standard errors. Penalized fits mark inference unavailable and omit se/vcov.

2 Python API

Constructor: cm.Poisson

Use fit(x, y) with nonnegative count-like outcomes. predict(x) returns fitted conditional means. The class also supports bootstrap(B, seed=None).

Code 
print(inspect.signature(cm.Poisson))
Code 
cls = cm.Poisson
display(HTML(html_table(["Public method"], public_methods(cls))))

3 Minimal example

Code 
rng = np.random.default_rng(7)
x = rng.normal(size=(250, 2))
mu = np.exp(0.2 + x @ np.array([0.4, -0.25]))
y = rng.poisson(mu).astype(float)
model = cm.Poisson(max_iterations=200, tolerance=1e-08)
model.fit(x, y)
print(model.summary(vcov='vanilla')['coef'])
print(model.summary(vcov='sandwich')['coef_se'])
print(model.predict(x[:3]))

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.

Code 
rng = np.random.default_rng(107)
x = rng.normal(size=(100, 2))
y = rng.poisson(np.exp(0.2 + x @ np.array([0.4, -0.25]))).astype(float)
model = cm.Poisson(max_iterations=200)
model.fit(x, y)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))