Logit Example

This page mirrors examples/logit_example.py.

1 Fit A Binary Logit Model

import numpy as np
from pprint import pprint

from crabbymetrics import Logit

np.set_printoptions(precision=4, suppress=True)

rng = np.random.default_rng(2)
n = 800
k = 4
beta = np.array([1.2, -0.8, 0.4, -1.1])
intercept = 0.3

x = rng.normal(size=(n, k))
logits = intercept + x @ beta
probs = 1.0 / (1.0 + np.exp(-logits))
y = rng.binomial(1, probs).astype(np.int32)

model = Logit(alpha=1.0, max_iterations=200)
model.fit(x, y)

print("true intercept:", intercept)
print("true coef:", beta)
pprint(model.summary())

true intercept: 0.3
true coef: [ 1.2 -0.8  0.4 -1.1]
{'coef': array([ 1.1245, -0.785 ,  0.4493, -1.1894]),
 'coef_se': array([0.1058, 0.1029, 0.0934, 0.1113]),
 'intercept': 0.2866745643642197,
 'intercept_se': 0.09089945628323781,
 'vcov': array([[ 0.0083,  0.0014, -0.001 ,  0.0007, -0.0008],
       [ 0.0014,  0.0112, -0.0028,  0.0017, -0.004 ],
       [-0.001 , -0.0028,  0.0106, -0.0004,  0.0031],
       [ 0.0007,  0.0017, -0.0004,  0.0087, -0.0016],
       [-0.0008, -0.004 ,  0.0031, -0.0016,  0.0124]])}

2 Prediction surfaces

predict_lin() returns the latent index \(x_i'\hat\beta + \hat\alpha\). predict() applies the inverse-logit link to return fitted probabilities. predict_label() thresholds those probabilities into class labels.

check = x[:8]
out = {
    "eta": model.predict_lin(check),
    "probability": model.predict(check),
    "label@0.50": model.predict_label(check),
    "label@0.35": model.predict_label(check, cutoff=0.35),
}
pprint(out)

{'eta': array([ 3.628 ,  0.3457,  1.8463,  0.8611,  2.4948,  0.7456,  1.4082,
       -0.2518]),
 'label@0.35': array([1, 1, 1, 1, 1, 1, 1, 1], dtype=int32),
 'label@0.50': array([1, 1, 1, 1, 1, 1, 1, 0], dtype=int32),
 'probability': array([0.9741, 0.5856, 0.8637, 0.7029, 0.9238, 0.6782, 0.8035, 0.4374])}