Predict#

predict() returns the mean on the response scale for new rows, with an optional offset and a choice of conditional or population random effects. relativities() returns plot-ready relativity tables for every feature, the multiplicative form a rating engine wants from a log-link model (under other links they are exponentiated link-scale contributions, not factors of the mean); reconstruct_feature() returns one feature’s fitted curve or effect on its original scale.

predict

Predict the response mean for new data.

relativities

Extract plot-ready relativity DataFrames for all features.

reconstruct_feature

Reconstruct a fitted feature's curve or effect on its original scale.

Example#

The same simulated motor book as the rest of this section: 4,000 policies, a non-linear age effect, four regions and a mild vehicle-power slope, with exposure carried as a log offset.

import numpy as np
import pandas as pd

from superglm import Categorical, Numeric, Spline, SuperGLM

rng = np.random.default_rng(0)
n = 4000
region = rng.choice(["North", "South", "East", "West"], n, p=[0.35, 0.3, 0.2, 0.15])
age = rng.uniform(18, 80, n)
veh_power = rng.uniform(4, 12, n)
exposure = rng.uniform(0.1, 1.0, n)
region_effect = pd.Series(region).map(
    {"North": 0.0, "South": 0.25, "East": -0.2, "West": 0.4}
).to_numpy()
log_rate = (
    -1.2
    + 1.1 * np.exp(-((age - 24) ** 2) / 90.0)
    + 0.004 * (age - 50) ** 2 / 10.0
    + region_effect
    + 0.09 * (veh_power - 8)
)
claims = rng.poisson(np.exp(log_rate) * exposure)
X = pd.DataFrame({"age": age, "region": region, "veh_power": veh_power})
offset = np.log(exposure)

model = SuperGLM(
    family="poisson",
    features={
        "age": Spline(kind="cr", k=10),
        "region": Categorical(),
        "veh_power": Numeric(),
    },
).fit_reml(X, claims, offset=offset)
model.reml_diagnostics()["converged"]

True

Three hand-written policies are enough to price. The model was fitted with exposure in the offset, so predict with no offset returns the expected claim count at one unit of exposure — a rate. Pass the offset for the exposure you are actually rating and the mean scales with it: at half a year every number below halves, because the offset enters the log link with a coefficient of one.

new_policies = pd.DataFrame(
    {
        "age": [22.0, 45.0, 70.0],
        "region": ["West", "North", "East"],
        "veh_power": [10.0, 7.0, 6.0],
    }
)
new_policies.assign(
    rate=model.predict(new_policies),
    half_year=model.predict(new_policies, offset=np.log(np.full(3, 0.5))),
).round(4)
age region veh_power rate half_year
0 22.0 West 10.0 1.8437 0.9218
1 45.0 North 7.0 0.2886 0.1443
2 70.0 East 6.0 0.2160 0.1080

relativities is the rating-engine view of the same fit: one table per feature, multiplicative because the link is log. The region table is keyed by level against the reference level, and the ordering it recovers — East cheapest, then North, South and West — is the ordering the data was simulated with.

model.relativities()["region"].round(3)
level relativity log_relativity
0 East 0.805 -0.217
1 North 1.000 0.000
2 South 1.435 0.361
3 West 1.493 0.401

reconstruct_feature returns one feature’s fitted curve on its original scale, with the interior knots and the coefficients in the original basis alongside, which is what an external renderer or a rating engine needs to redraw the smooth without SuperGLM in the loop.

age_curve = model.reconstruct_feature("age")
print("interior knots:", np.round(age_curve["knots_interior"], 1))
pd.DataFrame(
    {key: age_curve[key] for key in ("x", "log_relativity", "relativity")}
).head().round(3)

interior knots: [24.9 31.8 38.7 45.6 52.4 59.3 66.2 73.1]
x log_relativity relativity
0 18.007 0.988 2.687
1 18.318 0.981 2.668
2 18.630 0.974 2.649
3 18.941 0.967 2.630
4 19.253 0.960 2.611
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