models.actual_vs_expected()

Actual against expected by period for a stored model’s predictions on

Usage

models.actual_vs_expected(
    periods,
    family,
    y,
    mu,
    weights=None,
    dispersion=1.0,
    theta=None,
    power=None
)

new data, with each period’s z-score under the model and a test for drift.

A = sum(w * y) and E = sum(w * mu) per period; the z-score is (A - E) / sqrt(dispersion * sum(w * V(mu))) with the family’s variance function V, about standard normal while the model holds. trend is the slope of A / E - 1 per period step (periods in sorted order), weighted by each period’s precision.

Parameters

periods: list of int or str

One period label per row.

family: str

y: list of float

Actuals.

mu: list of float

The model’s predicted means.

weights: list of float = None

Prior weights as fitted (exposure for a rate); leave out for counts with exposure in the offset.

dispersion: float = 1.0

theta: float = None

Negative binomial theta, Tweedie power.

power: float = None

Negative binomial theta, Tweedie power.

Returns

dict

periods (a list of dicts with period, n, weight, actual, expected, ratio, std_dev and z), total (the same without period), trend, trend_std_error and trend_z.

Examples

>>> from prospicio.models import actual_vs_expected
>>> m = actual_vs_expected([2023, 2023, 2024, 2024], "poisson",
...                        [1.0, 3.0, 2.0, 6.0], [2.0, 2.0, 2.0, 2.0])
>>> m["periods"][1]["ratio"], m["periods"][1]["z"]

(2.0, 2.0)