models.GlmFit

A fitted GLM, from Glm.fit.

Usage

models.GlmFit()

Attributes

Name	Description
aic	AIC, -2 loglik + 2 p.
coefficients	Estimated coefficients.
covariance	Covariance of the coefficients, as a list of rows.
deviance	Residual deviance.
df_resid	Residual degrees of freedom.
dispersion	Dispersion.
fitted	Fitted means on the training data.
input_hash	Hash of the training data (design, offset, weights, response).
iterations	IRLS iterations used.
log_likelihood	Log-likelihood.
names	Coefficient names.
null_deviance	Deviance of the intercept-and-offset model.
p_values	Two-sided p-values (normal for a fixed dispersion, Student’s t when
std_errors	Standard errors.

---

aic

AIC, -2 loglik + 2 p.

aic: float

---

coefficients

Estimated coefficients.

coefficients: list[float]

---

covariance

Covariance of the coefficients, as a list of rows.

covariance: list[list[float]]

---

deviance

Residual deviance.

deviance: float

---

df_resid

Residual degrees of freedom.

df_resid: float

---

dispersion

Dispersion.

dispersion: float

---

fitted

Fitted means on the training data.

fitted: list[float]

---

input_hash

Hash of the training data (design, offset, weights, response).

input_hash: str

---

iterations

IRLS iterations used.

iterations: int

---

log_likelihood

Log-likelihood.

log_likelihood: float

---

names

Coefficient names.

names: list[str]

---

null_deviance

Deviance of the intercept-and-offset model.

null_deviance: float

---

p_values

Two-sided p-values (normal for a fixed dispersion, Student’s t when

p_values: list[float]

it is estimated).

---

std_errors

Standard errors.

std_errors: list[float]

Methods

Name	Description
from_json()	Reads an artifact written by to_json.
predict()	Expected response for each row.
predict_distribution()	Joint predictive distribution across the rows, with parameter and
robust_covariance()	Sandwich (heteroskedasticity- or cluster-robust) covariance of the
robust_std_errors()	Square roots of the diagonal of robust_covariance, with the same
to_json()	The fit as a versioned JSON artifact: spec, estimates, covariance,

---

from_json()

Reads an artifact written by to_json.

Usage

from_json(text)

Parameters

text: str

Returns

GlmFit

Raises

ValueError

For malformed JSON, another format, a newer format version or inconsistent fields.

---

predict()

Expected response for each row.

Usage

predict(design)

Parameters

design: Design

Same columns as the training design.

Returns

list of float

---

predict_distribution()

Joint predictive distribution across the rows, with parameter and

Usage

predict_distribution(design, n_sims, seed, parameters="normal")

process uncertainty, keyed row = 0, 1, ....

Parameters

design: Design

n_sims: int

seed: int

parameters: (normal, mean_preserving, fixed) = "normal"

How the coefficients are drawn: beta ~ N(beta_hat, Sigma) (through a log link the draws’ mean is mu_hat * exp(x' Sigma x / 2)); the same with each row’s linear predictor shifted so its draws average the fitted mean exactly (log or identity link); or fixed at beta_hat (process uncertainty only).

Returns

PredictiveDistribution

---

robust_covariance()

Sandwich (heteroskedasticity- or cluster-robust) covariance of the

Usage

robust_covariance(design, y, kind="HC0", groups=None)

coefficients, as statsmodels’ cov_type="HC0" and "cluster".

It stays valid when the variance function or dispersion is wrong, as long as the mean is right. The dispersion cancels. For a non-canonical link it uses the observed information, as statsmodels does (R’s sandwich uses the expected).

Parameters

design: Design

The design the model was fitted on.

y: list of float

The response the model was fitted on.

kind: (HC0, HC1, cluster) = "HC0"

"HC1" scales HC0 by n / (n - p); "cluster" sums the scores within each cluster and scales by G / (G - 1) * (n - 1) / (n - p).

groups: list of int or str = None

One cluster label per row, for kind="cluster": a policy or an event, say.

Returns

list of list of float

Examples

>>> from prospicio.models import Design, Glm
>>> d = Design([[1.0] * 6, [0.0, 0.0, 0.0, 1.0, 1.0, 1.0]], ["(Intercept)", "x"])
>>> y = [1.0, 2.0, 6.0, 1.0, 4.0, 2.0]
>>> fit = Glm("poisson").fit(d, y)
>>> round(fit.robust_covariance(d, y)[0][0] * 81, 10)

14.0

>>> se = fit.robust_std_errors(d, y, "cluster", groups=[1, 1, 2, 2, 3, 3])

---

robust_std_errors()

Square roots of the diagonal of robust_covariance, with the same

Usage

robust_std_errors(design, y, kind="HC0", groups=None)

arguments.

Parameters

design: Design

y: list of float

kind: (HC0, HC1, cluster) = "HC0"

groups: list of int or str = None

Returns

list of float

---

to_json()

The fit as a versioned JSON artifact: spec, estimates, covariance,

Usage

to_json()

fit statistics, fitted values and provenance (crate version and a hash of the training data). GlmFit.from_json reads it back exactly; pickling uses it too.

Returns

str

Examples

>>> import pickle
>>> from prospicio.models import Design, Glm, GlmFit
>>> d = Design([[1.0] * 4, [0.0, 1.0, 2.0, 3.0]], ["(Intercept)", "x"])
>>> fit = Glm("poisson").fit(d, [1.0, 2.0, 2.0, 5.0])
>>> GlmFit.from_json(fit.to_json()).coefficients == fit.coefficients

True

>>> pickle.loads(pickle.dumps(fit)).input_hash == fit.input_hash

True