## models.GlmFit


A fitted GLM, from [Glm.fit](models.Glm.md#prospicio.models.Glm.fit).


Usage


``` python
models.GlmFit()
```


## Attributes

| Name | Description |
|----|----|
| [aic](#aic) | AIC, `-2 loglik + 2 p`. |
| [coefficients](#coefficients) | Estimated coefficients. |
| [covariance](#covariance) | Covariance of the coefficients, as a list of rows. |
| [deviance](#deviance) | Residual deviance. |
| [df_resid](#df_resid) | Residual degrees of freedom. |
| [dispersion](#dispersion) | Dispersion. |
| [fitted](#fitted) | Fitted means on the training data. |
| [input_hash](#input_hash) | Hash of the training data (design, offset, weights, response). |
| [iterations](#iterations) | IRLS iterations used. |
| [log_likelihood](#log_likelihood) | Log-likelihood. |
| [names](#names) | Coefficient names. |
| [null_deviance](#null_deviance) | Deviance of the intercept-and-offset model. |
| [p_values](#p_values) | Two-sided p-values (normal for a fixed dispersion, Student's t when |
| [std_errors](#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()](#from_json) | Reads an artifact written by [to_json](distributions.to_json.md#prospicio.distributions.to_json). |
| [predict()](#predict) | Expected response for each row. |
| [predict_distribution()](#predict_distribution) | Joint predictive distribution across the rows, with parameter and |
| [robust_covariance()](#robust_covariance) | Sandwich (heteroskedasticity- or cluster-robust) covariance of the |
| [robust_std_errors()](#robust_std_errors) | Square roots of the diagonal of [robust_covariance](models.GlmFit.md#prospicio.models.GlmFit.robust_covariance), with the same |
| [to_json()](#to_json) | The fit as a versioned JSON artifact: spec, estimates, covariance, |

------------------------------------------------------------------------


#### from_json()


Reads an artifact written by [to_json](distributions.to_json.md#prospicio.distributions.to_json).


Usage


``` python
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


``` python
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


``` python
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


``` python
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

``` python
>>> 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

``` python
>>> 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](models.GlmFit.md#prospicio.models.GlmFit.robust_covariance), with the same


Usage


``` python
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


``` python
to_json()
```


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


##### Returns


`str`  


##### Examples

``` python
>>> 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

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

True