Generalized Linear Models in Python

# Glimpy

glimpy is a Python module for fitting generalized linear models. It's based on the scikit-learn API to facilitate use with other scikit-learn tools (pipelines, cross-validation, etc.). Models are fit using the statsmodels package.

## Installation

pip install glimpy

## Important Notes

glimpy makes a few important departures from the scikit-learn API

#### Don't Regularize by Default

sklearn.linear_model.LogisticRegression regularizes by default. Its regularization paramater C is modeled after the SVM regularization parameter so lower values imply more regularization.

Glimpy does use the C parameter to regularize, so lower values imply more regularization. Glimpy does not regularize by default.

#### Don't Penalize Intercept Coefficient

Scikit-Learn and statsmodels penalize the intercept coefficient. Glimpy does not penalize the intercept coefficient when fit with intercept=True. If you want the intercept coefficient to be penalized add an intercept term to your dataset X and fit with intercept=False

## Getting Started

Here is an example of a poisson GLM to help get you started

We will simulate an experiment where we want to determine how an individual's age and weight influence the number of hospital visits they can expect to have in a given year.

>>> import numpy as np
>>> from scipy.stats import poisson
>>> from glimpy import GLM, Poisson
>>>
>>> np.random.seed(10)
>>> n_samples = 1000


Now we will simulate some data where observed individuals have ages ranging from 30 to 70, and weights normally distributed centered around 150 lbs.

>>> age = np.random.uniform(30, 70, n_samples)
>>> weight = np.random.normal(150, 20, n_samples)


Then we will have the expected number of hospital visits vary according to the following equation. We will sample from a poisson distribution with those means to get a sample of observed hospital visits

>>> expected_visits = np.exp(-10 + age * 0.05 + weight * 0.08)
>>> observed_visits = poisson.rvs(expected_visits)


Now we can fit a GLM object to try to recover the formula we specified above

>>> X = np.vstack([age, weight]).T
>>> y = observed_visits
>>> pglm = GLM(fit_intercept=True, family=Poisson())
>>> pglm.fit(X, y)
>>> print(pglm.summary())
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable:                      y   No. Observations:                 1000
Model:                            GLM   Df Residuals:                      997
Model Family:                 Poisson   Df Model:                            2
Method:                          IRLS   Log-Likelihood:                -3619.1
Date:                Thu, 09 Jan 2020   Deviance:                       967.43
Time:                        22:31:35   Pearson chi2:                     961.
No. Iterations:                     6
Covariance Type:            nonrobust
==============================================================================
coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const        -10.0132      0.020   -509.601      0.000     -10.052      -9.975
x1             0.0499      0.000    301.142      0.000       0.050       0.050
x2             0.0801      0.000    800.720      0.000       0.080       0.080
==============================================================================


## Scikit-Learn Integration

The upshot of glimpy is that you can use easily use your favorite scikit-learn tools with glimpy GLMs. For example, you can use the scikit-learn cross_val_score

>>> from sklearn.model_selection import cross_val_score
>>> print(cross_val_score(pglm, X, y, cv=4))
[-263.11969239 -288.58713533 -205.7032204  -220.68304592]


The following example demonstrates how to use glimpy alongside scikit-learn to perform grid search over elastic-net hyperparameters

>>> import statsmodels.api as sm
>>> from glimpy import GLM, Gamma
>>> from sklearn.preprocessing import StandardScaler
>>> from sklearn.pipeline import Pipeline
>>> from sklearn import datasets
>>> from sklearn.model_selection import GridSearchCV
>>>
>>>
>>> scaler = StandardScaler()
>>> gamma_glm = GLM(fit_intercept=True, family=Gamma(sm.families.links.log()), penalty='elasticnet')
>>> gamma_pipeline = Pipeline([('scaler', scaler), ('glm', gamma_glm)])
>>> grid_search = GridSearchCV(gamma_pipeline,
>>>     param_grid=[{
>>>         'glm__C': [1e4, 1e5, 1e6],
>>>         'glm__l1_ratio': [0.1, 0.5, 0.9]
>>>     }],
>>>     cv=3
>>> )
>>>
>>> grid_search.fit(diabetes['data'], diabetes['target'])
>>> print(grid_search.best_params_)
{'glm__C': 1000000.0, 'glm__l1_ratio': 0.1}


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