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py-glm

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Generalized Linear Models in Sklearn Style

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# py-glm: Generalized Linear Models in Python

`py-glm` is a library for fitting, inspecting, and evaluating Generalized Linear Models in python.

## Installation

The `py-glm` library can be installed directly from github.

```
pip install git+https://github.com/madrury/py-glm.git
```

## Features

### Model Fitting

`py-glm` supports models from various exponential families:

```python
from glm.glm import GLM
from glm.families import Gaussian, Bernoulli, Poisson, Exponential

linear_model = GLM(family=Gaussian())
logistic_model = GLM(family=Bernoulli())
poisson_model = GLM(family=Poisson())
exponential_model = GLM(family=Exponential())
```

Models with dispersion parameters are also supported.  The dispersion parameters
in these models are estimated using the deviance.

```python
from glm.families import QuasiPoisson, Gamma

quasi_poisson_model = GLM(family=QuasiPoisson())
gamma_model = GLM(family=Gamma())
```

Fitting a model proceeds in `sklearn` style, and uses the Fisher scoring algorithm:

```python
logistic_model.fit(X, y_logistic)
```

If your data resides in a `pandas.DataFrame`, you can pass this to `fit` along with a model formula.

```
logistic_model.fit(X, formula="y ~ Moshi + SwimSwim")
```

Offsets and sample weights are supported when fitting:

```python
linear_model.fit(X, y_linear, sample_weights=sample_weights)
poisson_nmodel.fit(X, y_poisson, offset=np.log(expos))
```

Predictions are also made in sklearn style:

```python
logistic_model.predict(X)
```

**Note:** There is one major place we deviate from the sklearn interface.  The `predict` method on a `GLM` object **always** returns an estimate of the conditional expectation `E[y | X]`.  This is in contrast to sklearn behavior for classification models, where it returns a class assignment.  We make this choice so that the `py-glm` library is consistent with its use of `predict`.  If the user would like class assignments from a model, they will need to threshold the probability returned by `predict` manually.

### Inference

Once the model is fit, parameter estimates, parameter covariance estimates, and p-values from a standard z-test are available:

```python
logistic_model.coef_
logistic_model.coef_covariance_matrix_
logistic_model.coef_standard_error_
logistic_model.p_values_
```

To get a quick summary, use the `summary` method:

```
logistic_model.summary()

Binomial GLM Model Summary.
===============================================
Name         Parameter Estimate  Standard Error
-----------------------------------------------
Intercept                  1.02            0.01
Moshi                     -2.00            0.02
SwimSwim                   1.00            0.02
```

Re-sampling methods are also supported in the `simulation` subpackage: the
parametric and non-parametric bootstraps:

```python
from glm.simulation import Simulation

sim = Simulation(logistic_model)
sim.parametric_bootstrap(X, n_sim=1000)
sim.non_parametric_bootstrap(X, n_sim=1000)
```

## Regularization

Ridge regression is supported for each model (note, the regularization parameter is called `alpha` instead of `lambda` due to `lambda` being a reserved word in python):

```python
logistic_model.fit(X, y_logistic, alpha=1.0)
```

## References

* Marlene Müller (2004). [Generalized Linear Models](http://www.marlenemueller.de/publications/HandbookCS.pdf).

## Warning

The `glmnet` code included in `glm.glmnet` is **experimental**.  Please use at your own risk.

py-glm

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