docs/source/gettingstarted.rst
This very simple case-study is designed to get you up-and-running quickly with
statsmodels. Starting from raw data, we will show the steps needed to
estimate a statistical model and to draw a diagnostic plot. We will only use
functions provided by statsmodels or its pandas and patsy
dependencies.
After installing statsmodels and its dependencies <install.html>_, we load a
few modules and functions:
.. ipython:: python
import statsmodels.api as sm
import pandas
from patsy import dmatrices
pandas <https://pandas.pydata.org/>_ builds on numpy arrays to provide
rich data structures and data analysis tools. The pandas.DataFrame function
provides labelled arrays of (potentially heterogenous) data, similar to the
R "data.frame". The pandas.read_csv function can be used to convert a
comma-separated values file to a DataFrame object.
patsy <https://github.com/pydata/patsy>_ is a Python library for describing
statistical models and building Design Matrices <https://en.wikipedia.org/wiki/Design_matrix>_ using R-like formulas.
.. note::
This example uses the API interface. See :ref:importpaths for information on
the difference between importing the API interfaces (statsmodels.api and
statsmodels.tsa.api) and directly importing from the module that defines
the model.
We download the Guerry dataset <https://vincentarelbundock.github.io/Rdatasets/doc/HistData/Guerry.html>, a
collection of historical data used in support of Andre-Michel Guerry's 1833
Essay on the Moral Statistics of France. The data set is hosted online in
comma-separated values format (CSV) by the Rdatasets <https://github.com/vincentarelbundock/Rdatasets/> repository.
We could download the file locally and then load it using read_csv, but
pandas takes care of all of this automatically for us:
.. ipython:: python
df = sm.datasets.get_rdataset("Guerry", "HistData").data
The Input/Output doc page <iolib.html>_ shows how to import from various
other formats.
We select the variables of interest and look at the bottom 5 rows:
.. ipython:: python
vars = ['Department', 'Lottery', 'Literacy', 'Wealth', 'Region']
df = df[vars]
df[-5:]
Notice that there is one missing observation in the Region column. We
eliminate it using a DataFrame method provided by pandas:
.. ipython:: python
df = df.dropna()
df[-5:]
We want to know whether literacy rates in the 86 French departments are associated with per capita wagers on the Royal Lottery in the 1820s. We need to control for the level of wealth in each department, and we also want to include a series of dummy variables on the right-hand side of our regression equation to control for unobserved heterogeneity due to regional effects. The model is estimated using ordinary least squares regression (OLS).
To fit most of the models covered by statsmodels, you will need to create
two design matrices. The first is a matrix of endogenous variable(s) (i.e.
dependent, response, regressand, etc.). The second is a matrix of exogenous
variable(s) (i.e. independent, predictor, regressor, etc.). The OLS coefficient
estimates are calculated as usual:
.. math::
\hat{\beta} = (X'X)^{-1} X'y
where :math:y is an :math:N \times 1 column of data on lottery wagers per
capita (Lottery). :math:X is :math:N \times 7 with an intercept, the
Literacy and Wealth variables, and 4 region binary variables.
The patsy module provides a convenient function to prepare design matrices
using R-like formulas. You can find more information here <https://patsy.readthedocs.io/en/latest/>_.
We use patsy's dmatrices function to create design matrices:
.. ipython:: python
y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe')
The resulting matrices/data frames look like this:
.. ipython:: python
y[:3]
X[:3]
Notice that dmatrices has
pandas DataFrames instead of simple numpy arrays. This is useful because DataFrames allow statsmodels to carry-over meta-data (e.g. variable names) when reporting results.The above behavior can of course be altered. See the patsy doc pages <https://patsy.readthedocs.io/en/latest/>_.
Fitting a model in statsmodels typically involves 3 easy steps:
For OLS, this is achieved by:
.. ipython:: python
mod = sm.OLS(y, X) # Describe model
res = mod.fit() # Fit model
print(res.summary()) # Summarize model
The res object has many useful attributes. For example, we can extract
parameter estimates and r-squared by typing:
.. ipython:: python
res.params
res.rsquared
Type dir(res) for a full list of attributes.
For more information and examples, see the Regression doc page <regression.html>_
statsmodels allows you to conduct a range of useful regression diagnostics and specification tests <stats.html#residual-diagnostics-and-specification-tests>_. For instance,
apply the Rainbow test for linearity (the null hypothesis is that the
relationship is properly modelled as linear):
.. ipython:: python
sm.stats.linear_rainbow(res)
Admittedly, the output produced above is not very verbose, but we know from
reading the docstring <generated/statsmodels.stats.diagnostic.linear_rainbow.html>_
(also, print(sm.stats.linear_rainbow.__doc__)) that the
first number is an F-statistic and that the second is the p-value.
statsmodels also provides graphics functions. For example, we can draw a
plot of partial regression for a set of regressors by:
.. ipython:: python
@savefig gettingstarted_0.png
sm.graphics.plot_partregress('Lottery', 'Wealth', ['Region', 'Literacy'],
data=df, obs_labels=False)
Documentation can be accessed from an IPython session
using :func:~statsmodels.tools.web.webdoc.
.. autosummary:: :nosignatures: :toctree: generated/
~statsmodels.tools.web.webdoc
Congratulations! You're ready to move on to other topics in the
Table of Contents <index.html#table-of-contents>_