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, we load a few modules and functions:
In [1]: import statsmodels.api as sm
In [2]: import pandas
In [3]: from patsy import dmatrices
pandas 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 is a Python library for describing statistical models and building Design Matrices using R-like formulas.
We download the Guerry dataset, 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 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:
In [4]: url = "http://vincentarelbundock.github.com/Rdatasets/csv/HistData/Guerry.csv"
...: #the next two lines are not necessary with a recent version of pandas
...:
In [6]: from urllib2 import urlopen
In [7]: url = urlopen(url)
---------------------------------------------------------------------------
URLError Traceback (most recent call last)
<ipython-input-7-baebfb7a69e3> in <module>()
----> 1 url = urlopen(url)
/usr/lib/python2.7/urllib2.pyc in urlopen(url, data, timeout)
125 if _opener is None:
126 _opener = build_opener()
--> 127 return _opener.open(url, data, timeout)
128
129 def install_opener(opener):
/usr/lib/python2.7/urllib2.pyc in open(self, fullurl, data, timeout)
402 req = meth(req)
403
--> 404 response = self._open(req, data)
405
406 # post-process response
/usr/lib/python2.7/urllib2.pyc in _open(self, req, data)
420 protocol = req.get_type()
421 result = self._call_chain(self.handle_open, protocol, protocol +
--> 422 '_open', req)
423 if result:
424 return result
/usr/lib/python2.7/urllib2.pyc in _call_chain(self, chain, kind, meth_name, *args)
380 func = getattr(handler, meth_name)
381
--> 382 result = func(*args)
383 if result is not None:
384 return result
/usr/lib/python2.7/urllib2.pyc in http_open(self, req)
1212
1213 def http_open(self, req):
-> 1214 return self.do_open(httplib.HTTPConnection, req)
1215
1216 http_request = AbstractHTTPHandler.do_request_
/usr/lib/python2.7/urllib2.pyc in do_open(self, http_class, req)
1182 except socket.error, err: # XXX what error?
1183 h.close()
-> 1184 raise URLError(err)
1185 else:
1186 try:
URLError: <urlopen error [Errno -2] Name or service not known>
In [8]: df = pandas.read_csv(url)
---------------------------------------------------------------------------
URLError Traceback (most recent call last)
<ipython-input-8-4107a55c8bef> in <module>()
----> 1 df = pandas.read_csv(url)
/usr/lib/python2.7/dist-packages/pandas/io/parsers.pyc in parser_f(filepath_or_buffer, sep, dialect, compression, doublequote, escapechar, quotechar, quoting, skipinitialspace, lineterminator, header, index_col, names, prefix, skiprows, skipfooter, skip_footer, na_values, na_fvalues, true_values, false_values, delimiter, converters, dtype, usecols, engine, delim_whitespace, as_recarray, na_filter, compact_ints, use_unsigned, low_memory, buffer_lines, warn_bad_lines, error_bad_lines, keep_default_na, thousands, comment, decimal, parse_dates, keep_date_col, dayfirst, date_parser, memory_map, nrows, iterator, chunksize, verbose, encoding, squeeze, mangle_dupe_cols, tupleize_cols, infer_datetime_format)
418 infer_datetime_format=infer_datetime_format)
419
--> 420 return _read(filepath_or_buffer, kwds)
421
422 parser_f.__name__ = name
/usr/lib/python2.7/dist-packages/pandas/io/parsers.pyc in _read(filepath_or_buffer, kwds)
204
205 filepath_or_buffer, _ = get_filepath_or_buffer(filepath_or_buffer,
--> 206 encoding)
207
208 if kwds.get('date_parser', None) is not None:
/usr/lib/python2.7/dist-packages/pandas/io/common.pyc in get_filepath_or_buffer(filepath_or_buffer, encoding)
116
117 if _is_url(filepath_or_buffer):
--> 118 req = _urlopen(str(filepath_or_buffer))
119 return maybe_read_encoded_stream(req, encoding)
120
/usr/lib/python2.7/urllib2.pyc in urlopen(url, data, timeout)
125 if _opener is None:
126 _opener = build_opener()
--> 127 return _opener.open(url, data, timeout)
128
129 def install_opener(opener):
/usr/lib/python2.7/urllib2.pyc in open(self, fullurl, data, timeout)
402 req = meth(req)
403
--> 404 response = self._open(req, data)
405
406 # post-process response
/usr/lib/python2.7/urllib2.pyc in _open(self, req, data)
420 protocol = req.get_type()
421 result = self._call_chain(self.handle_open, protocol, protocol +
--> 422 '_open', req)
423 if result:
424 return result
/usr/lib/python2.7/urllib2.pyc in _call_chain(self, chain, kind, meth_name, *args)
380 func = getattr(handler, meth_name)
381
--> 382 result = func(*args)
383 if result is not None:
384 return result
/usr/lib/python2.7/urllib2.pyc in http_open(self, req)
1212
1213 def http_open(self, req):
-> 1214 return self.do_open(httplib.HTTPConnection, req)
1215
1216 http_request = AbstractHTTPHandler.do_request_
/usr/lib/python2.7/urllib2.pyc in do_open(self, http_class, req)
1182 except socket.error, err: # XXX what error?
1183 h.close()
-> 1184 raise URLError(err)
1185 else:
1186 try:
URLError: <urlopen error [Errno -2] Name or service not known>
The Input/Output doc page shows how to import from various other formats.
We select the variables of interest and look at the bottom 5 rows:
In [9]: vars = ['Department', 'Lottery', 'Literacy', 'Wealth', 'Region']
In [10]: df = df[vars]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-10-97b909d2ba47> in <module>()
----> 1 df = df[vars]
NameError: name 'df' is not defined
In [11]: df[-5:]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-11-387a2dedaa82> in <module>()
----> 1 df[-5:]
NameError: name 'df' is not defined
Notice that there is one missing observation in the Region column. We eliminate it using a DataFrame method provided by pandas:
In [12]: df = df.dropna()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-12-c783d194b823> in <module>()
----> 1 df = df.dropna()
NameError: name 'df' is not defined
In [13]: df[-5:]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-13-387a2dedaa82> in <module>()
----> 1 df[-5:]
NameError: name 'df' is not defined
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:
\hat{\beta} = (X'X)^{-1} X'y
where y is an N \times 1 column of data on lottery wagers per capita (Lottery). X is 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: http://patsy.readthedocs.org
We use patsy‘s dmatrices function to create design matrices:
In [14]: y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-14-b205df6907aa> in <module>()
----> 1 y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe')
NameError: name 'df' is not defined
The resulting matrices/data frames look like this:
In [15]: y[:3]
Out[15]: array([ 5.8122, 5.1196, 5.9602])
In [16]: X[:3]
Out[16]:
array([[ 0. , 1. ],
[ 0.4082, 1. ],
[ 0.8163, 1. ]])
Notice that dmatrices has
The above behavior can of course be altered. See the patsy doc pages.
Fitting a model in statsmodels typically involves 3 easy steps:
For OLS, this is achieved by:
In [17]: mod = sm.OLS(y, X) # Describe model
In [18]: res = mod.fit() # Fit model
In [19]: print res.summary() # Summarize model
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.879
Model: OLS Adj. R-squared: 0.876
Method: Least Squares F-statistic: 347.7
Date: Fri, 14 Mar 2014 Prob (F-statistic): 1.25e-23
Time: 00:01:08 Log-Likelihood: -68.470
No. Observations: 50 AIC: 140.9
Df Residuals: 48 BIC: 144.8
Df Model: 1
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
x1 0.4349 0.023 18.647 0.000 0.388 0.482
const 5.2426 0.271 19.370 0.000 4.698 5.787
==============================================================================
Omnibus: 10.697 Durbin-Watson: 2.200
Prob(Omnibus): 0.005 Jarque-Bera (JB): 29.315
Skew: 0.153 Prob(JB): 4.31e-07
Kurtosis: 6.739 Cond. No. 23.0
==============================================================================
The res object has many useful attributes. For example, we can extract parameter estimates and r-squared by typing:
In [20]: res.params
Out[20]: array([ 0.4349, 5.2426])
In [21]: res.rsquared
Out[21]: 0.87870418171230524
Type dir(res) for a full list of attributes.
For more information and examples, see the Regression doc page
statsmodels allows you to conduct a range of useful regression diagnostics and specification tests. For instance, apply the Rainbow test for linearity (the null hypothesis is that the relationship is properly modelled as linear):
In [22]: sm.stats.linear_rainbow(res)
Out[22]: (2.9071343288437821, 0.0061298269187520125)
Admittedly, the output produced above is not very verbose, but we know from reading the docstring (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:
In [23]: from statsmodels.graphics.regressionplots import plot_partregress
In [24]: plot_partregress(res)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-24-e05de258c07b> in <module>()
----> 1 plot_partregress(res)
TypeError: plot_partregress() takes at least 3 arguments (1 given)
Congratulations! You’re ready to move on to other topics in the Table of Contents