Fitting models using R-style formulas¶
Since version 0.5.0, statsmodels
allows users to fit statistical
models using R-style formulas. Internally, statsmodels
uses the
patsy package to convert formulas and
data to the matrices that are used in model fitting. The formula
framework is quite powerful; this tutorial only scratches the surface. A
full description of the formula language can be found in the patsy
docs:
Loading modules and functions¶
In [1]: import statsmodels.formula.api as smf
In [2]: import numpy as np
In [3]: import pandas
Notice that we called statsmodels.formula.api
instead of the usual
statsmodels.api
. The formula.api
hosts many of the same
functions found in api
(e.g. OLS, GLM), but it also holds lower case
counterparts for most of these models. In general, lower case models
accept formula
and df
arguments, whereas upper case ones take
endog
and exog
design matrices. formula
accepts a string
which describes the model in terms of a patsy
formula. df
takes
a pandas data frame.
dir(smf)
will print a list of available models.
Formula-compatible models have the following generic call signature:
(formula, data, subset=None, *args, **kwargs)
OLS regression using formulas¶
To begin, we fit the linear model described on the Getting Started page. Download the data, subset columns, and list-wise delete to remove missing observations:
In [4]: df = sm.datasets.get_rdataset("Guerry", "HistData", cache=True).data
---------------------------------------------------------------------------
gaierror Traceback (most recent call last)
/usr/lib/python3.6/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1317 h.request(req.get_method(), req.selector, req.data, headers,
-> 1318 encode_chunked=req.has_header('Transfer-encoding'))
1319 except OSError as err: # timeout error
/usr/lib/python3.6/http/client.py in request(self, method, url, body, headers, encode_chunked)
1238 """Send a complete request to the server."""
-> 1239 self._send_request(method, url, body, headers, encode_chunked)
1240
/usr/lib/python3.6/http/client.py in _send_request(self, method, url, body, headers, encode_chunked)
1284 body = _encode(body, 'body')
-> 1285 self.endheaders(body, encode_chunked=encode_chunked)
1286
/usr/lib/python3.6/http/client.py in endheaders(self, message_body, encode_chunked)
1233 raise CannotSendHeader()
-> 1234 self._send_output(message_body, encode_chunked=encode_chunked)
1235
/usr/lib/python3.6/http/client.py in _send_output(self, message_body, encode_chunked)
1025 del self._buffer[:]
-> 1026 self.send(msg)
1027
/usr/lib/python3.6/http/client.py in send(self, data)
963 if self.auto_open:
--> 964 self.connect()
965 else:
/usr/lib/python3.6/http/client.py in connect(self)
1391
-> 1392 super().connect()
1393
/usr/lib/python3.6/http/client.py in connect(self)
935 self.sock = self._create_connection(
--> 936 (self.host,self.port), self.timeout, self.source_address)
937 self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)
/usr/lib/python3.6/socket.py in create_connection(address, timeout, source_address)
703 err = None
--> 704 for res in getaddrinfo(host, port, 0, SOCK_STREAM):
705 af, socktype, proto, canonname, sa = res
/usr/lib/python3.6/socket.py in getaddrinfo(host, port, family, type, proto, flags)
744 addrlist = []
--> 745 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
746 af, socktype, proto, canonname, sa = res
gaierror: [Errno -2] Name or service not known
During handling of the above exception, another exception occurred:
URLError Traceback (most recent call last)
<ipython-input-4-cab9fdf84142> in <module>()
----> 1 df = sm.datasets.get_rdataset("Guerry", "HistData", cache=True).data
/build/statsmodels-pH_Txj/statsmodels-0.8.0/.pybuild/pythonX.Y_3.6/build/statsmodels/datasets/utils.py in get_rdataset(dataname, package, cache)
288 "master/doc/"+package+"/rst/")
289 cache = _get_cache(cache)
--> 290 data, from_cache = _get_data(data_base_url, dataname, cache)
291 data = read_csv(data, index_col=0)
292 data = _maybe_reset_index(data)
/build/statsmodels-pH_Txj/statsmodels-0.8.0/.pybuild/pythonX.Y_3.6/build/statsmodels/datasets/utils.py in _get_data(base_url, dataname, cache, extension)
219 url = base_url + (dataname + ".%s") % extension
220 try:
--> 221 data, from_cache = _urlopen_cached(url, cache)
222 except HTTPError as err:
223 if '404' in str(err):
/build/statsmodels-pH_Txj/statsmodels-0.8.0/.pybuild/pythonX.Y_3.6/build/statsmodels/datasets/utils.py in _urlopen_cached(url, cache)
210 # not using the cache or didn't find it in cache
211 if not from_cache:
--> 212 data = urlopen(url).read()
213 if cache is not None: # then put it in the cache
214 _cache_it(data, cache_path)
/usr/lib/python3.6/urllib/request.py in urlopen(url, data, timeout, cafile, capath, cadefault, context)
221 else:
222 opener = _opener
--> 223 return opener.open(url, data, timeout)
224
225 def install_opener(opener):
/usr/lib/python3.6/urllib/request.py in open(self, fullurl, data, timeout)
524 req = meth(req)
525
--> 526 response = self._open(req, data)
527
528 # post-process response
/usr/lib/python3.6/urllib/request.py in _open(self, req, data)
542 protocol = req.type
543 result = self._call_chain(self.handle_open, protocol, protocol +
--> 544 '_open', req)
545 if result:
546 return result
/usr/lib/python3.6/urllib/request.py in _call_chain(self, chain, kind, meth_name, *args)
502 for handler in handlers:
503 func = getattr(handler, meth_name)
--> 504 result = func(*args)
505 if result is not None:
506 return result
/usr/lib/python3.6/urllib/request.py in https_open(self, req)
1359 def https_open(self, req):
1360 return self.do_open(http.client.HTTPSConnection, req,
-> 1361 context=self._context, check_hostname=self._check_hostname)
1362
1363 https_request = AbstractHTTPHandler.do_request_
/usr/lib/python3.6/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1318 encode_chunked=req.has_header('Transfer-encoding'))
1319 except OSError as err: # timeout error
-> 1320 raise URLError(err)
1321 r = h.getresponse()
1322 except:
URLError: <urlopen error [Errno -2] Name or service not known>
In [5]: df = df[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()