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/python3.5/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1253 try:
-> 1254 h.request(req.get_method(), req.selector, req.data, headers)
1255 except OSError as err: # timeout error
/usr/lib/python3.5/http/client.py in request(self, method, url, body, headers)
1106 """Send a complete request to the server."""
-> 1107 self._send_request(method, url, body, headers)
1108
/usr/lib/python3.5/http/client.py in _send_request(self, method, url, body, headers)
1151 body = _encode(body, 'body')
-> 1152 self.endheaders(body)
1153
/usr/lib/python3.5/http/client.py in endheaders(self, message_body)
1102 raise CannotSendHeader()
-> 1103 self._send_output(message_body)
1104
/usr/lib/python3.5/http/client.py in _send_output(self, message_body)
933
--> 934 self.send(msg)
935 if message_body is not None:
/usr/lib/python3.5/http/client.py in send(self, data)
876 if self.auto_open:
--> 877 self.connect()
878 else:
/usr/lib/python3.5/http/client.py in connect(self)
1252
-> 1253 super().connect()
1254
/usr/lib/python3.5/http/client.py in connect(self)
848 self.sock = self._create_connection(
--> 849 (self.host,self.port), self.timeout, self.source_address)
850 self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)
/usr/lib/python3.5/socket.py in create_connection(address, timeout, source_address)
693 err = None
--> 694 for res in getaddrinfo(host, port, 0, SOCK_STREAM):
695 af, socktype, proto, canonname, sa = res
/usr/lib/python3.5/socket.py in getaddrinfo(host, port, family, type, proto, flags)
732 addrlist = []
--> 733 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
734 af, socktype, proto, canonname, sa = res
gaierror: [Errno -3] Temporary failure in name resolution
During handling of the above exception, another exception occurred:
URLError Traceback (most recent call last)
<ipython-input-4-8c6e29b11c8f> in <module>()
----> 1 df = sm.datasets.get_rdataset("Guerry", "HistData", cache=True).data
/build/statsmodels-0.8.0/.pybuild/pythonX.Y_3.5/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-0.8.0/.pybuild/pythonX.Y_3.5/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-0.8.0/.pybuild/pythonX.Y_3.5/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/python3.5/urllib/request.py in urlopen(url, data, timeout, cafile, capath, cadefault, context)
161 else:
162 opener = _opener
--> 163 return opener.open(url, data, timeout)
164
165 def install_opener(opener):
/usr/lib/python3.5/urllib/request.py in open(self, fullurl, data, timeout)
464 req = meth(req)
465
--> 466 response = self._open(req, data)
467
468 # post-process response
/usr/lib/python3.5/urllib/request.py in _open(self, req, data)
482 protocol = req.type
483 result = self._call_chain(self.handle_open, protocol, protocol +
--> 484 '_open', req)
485 if result:
486 return result
/usr/lib/python3.5/urllib/request.py in _call_chain(self, chain, kind, meth_name, *args)
442 for handler in handlers:
443 func = getattr(handler, meth_name)
--> 444 result = func(*args)
445 if result is not None:
446 return result
/usr/lib/python3.5/urllib/request.py in https_open(self, req)
1295 def https_open(self, req):
1296 return self.do_open(http.client.HTTPSConnection, req,
-> 1297 context=self._context, check_hostname=self._check_hostname)
1298
1299 https_request = AbstractHTTPHandler.do_request_
/usr/lib/python3.5/urllib/request.py in do_open(self, http_class, req, **http_conn_args)
1254 h.request(req.get_method(), req.selector, req.data, headers)
1255 except OSError as err: # timeout error
-> 1256 raise URLError(err)
1257 r = h.getresponse()
1258 except:
URLError: <urlopen error [Errno -3] Temporary failure in name resolution>
In [5]: df = df[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-5-c0f7df8f22c7> in <module>()
----> 1 df = df[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()
NameError: name 'df' is not defined
In [6]: df.head()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-6-2569c44faf66> in <module>()
----> 1 df.head()
NameError: name 'df' is not defined
Fit the model:
In [7]: mod = smf.ols(formula='Lottery ~ Literacy + Wealth + Region', data=df)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-7-fc74d7ce0f53> in <module>()
----> 1 mod = smf.ols(formula='Lottery ~ Literacy + Wealth + Region', data=df)
NameError: name 'df' is not defined
In [8]: res = mod.fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-8-deef2687e692> in <module>()
----> 1 res = mod.fit()
NameError: name 'mod' is not defined
In [9]: print(res.summary())
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-9-a8dc848a1f25> in <module>()
----> 1 print(res.summary())
NameError: name 'res' is not defined
Categorical variables¶
Looking at the summary printed above, notice that patsy determined
that elements of Region were text strings, so it treated Region as a
categorical variable. patsy’s default is also to include an
intercept, so we automatically dropped one of the Region categories.
If Region had been an integer variable that we wanted to treat
explicitly as categorical, we could have done so by using the C()
operator:
In [10]: res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-10-512c713f4dd3> in <module>()
----> 1 res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit()
NameError: name 'df' is not defined
In [11]: print(res.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-11-c61a950343b4> in <module>()
----> 1 print(res.params)
NameError: name 'res' is not defined
Examples more advanced features patsy’s categorical variables
function can be found here: Patsy: Contrast Coding Systems for
categorical variables
Operators¶
We have already seen that “~” separates the left-hand side of the model from the right-hand side, and that “+” adds new columns to the design matrix.
Removing variables¶
The “-” sign can be used to remove columns/variables. For instance, we can remove the intercept from a model by:
In [12]: res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-12-01cb7f19a578> in <module>()
----> 1 res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit()
NameError: name 'df' is not defined
In [13]: print(res.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-13-c61a950343b4> in <module>()
----> 1 print(res.params)
NameError: name 'res' is not defined
Multiplicative interactions¶
“:” adds a new column to the design matrix with the product of the other two columns. “*” will also include the individual columns that were multiplied together:
In [14]: res1 = smf.ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-14-b102884e9732> in <module>()
----> 1 res1 = smf.ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit()
NameError: name 'df' is not defined
In [15]: res2 = smf.ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-15-e7613c271b74> in <module>()
----> 1 res2 = smf.ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit()
NameError: name 'df' is not defined
In [16]: print(res1.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-16-9e7f9958623f> in <module>()
----> 1 print(res1.params)
NameError: name 'res1' is not defined
In [17]: print(res2.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-17-5ef235c70f25> in <module>()
----> 1 print(res2.params)
NameError: name 'res2' is not defined
Many other things are possible with operators. Please consult the patsy docs to learn more.
Functions¶
You can apply vectorized functions to the variables in your model:
In [18]: res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-18-4fe1546acec0> in <module>()
----> 1 res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit()
NameError: name 'df' is not defined
In [19]: print(res.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-19-c61a950343b4> in <module>()
----> 1 print(res.params)
NameError: name 'res' is not defined
Define a custom function:
In [20]: def log_plus_1(x):
....: return np.log(x) + 1.
....:
In [21]: print(res.params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-21-c61a950343b4> in <module>()
----> 1 print(res.params)
NameError: name 'res' is not defined
Namespaces¶
Notice that all of the above examples use the calling namespace to look for the functions to apply. The namespace used can be controlled via the eval_env keyword. For example, you may want to give a custom namespace using the patsy.EvalEnvironment or you may want to use a “clean” namespace, which we provide by passing eval_func=-1. The default is to use the caller’s namespace. This can have (un)expected consequences, if, for example, someone has a variable names C in the user namespace or in their data structure passed to patsy, and C is used in the formula to handle a categorical variable. See the Patsy API Reference for more information.
Using formulas with models that do not (yet) support them¶
Even if a given statsmodels function does not support formulas, you
can still use patsy’s formula language to produce design matrices.
Those matrices can then be fed to the fitting function as endog and
exog arguments.
To generate numpy arrays:
In [22]: import patsy
In [23]: f = 'Lottery ~ Literacy * Wealth'
In [24]: y, X = patsy.dmatrices(f, df, return_type='dataframe')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-24-418e6636605c> in <module>()
----> 1 y, X = patsy.dmatrices(f, df, return_type='dataframe')
NameError: name 'df' is not defined
In [25]: print(y[:5])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-25-8b56dfab7799> in <module>()
----> 1 print(y[:5])
NameError: name 'y' is not defined
In [26]: print(X[:5])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-26-7dbdd9618cc6> in <module>()
----> 1 print(X[:5])
NameError: name 'X' is not defined
To generate pandas data frames:
In [27]: f = 'Lottery ~ Literacy * Wealth'
In [28]: y, X = patsy.dmatrices(f, df, return_type='dataframe')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-28-418e6636605c> in <module>()
----> 1 y, X = patsy.dmatrices(f, df, return_type='dataframe')
NameError: name 'df' is not defined
In [29]: print(y[:5])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-29-8b56dfab7799> in <module>()
----> 1 print(y[:5])
NameError: name 'y' is not defined
In [30]: print(X[:5])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-30-7dbdd9618cc6> in <module>()
----> 1 print(X[:5])
NameError: name 'X' is not defined
In [31]: print(smf.OLS(y, X).fit().summary())
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-31-6bf304b23cf5> in <module>()
----> 1 print(smf.OLS(y, X).fit().summary())
NameError: name 'y' is not defined