Linear Mixed Effects Models¶
Linear Mixed Effects models are used for regression analyses involving dependent data. Such data arise when working with longitudinal and other study designs in which multiple observations are made on each subject. Two specific mixed effects models are random intercepts models, where all responses in a single group are additively shifted by a value that is specific to the group, and random slopes models, where the values follow a mean trajectory that is linear in observed covariates, with both the slopes and intercept being specific to the group. The Statsmodels MixedLM implementation allows arbitrary random effects design matrices to be specified for the groups, so these and other types of random effects models can all be fit.
The Statsmodels LME framework currently supports post-estimation inference via Wald tests and confidence intervals on the coefficients, profile likelihood analysis, likelihood ratio testing, and AIC. Some limitations of the current implementation are that it does not support structure more complex on the residual errors (they are always homoscedastic), and it does not support crossed random effects. We hope to implement these features for the next release.
Examples¶
In [1]: import statsmodels.api as sm
In [2]: import statsmodels.formula.api as smf
In [3]: data = sm.datasets.get_rdataset("dietox", "geepack", 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-3-dd9bcc886be5> in <module>()
----> 1 data = sm.datasets.get_rdataset("dietox", "geepack", 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 [4]: md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"])