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Generalized Estimating Equations

Generalized Estimating Equations estimate generalized linear models for panel, cluster or repeated measures data when the observations are possibly correlated withing a cluster but uncorrelated across clusters. It supports estimation of the same one-parameter exponential families as Generalized Linear models (GLM).

See Module Reference for commands and arguments.

Examples

The following illustrates a Poisson regression with exchangeable correlation within clusters using data on epilepsy seizures.

In [1]: import statsmodels.api as sm

In [2]: import statsmodels.formula.api as smf

In [3]: data = sm.datasets.get_rdataset('epil', package='MASS').data
---------------------------------------------------------------------------
URLError                                  Traceback (most recent call last)
<ipython-input-3-4e55b8bec212> in <module>()
----> 1 data = sm.datasets.get_rdataset('epil', package='MASS').data

/build/statsmodels-0.8.0/debian/python-statsmodels/usr/lib/python2.7/dist-packages/statsmodels/datasets/utils.pyc 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/debian/python-statsmodels/usr/lib/python2.7/dist-packages/statsmodels/datasets/utils.pyc 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/debian/python-statsmodels/usr/lib/python2.7/dist-packages/statsmodels/datasets/utils.pyc 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/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 https_open(self, req)
   1220 
   1221         def https_open(self, req):
-> 1222             return self.do_open(httplib.HTTPSConnection, req)
   1223 
   1224         https_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 [4]: fam = sm.families.Poisson()

In [5]: ind = sm.cov_struct.Exchangeable()

In [6]: mod = smf.gee("y ~ age + trt + base", "subject", data,
   ...:                cov_struct=ind, family=fam)
   ...: 
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
<ipython-input-6-f8d3b31d24f3> in <module>()
      1 mod = smf.gee("y ~ age + trt + base", "subject", data,
----> 2                cov_struct=ind, family=fam)

/build/statsmodels-0.8.0/debian/python-statsmodels/usr/lib/python2.7/dist-packages/statsmodels/genmod/generalized_estimating_equations.pyc in from_formula(cls, formula, groups, data, subset, time, offset, exposure, *args, **kwargs)
    668 
    669         if type(groups) == str:
--> 670             groups = data[groups]
    671 
    672         if type(time) == str:

KeyError: 'subject'

In [7]: res = mod.fit()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-7-deef2687e692> in <module>()
----> 1 res = mod.fit()

NameError: name 'mod' is not defined

In [8]: print(res.summary())
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-8-a8dc848a1f25> in <module>()
----> 1 print(res.summary())

NameError: name 'res' is not defined

Several notebook examples of the use of GEE can be found on the Wiki: Wiki notebooks for GEE

References

  • KY Liang and S Zeger. “Longitudinal data analysis using generalized linear models”. Biometrika (1986) 73 (1): 13-22.
  • S Zeger and KY Liang. “Longitudinal Data Analysis for Discrete and Continuous Outcomes”. Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130
  • A Rotnitzky and NP Jewell (1990). “Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data”, Biometrika, 77, 485-497.
  • Xu Guo and Wei Pan (2002). “Small sample performance of the score test in GEE”. http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf
  • LA Mancl LA, TA DeRouen (2001). A covariance estimator for GEE with improved small-sample properties. Biometrics. 2001 Mar;57(1):126-34.

Module Reference

Model Class

GEE(endog, exog, groups[, time, family, ...]) Estimation of marginal regression models using Generalized Estimating Equations (GEE).

Results Classes

GEEResults(model, params, cov_params, scale) This class summarizes the fit of a marginal regression model using GEE.
GEEMargins(results, args[, kwargs]) Estimated marginal effects for a regression model fit with GEE.

Dependence Structures

The dependence structures currently implemented are

CovStruct([cov_nearest_method]) A base class for correlation and covariance structures of grouped data.
Autoregressive([dist_func]) A first-order autoregressive working dependence structure.
Exchangeable() An exchangeable working dependence structure.
GlobalOddsRatio(endog_type) Estimate the global odds ratio for a GEE with ordinal or nominal data.
Independence([cov_nearest_method]) An independence working dependence structure.
Nested([cov_nearest_method]) A nested working dependence structure.

Families

The distribution families are the same as for GLM, currently implemented are

Family(link, variance) The parent class for one-parameter exponential families.
Binomial([link]) Binomial exponential family distribution.
Gamma([link]) Gamma exponential family distribution.
Gaussian([link]) Gaussian exponential family distribution.
InverseGaussian([link]) InverseGaussian exponential family.
NegativeBinomial([link, alpha]) Negative Binomial exponential family.
Poisson([link]) Poisson exponential family.