442 lines
14 KiB
Python
442 lines
14 KiB
Python
"""
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Sandbox Panel Estimators
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References
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-----------
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Baltagi, Badi H. `Econometric Analysis of Panel Data.` 4th ed. Wiley, 2008.
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"""
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from functools import reduce
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import numpy as np
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from statsmodels.regression.linear_model import GLS
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__all__ = ["PanelModel"]
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from pandas import Panel
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def group(X):
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"""
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Returns unique numeric values for groups without sorting.
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Examples
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--------
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>>> X = np.array(['a','a','b','c','b','c'])
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>>> group(X)
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>>> g
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array([ 0., 0., 1., 2., 1., 2.])
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"""
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uniq_dict = {}
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group = np.zeros(len(X))
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for i in range(len(X)):
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if not X[i] in uniq_dict:
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uniq_dict.update({X[i] : len(uniq_dict)})
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group[i] = uniq_dict[X[i]]
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return group
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def repanel_cov(groups, sigmas):
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'''calculate error covariance matrix for random effects model
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Parameters
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----------
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groups : ndarray, (nobs, nre) or (nobs,)
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array of group/category observations
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sigma : ndarray, (nre+1,)
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array of standard deviations of random effects,
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last element is the standard deviation of the
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idiosyncratic error
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Returns
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-------
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omega : ndarray, (nobs, nobs)
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covariance matrix of error
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omegainv : ndarray, (nobs, nobs)
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inverse covariance matrix of error
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omegainvsqrt : ndarray, (nobs, nobs)
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squareroot inverse covariance matrix of error
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such that omega = omegainvsqrt * omegainvsqrt.T
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Notes
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-----
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This does not use sparse matrices and constructs nobs by nobs
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matrices. Also, omegainvsqrt is not sparse, i.e. elements are non-zero
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'''
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if groups.ndim == 1:
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groups = groups[:,None]
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nobs, nre = groups.shape
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omega = sigmas[-1]*np.eye(nobs)
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for igr in range(nre):
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group = groups[:,igr:igr+1]
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groupuniq = np.unique(group)
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dummygr = sigmas[igr] * (group == groupuniq).astype(float)
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omega += np.dot(dummygr, dummygr.T)
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ev, evec = np.linalg.eigh(omega) #eig does not work
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omegainv = np.dot(evec, (1/ev * evec).T)
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omegainvhalf = evec/np.sqrt(ev)
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return omega, omegainv, omegainvhalf
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class PanelData(Panel):
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pass
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class PanelModel:
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"""
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An abstract statistical model class for panel (longitudinal) datasets.
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Parameters
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----------
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endog : array_like or str
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If a pandas object is used then endog should be the name of the
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endogenous variable as a string.
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# exog
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# panel_arr
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# time_arr
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panel_data : pandas.Panel object
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Notes
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-----
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If a pandas object is supplied it is assumed that the major_axis is time
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and that the minor_axis has the panel variable.
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"""
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def __init__(self, endog=None, exog=None, panel=None, time=None,
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xtnames=None, equation=None, panel_data=None):
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if panel_data is None:
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# if endog == None and exog == None and panel == None and \
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# time == None:
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# raise ValueError("If pandel_data is False then endog, exog, \
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#panel_arr, and time_arr cannot be None.")
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self.initialize(endog, exog, panel, time, xtnames, equation)
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# elif aspandas != False:
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# if not isinstance(endog, str):
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# raise ValueError("If a pandas object is supplied then endog \
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#must be a string containing the name of the endogenous variable")
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# if not isinstance(aspandas, Panel):
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# raise ValueError("Only pandas.Panel objects are supported")
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# self.initialize_pandas(endog, aspandas, panel_name)
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def initialize(self, endog, exog, panel, time, xtnames, equation):
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"""
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Initialize plain array model.
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See PanelModel
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"""
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#TODO: for now, we are going assume a constant, and then make the first
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#panel the base, add a flag for this....
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# get names
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names = equation.split(" ")
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self.endog_name = names[0]
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exog_names = names[1:] # this makes the order matter in the array
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self.panel_name = xtnames[0]
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self.time_name = xtnames[1]
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novar = exog.var(0) == 0
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if True in novar:
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cons_index = np.where(novar == 1)[0][0] # constant col. num
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exog_names.insert(cons_index, 'cons')
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self._cons_index = novar # used again in fit_fixed
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self.exog_names = exog_names
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self.endog = np.squeeze(np.asarray(endog))
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exog = np.asarray(exog)
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self.exog = exog
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self.panel = np.asarray(panel)
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self.time = np.asarray(time)
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self.paneluniq = np.unique(panel)
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self.timeuniq = np.unique(time)
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#TODO: this structure can possibly be extracted somewhat to deal with
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#names in general
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#TODO: add some dimension checks, etc.
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# def initialize_pandas(self, endog, aspandas):
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# """
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# Initialize pandas objects.
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#
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# See PanelModel.
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# """
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# self.aspandas = aspandas
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# endog = aspandas[endog].values
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# self.endog = np.squeeze(endog)
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# exog_name = aspandas.columns.tolist()
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# exog_name.remove(endog)
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# self.exog = aspandas.filterItems(exog_name).values
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#TODO: can the above be simplified to slice notation?
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# if panel_name != None:
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# self.panel_name = panel_name
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# self.exog_name = exog_name
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# self.endog_name = endog
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# self.time_arr = aspandas.major_axis
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#TODO: is time always handled correctly in fromRecords?
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# self.panel_arr = aspandas.minor_axis
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#TODO: all of this might need to be refactored to explicitly rely (internally)
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# on the pandas LongPanel structure for speed and convenience.
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# not sure this part is finished...
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#TODO: does not conform to new initialize
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def initialize_pandas(self, panel_data, endog_name, exog_name):
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self.panel_data = panel_data
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endog = panel_data[endog_name].values # does this create a copy?
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self.endog = np.squeeze(endog)
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if exog_name is None:
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exog_name = panel_data.columns.tolist()
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exog_name.remove(endog_name)
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self.exog = panel_data.filterItems(exog_name).values # copy?
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self._exog_name = exog_name
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self._endog_name = endog_name
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self._timeseries = panel_data.major_axis # might not need these
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self._panelseries = panel_data.minor_axis
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#TODO: this could be pulled out and just have a by kwd that takes
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# the panel or time array
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#TODO: this also needs to be expanded for 'twoway'
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def _group_mean(self, X, index='oneway', counts=False, dummies=False):
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"""
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Get group means of X by time or by panel.
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index default is panel
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"""
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if index == 'oneway':
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Y = self.panel
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uniq = self.paneluniq
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elif index == 'time':
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Y = self.time
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uniq = self.timeuniq
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else:
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raise ValueError("index %s not understood" % index)
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print(Y, uniq, uniq[:,None], len(Y), len(uniq), len(uniq[:,None]),
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index)
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#TODO: use sparse matrices
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dummy = (Y == uniq[:,None]).astype(float)
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if X.ndim > 1:
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mean = np.dot(dummy,X)/dummy.sum(1)[:,None]
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else:
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mean = np.dot(dummy,X)/dummy.sum(1)
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if counts is False and dummies is False:
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return mean
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elif counts is True and dummies is False:
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return mean, dummy.sum(1)
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elif counts is True and dummies is True:
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return mean, dummy.sum(1), dummy
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elif counts is False and dummies is True:
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return mean, dummy
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#TODO: Use kwd arguments or have fit_method methods?
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def fit(self, model=None, method=None, effects='oneway'):
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"""
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method : LSDV, demeaned, MLE, GLS, BE, FE, optional
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model :
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between
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fixed
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random
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pooled
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[gmm]
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effects :
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oneway
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time
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twoway
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femethod : demeaned (only one implemented)
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WLS
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remethod :
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swar -
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amemiya
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nerlove
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walhus
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Notes
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-----
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This is unfinished. None of the method arguments work yet.
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Only oneway effects should work.
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"""
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if method: # get rid of this with default
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method = method.lower()
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model = model.lower()
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if method and method not in ["lsdv", "demeaned", "mle",
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"gls", "be", "fe"]:
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# get rid of if method with default
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raise ValueError("%s not a valid method" % method)
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# if method == "lsdv":
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# self.fit_lsdv(model)
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if model == 'pooled':
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return GLS(self.endog, self.exog).fit()
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if model == 'between':
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return self._fit_btwn(method, effects)
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if model == 'fixed':
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return self._fit_fixed(method, effects)
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# def fit_lsdv(self, effects):
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# """
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# Fit using least squares dummy variables.
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#
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# Notes
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# -----
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# Should only be used for small `nobs`.
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# """
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# pdummies = None
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# tdummies = None
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def _fit_btwn(self, method, effects):
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# group mean regression or WLS
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if effects != "twoway":
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endog = self._group_mean(self.endog, index=effects)
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exog = self._group_mean(self.exog, index=effects)
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else:
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raise ValueError("%s effects is not valid for the between "
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"estimator" % effects)
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befit = GLS(endog, exog).fit()
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return befit
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def _fit_fixed(self, method, effects):
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endog = self.endog
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exog = self.exog
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demeantwice = False
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if effects in ["oneway","twoways"]:
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if effects == "twoways":
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demeantwice = True
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effects = "oneway"
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endog_mean, counts = self._group_mean(endog, index=effects,
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counts=True)
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exog_mean = self._group_mean(exog, index=effects)
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counts = counts.astype(int)
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endog = endog - np.repeat(endog_mean, counts)
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exog = exog - np.repeat(exog_mean, counts, axis=0)
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if demeantwice or effects == "time":
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endog_mean, dummies = self._group_mean(endog, index="time",
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dummies=True)
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exog_mean = self._group_mean(exog, index="time")
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# This allows unbalanced panels
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endog = endog - np.dot(endog_mean, dummies)
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exog = exog - np.dot(dummies.T, exog_mean)
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fefit = GLS(endog, exog[:,-self._cons_index]).fit()
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#TODO: might fail with one regressor
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return fefit
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class SURPanel(PanelModel):
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pass
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class SEMPanel(PanelModel):
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pass
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class DynamicPanel(PanelModel):
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pass
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if __name__ == "__main__":
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import numpy.lib.recfunctions as nprf
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import pandas
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from pandas import Panel
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import statsmodels.api as sm
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data = sm.datasets.grunfeld.load()
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# Baltagi does not include American Steel
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endog = data.endog[:-20]
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fullexog = data.exog[:-20]
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# fullexog.sort(order=['firm','year'])
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panel_arr = nprf.append_fields(fullexog, 'investment', endog, float,
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usemask=False)
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panel_df = pandas.DataFrame(panel_arr)
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panel_panda = panel_df.set_index(['year', 'firm']).to_panel()
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# the most cumbersome way of doing it as far as preprocessing by hand
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exog = fullexog[['value','capital']].view(float).reshape(-1,2)
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exog = sm.add_constant(exog, prepend=False)
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panel = group(fullexog['firm'])
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year = fullexog['year']
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panel_mod = PanelModel(endog, exog, panel, year, xtnames=['firm','year'],
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equation='invest value capital')
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# note that equation does not actually do anything but name the variables
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panel_ols = panel_mod.fit(model='pooled')
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panel_be = panel_mod.fit(model='between', effects='oneway')
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panel_fe = panel_mod.fit(model='fixed', effects='oneway')
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panel_bet = panel_mod.fit(model='between', effects='time')
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panel_fet = panel_mod.fit(model='fixed', effects='time')
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panel_fe2 = panel_mod.fit(model='fixed', effects='twoways')
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#see also Baltagi (3rd edt) 3.3 THE RANDOM EFFECTS MODEL p.35
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#for explicit formulas for spectral decomposition
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#but this works also for unbalanced panel
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#
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#I also just saw: 9.4.2 The Random Effects Model p.176 which is
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#partially almost the same as I did
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#
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#this needs to use sparse matrices for larger datasets
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#
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#"""
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#
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#import numpy as np
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#
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groups = np.array([0,0,0,1,1,2,2,2])
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nobs = groups.shape[0]
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groupuniq = np.unique(groups)
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periods = np.array([0,1,2,1,2,0,1,2])
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perioduniq = np.unique(periods)
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dummygr = (groups[:,None] == groupuniq).astype(float)
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dummype = (periods[:,None] == perioduniq).astype(float)
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sigma = 1.
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sigmagr = np.sqrt(2.)
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sigmape = np.sqrt(3.)
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#dummyall = np.c_[sigma*np.ones((nobs,1)), sigmagr*dummygr,
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# sigmape*dummype]
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#exclude constant ?
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dummyall = np.c_[sigmagr*dummygr, sigmape*dummype]
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# omega is the error variance-covariance matrix for the stacked
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# observations
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omega = np.dot(dummyall, dummyall.T) + sigma* np.eye(nobs)
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print(omega)
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print(np.linalg.cholesky(omega))
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ev, evec = np.linalg.eigh(omega) #eig does not work
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omegainv = np.dot(evec, (1/ev * evec).T)
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omegainv2 = np.linalg.inv(omega)
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omegacomp = np.dot(evec, (ev * evec).T)
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print(np.max(np.abs(omegacomp - omega)))
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#check
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#print(np.dot(omegainv,omega)
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print(np.max(np.abs(np.dot(omegainv,omega) - np.eye(nobs))))
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omegainvhalf = evec/np.sqrt(ev) #not sure whether ev should not be column
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print(np.max(np.abs(np.dot(omegainvhalf,omegainvhalf.T) - omegainv)))
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# now we can use omegainvhalf in GLS (instead of the cholesky)
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sigmas2 = np.array([sigmagr, sigmape, sigma])
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groups2 = np.column_stack((groups, periods))
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omega_, omegainv_, omegainvhalf_ = repanel_cov(groups2, sigmas2)
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print(np.max(np.abs(omega_ - omega)))
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print(np.max(np.abs(omegainv_ - omegainv)))
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print(np.max(np.abs(omegainvhalf_ - omegainvhalf)))
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# notation Baltagi (3rd) section 9.4.1 (Fixed Effects Model)
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Pgr = reduce(np.dot,[dummygr,
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np.linalg.inv(np.dot(dummygr.T, dummygr)),dummygr.T])
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Qgr = np.eye(nobs) - Pgr
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# within group effect: np.dot(Qgr, groups)
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# but this is not memory efficient, compared to groupstats
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print(np.max(np.abs(np.dot(Qgr, groups))))
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