733 lines
26 KiB
Python
733 lines
26 KiB
Python
#Splitting out maringal effects to see if they can be generalized
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from statsmodels.compat.python import lzip
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import numpy as np
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from scipy.stats import norm
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from statsmodels.tools.decorators import cache_readonly
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#### margeff helper functions ####
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#NOTE: todo marginal effects for group 2
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# group 2 oprobit, ologit, gologit, mlogit, biprobit
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def _check_margeff_args(at, method):
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"""
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Checks valid options for margeff
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"""
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if at not in ['overall','mean','median','zero','all']:
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raise ValueError("%s not a valid option for `at`." % at)
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if method not in ['dydx','eyex','dyex','eydx']:
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raise ValueError("method is not understood. Got %s" % method)
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def _check_discrete_args(at, method):
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"""
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Checks the arguments for margeff if the exogenous variables are discrete.
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"""
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if method in ['dyex','eyex']:
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raise ValueError("%s not allowed for discrete variables" % method)
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if at in ['median', 'zero']:
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raise ValueError("%s not allowed for discrete variables" % at)
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def _get_const_index(exog):
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"""
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Returns a boolean array of non-constant column indices in exog and
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an scalar array of where the constant is or None
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"""
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effects_idx = exog.var(0) != 0
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if np.any(~effects_idx):
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const_idx = np.where(~effects_idx)[0]
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else:
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const_idx = None
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return effects_idx, const_idx
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def _isdummy(X):
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"""
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Given an array X, returns the column indices for the dummy variables.
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Parameters
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----------
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X : array_like
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A 1d or 2d array of numbers
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Examples
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--------
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>>> X = np.random.randint(0, 2, size=(15,5)).astype(float)
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>>> X[:,1:3] = np.random.randn(15,2)
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>>> ind = _isdummy(X)
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>>> ind
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array([0, 3, 4])
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"""
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X = np.asarray(X)
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if X.ndim > 1:
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ind = np.zeros(X.shape[1]).astype(bool)
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max = (np.max(X, axis=0) == 1)
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min = (np.min(X, axis=0) == 0)
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remainder = np.all(X % 1. == 0, axis=0)
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ind = min & max & remainder
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if X.ndim == 1:
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ind = np.asarray([ind])
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return np.where(ind)[0]
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def _get_dummy_index(X, const_idx):
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dummy_ind = _isdummy(X)
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dummy = True
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if dummy_ind.size == 0: # do not waste your time
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dummy = False
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dummy_ind = None # this gets passed to stand err func
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return dummy_ind, dummy
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def _iscount(X):
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"""
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Given an array X, returns the column indices for count variables.
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Parameters
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----------
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X : array_like
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A 1d or 2d array of numbers
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Examples
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--------
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>>> X = np.random.randint(0, 10, size=(15,5)).astype(float)
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>>> X[:,1:3] = np.random.randn(15,2)
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>>> ind = _iscount(X)
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>>> ind
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array([0, 3, 4])
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"""
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X = np.asarray(X)
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remainder = np.logical_and(np.logical_and(np.all(X % 1. == 0, axis = 0),
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X.var(0) != 0), np.all(X >= 0, axis=0))
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dummy = _isdummy(X)
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remainder = np.where(remainder)[0].tolist()
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for idx in dummy:
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remainder.remove(idx)
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return np.array(remainder)
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def _get_count_index(X, const_idx):
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count_ind = _iscount(X)
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count = True
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if count_ind.size == 0: # do not waste your time
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count = False
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count_ind = None # for stand err func
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return count_ind, count
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def _get_margeff_exog(exog, at, atexog, ind):
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if atexog is not None: # user supplied
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if isinstance(atexog, dict):
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# assumes values are singular or of len(exog)
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for key in atexog:
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exog[:,key] = atexog[key]
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elif isinstance(atexog, np.ndarray): #TODO: handle DataFrames
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if atexog.ndim == 1:
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k_vars = len(atexog)
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else:
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k_vars = atexog.shape[1]
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try:
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assert k_vars == exog.shape[1]
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except:
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raise ValueError("atexog does not have the same number "
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"of variables as exog")
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exog = atexog
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#NOTE: we should fill in atexog after we process at
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if at == 'mean':
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exog = np.atleast_2d(exog.mean(0))
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elif at == 'median':
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exog = np.atleast_2d(np.median(exog, axis=0))
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elif at == 'zero':
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exog = np.zeros((1,exog.shape[1]))
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exog[0,~ind] = 1
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return exog
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def _get_count_effects(effects, exog, count_ind, method, model, params):
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"""
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If there's a count variable, the predicted difference is taken by
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subtracting one and adding one to exog then averaging the difference
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"""
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# this is the index for the effect and the index for count col in exog
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for i in count_ind:
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exog0 = exog.copy()
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exog0[:, i] -= 1
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effect0 = model.predict(params, exog0)
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exog0[:, i] += 2
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effect1 = model.predict(params, exog0)
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#NOTE: done by analogy with dummy effects but untested bc
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# stata does not handle both count and eydx anywhere
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if 'ey' in method:
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effect0 = np.log(effect0)
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effect1 = np.log(effect1)
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effects[:, i] = ((effect1 - effect0)/2)
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return effects
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def _get_dummy_effects(effects, exog, dummy_ind, method, model, params):
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"""
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If there's a dummy variable, the predicted difference is taken at
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0 and 1
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"""
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# this is the index for the effect and the index for dummy col in exog
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for i in dummy_ind:
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exog0 = exog.copy() # only copy once, can we avoid a copy?
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exog0[:,i] = 0
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effect0 = model.predict(params, exog0)
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#fittedvalues0 = np.dot(exog0,params)
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exog0[:,i] = 1
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effect1 = model.predict(params, exog0)
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if 'ey' in method:
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effect0 = np.log(effect0)
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effect1 = np.log(effect1)
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effects[:, i] = (effect1 - effect0)
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return effects
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def _effects_at(effects, at):
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if at == 'all':
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effects = effects
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elif at == 'overall':
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effects = effects.mean(0)
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else:
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effects = effects[0,:]
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return effects
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def _margeff_cov_params_dummy(model, cov_margins, params, exog, dummy_ind,
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method, J):
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r"""
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Returns the Jacobian for discrete regressors for use in margeff_cov_params.
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For discrete regressors the marginal effect is
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\Delta F = F(XB) | d = 1 - F(XB) | d = 0
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The row of the Jacobian for this variable is given by
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f(XB)*X | d = 1 - f(XB)*X | d = 0
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Where F is the default prediction of the model.
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"""
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for i in dummy_ind:
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exog0 = exog.copy()
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exog1 = exog.copy()
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exog0[:,i] = 0
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exog1[:,i] = 1
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dfdb0 = model._derivative_predict(params, exog0, method)
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dfdb1 = model._derivative_predict(params, exog1, method)
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dfdb = (dfdb1 - dfdb0)
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if dfdb.ndim >= 2: # for overall
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dfdb = dfdb.mean(0)
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if J > 1:
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K = dfdb.shape[1] // (J-1)
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cov_margins[i::K, :] = dfdb
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else:
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# dfdb could be too short if there are extra params, k_extra > 0
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cov_margins[i, :len(dfdb)] = dfdb # how each F changes with change in B
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return cov_margins
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def _margeff_cov_params_count(model, cov_margins, params, exog, count_ind,
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method, J):
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r"""
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Returns the Jacobian for discrete regressors for use in margeff_cov_params.
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For discrete regressors the marginal effect is
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\Delta F = F(XB) | d += 1 - F(XB) | d -= 1
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The row of the Jacobian for this variable is given by
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(f(XB)*X | d += 1 - f(XB)*X | d -= 1) / 2
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where F is the default prediction for the model.
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"""
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for i in count_ind:
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exog0 = exog.copy()
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exog0[:,i] -= 1
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dfdb0 = model._derivative_predict(params, exog0, method)
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exog0[:,i] += 2
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dfdb1 = model._derivative_predict(params, exog0, method)
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dfdb = (dfdb1 - dfdb0)
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if dfdb.ndim >= 2: # for overall
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dfdb = dfdb.mean(0) / 2
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if J > 1:
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K = dfdb.shape[1] / (J-1)
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cov_margins[i::K, :] = dfdb
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else:
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# dfdb could be too short if there are extra params, k_extra > 0
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cov_margins[i, :len(dfdb)] = dfdb # how each F changes with change in B
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return cov_margins
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def margeff_cov_params(model, params, exog, cov_params, at, derivative,
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dummy_ind, count_ind, method, J):
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"""
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Computes the variance-covariance of marginal effects by the delta method.
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Parameters
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----------
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model : model instance
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The model that returned the fitted results. Its pdf method is used
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for computing the Jacobian of discrete variables in dummy_ind and
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count_ind
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params : array_like
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estimated model parameters
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exog : array_like
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exogenous variables at which to calculate the derivative
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cov_params : array_like
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The variance-covariance of the parameters
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at : str
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Options are:
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- 'overall', The average of the marginal effects at each
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observation.
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- 'mean', The marginal effects at the mean of each regressor.
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- 'median', The marginal effects at the median of each regressor.
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- 'zero', The marginal effects at zero for each regressor.
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- 'all', The marginal effects at each observation.
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Only overall has any effect here.you
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derivative : function or array_like
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If a function, it returns the marginal effects of the model with
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respect to the exogenous variables evaluated at exog. Expected to be
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called derivative(params, exog). This will be numerically
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differentiated. Otherwise, it can be the Jacobian of the marginal
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effects with respect to the parameters.
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dummy_ind : array_like
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Indices of the columns of exog that contain dummy variables
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count_ind : array_like
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Indices of the columns of exog that contain count variables
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Notes
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-----
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For continuous regressors, the variance-covariance is given by
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Asy. Var[MargEff] = [d margeff / d params] V [d margeff / d params]'
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where V is the parameter variance-covariance.
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The outer Jacobians are computed via numerical differentiation if
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derivative is a function.
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"""
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if callable(derivative):
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from statsmodels.tools.numdiff import approx_fprime_cs
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params = params.ravel('F') # for Multinomial
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try:
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jacobian_mat = approx_fprime_cs(params, derivative,
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args=(exog,method))
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except TypeError: # norm.cdf does not take complex values
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from statsmodels.tools.numdiff import approx_fprime
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jacobian_mat = approx_fprime(params, derivative,
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args=(exog,method))
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if at == 'overall':
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jacobian_mat = np.mean(jacobian_mat, axis=1)
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else:
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jacobian_mat = jacobian_mat.squeeze() # exog was 2d row vector
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if dummy_ind is not None:
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jacobian_mat = _margeff_cov_params_dummy(model, jacobian_mat,
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params, exog, dummy_ind, method, J)
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if count_ind is not None:
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jacobian_mat = _margeff_cov_params_count(model, jacobian_mat,
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params, exog, count_ind, method, J)
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else:
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jacobian_mat = derivative
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#NOTE: this will not go through for at == 'all'
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return np.dot(np.dot(jacobian_mat, cov_params), jacobian_mat.T)
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def margeff_cov_with_se(model, params, exog, cov_params, at, derivative,
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dummy_ind, count_ind, method, J):
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"""
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See margeff_cov_params.
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Same function but returns both the covariance of the marginal effects
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and their standard errors.
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"""
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cov_me = margeff_cov_params(model, params, exog, cov_params, at,
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derivative, dummy_ind,
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count_ind, method, J)
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return cov_me, np.sqrt(np.diag(cov_me))
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def margeff():
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raise NotImplementedError
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def _check_at_is_all(method):
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if method['at'] == 'all':
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raise ValueError("Only margeff are available when `at` is "
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"'all'. Please input specific points if you would "
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"like to do inference.")
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_transform_names = dict(dydx='dy/dx',
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eyex='d(lny)/d(lnx)',
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dyex='dy/d(lnx)',
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eydx='d(lny)/dx')
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class Margins:
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"""
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Mostly a do nothing class. Lays out the methods expected of a sub-class.
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This is just a sketch of what we may want out of a general margins class.
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I (SS) need to look at details of other models.
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"""
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def __init__(self, results, get_margeff, derivative, dist=None,
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margeff_args=()):
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self._cache = {}
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self.results = results
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self.dist = dist
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self.get_margeff(margeff_args)
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def _reset(self):
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self._cache = {}
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def get_margeff(self, *args, **kwargs):
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self._reset()
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self.margeff = self.get_margeff(*args)
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@cache_readonly
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def tvalues(self):
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raise NotImplementedError
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@cache_readonly
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def cov_margins(self):
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raise NotImplementedError
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@cache_readonly
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def margins_se(self):
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raise NotImplementedError
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def summary_frame(self):
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raise NotImplementedError
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@cache_readonly
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def pvalues(self):
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raise NotImplementedError
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def conf_int(self, alpha=.05):
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raise NotImplementedError
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def summary(self, alpha=.05):
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raise NotImplementedError
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#class DiscreteMargins(Margins):
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class DiscreteMargins:
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"""Get marginal effects of a Discrete Choice model.
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Parameters
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----------
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results : DiscreteResults instance
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The results instance of a fitted discrete choice model
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args : tuple
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Args are passed to `get_margeff`. This is the same as
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results.get_margeff. See there for more information.
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kwargs : dict
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Keyword args are passed to `get_margeff`. This is the same as
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results.get_margeff. See there for more information.
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"""
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def __init__(self, results, args, kwargs={}):
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self._cache = {}
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self.results = results
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self.get_margeff(*args, **kwargs)
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def _reset(self):
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self._cache = {}
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@cache_readonly
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def tvalues(self):
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_check_at_is_all(self.margeff_options)
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return self.margeff / self.margeff_se
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def summary_frame(self, alpha=.05):
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"""
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Returns a DataFrame summarizing the marginal effects.
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Parameters
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----------
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alpha : float
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Number between 0 and 1. The confidence intervals have the
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probability 1-alpha.
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Returns
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-------
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frame : DataFrames
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A DataFrame summarizing the marginal effects.
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Notes
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-----
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The dataframe is created on each call and not cached, as are the
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tables build in `summary()`
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"""
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_check_at_is_all(self.margeff_options)
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results = self.results
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model = self.results.model
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from pandas import DataFrame, MultiIndex
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names = [_transform_names[self.margeff_options['method']],
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'Std. Err.', 'z', 'Pr(>|z|)',
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'Conf. Int. Low', 'Cont. Int. Hi.']
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ind = self.results.model.exog.var(0) != 0 # True if not a constant
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exog_names = self.results.model.exog_names
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k_extra = getattr(model, 'k_extra', 0)
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if k_extra > 0:
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exog_names = exog_names[:-k_extra]
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var_names = [name for i,name in enumerate(exog_names) if ind[i]]
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if self.margeff.ndim == 2:
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# MNLogit case
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ci = self.conf_int(alpha)
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table = np.column_stack([i.ravel("F") for i in
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[self.margeff, self.margeff_se, self.tvalues,
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self.pvalues, ci[:, 0, :], ci[:, 1, :]]])
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_, yname_list = results._get_endog_name(model.endog_names,
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None, all=True)
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ynames = np.repeat(yname_list, len(var_names))
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xnames = np.tile(var_names, len(yname_list))
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index = MultiIndex.from_tuples(list(zip(ynames, xnames)),
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names=['endog', 'exog'])
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else:
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table = np.column_stack((self.margeff, self.margeff_se, self.tvalues,
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self.pvalues, self.conf_int(alpha)))
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index=var_names
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return DataFrame(table, columns=names, index=index)
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@cache_readonly
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def pvalues(self):
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_check_at_is_all(self.margeff_options)
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return norm.sf(np.abs(self.tvalues)) * 2
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def conf_int(self, alpha=.05):
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"""
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Returns the confidence intervals of the marginal effects
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Parameters
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----------
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alpha : float
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Number between 0 and 1. The confidence intervals have the
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probability 1-alpha.
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Returns
|
|
-------
|
|
conf_int : ndarray
|
|
An array with lower, upper confidence intervals for the marginal
|
|
effects.
|
|
"""
|
|
_check_at_is_all(self.margeff_options)
|
|
me_se = self.margeff_se
|
|
q = norm.ppf(1 - alpha / 2)
|
|
lower = self.margeff - q * me_se
|
|
upper = self.margeff + q * me_se
|
|
return np.asarray(lzip(lower, upper))
|
|
|
|
def summary(self, alpha=.05):
|
|
"""
|
|
Returns a summary table for marginal effects
|
|
|
|
Parameters
|
|
----------
|
|
alpha : float
|
|
Number between 0 and 1. The confidence intervals have the
|
|
probability 1-alpha.
|
|
|
|
Returns
|
|
-------
|
|
Summary : SummaryTable
|
|
A SummaryTable instance
|
|
"""
|
|
_check_at_is_all(self.margeff_options)
|
|
results = self.results
|
|
model = results.model
|
|
title = model.__class__.__name__ + " Marginal Effects"
|
|
method = self.margeff_options['method']
|
|
top_left = [('Dep. Variable:', [model.endog_names]),
|
|
('Method:', [method]),
|
|
('At:', [self.margeff_options['at']]),]
|
|
|
|
from statsmodels.iolib.summary import (Summary, summary_params,
|
|
table_extend)
|
|
exog_names = model.exog_names[:] # copy
|
|
smry = Summary()
|
|
|
|
# TODO: sigh, we really need to hold on to this in _data...
|
|
_, const_idx = _get_const_index(model.exog)
|
|
if const_idx is not None:
|
|
exog_names.pop(const_idx[0])
|
|
if getattr(model, 'k_extra', 0) > 0:
|
|
exog_names = exog_names[:-model.k_extra]
|
|
|
|
J = int(getattr(model, "J", 1))
|
|
if J > 1:
|
|
yname, yname_list = results._get_endog_name(model.endog_names,
|
|
None, all=True)
|
|
else:
|
|
yname = model.endog_names
|
|
yname_list = [yname]
|
|
|
|
smry.add_table_2cols(self, gleft=top_left, gright=[],
|
|
yname=yname, xname=exog_names, title=title)
|
|
|
|
# NOTE: add_table_params is not general enough yet for margeff
|
|
# could use a refactor with getattr instead of hard-coded params
|
|
# tvalues etc.
|
|
table = []
|
|
conf_int = self.conf_int(alpha)
|
|
margeff = self.margeff
|
|
margeff_se = self.margeff_se
|
|
tvalues = self.tvalues
|
|
pvalues = self.pvalues
|
|
if J > 1:
|
|
for eq in range(J):
|
|
restup = (results, margeff[:,eq], margeff_se[:,eq],
|
|
tvalues[:,eq], pvalues[:,eq], conf_int[:,:,eq])
|
|
tble = summary_params(restup, yname=yname_list[eq],
|
|
xname=exog_names, alpha=alpha, use_t=False,
|
|
skip_header=True)
|
|
tble.title = yname_list[eq]
|
|
# overwrite coef with method name
|
|
header = ['', _transform_names[method], 'std err', 'z',
|
|
'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']']
|
|
tble.insert_header_row(0, header)
|
|
table.append(tble)
|
|
|
|
table = table_extend(table, keep_headers=True)
|
|
else:
|
|
restup = (results, margeff, margeff_se, tvalues, pvalues, conf_int)
|
|
table = summary_params(restup, yname=yname, xname=exog_names,
|
|
alpha=alpha, use_t=False, skip_header=True)
|
|
header = ['', _transform_names[method], 'std err', 'z',
|
|
'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']']
|
|
table.insert_header_row(0, header)
|
|
|
|
smry.tables.append(table)
|
|
return smry
|
|
|
|
def get_margeff(self, at='overall', method='dydx', atexog=None,
|
|
dummy=False, count=False):
|
|
"""Get marginal effects of the fitted model.
|
|
|
|
Parameters
|
|
----------
|
|
at : str, optional
|
|
Options are:
|
|
|
|
- 'overall', The average of the marginal effects at each
|
|
observation.
|
|
- 'mean', The marginal effects at the mean of each regressor.
|
|
- 'median', The marginal effects at the median of each regressor.
|
|
- 'zero', The marginal effects at zero for each regressor.
|
|
- 'all', The marginal effects at each observation. If `at` is all
|
|
only margeff will be available.
|
|
|
|
Note that if `exog` is specified, then marginal effects for all
|
|
variables not specified by `exog` are calculated using the `at`
|
|
option.
|
|
method : str, optional
|
|
Options are:
|
|
|
|
- 'dydx' - dy/dx - No transformation is made and marginal effects
|
|
are returned. This is the default.
|
|
- 'eyex' - estimate elasticities of variables in `exog` --
|
|
d(lny)/d(lnx)
|
|
- 'dyex' - estimate semi-elasticity -- dy/d(lnx)
|
|
- 'eydx' - estimate semi-elasticity -- d(lny)/dx
|
|
|
|
Note that tranformations are done after each observation is
|
|
calculated. Semi-elasticities for binary variables are computed
|
|
using the midpoint method. 'dyex' and 'eyex' do not make sense
|
|
for discrete variables.
|
|
atexog : array_like, optional
|
|
Optionally, you can provide the exogenous variables over which to
|
|
get the marginal effects. This should be a dictionary with the key
|
|
as the zero-indexed column number and the value of the dictionary.
|
|
Default is None for all independent variables less the constant.
|
|
dummy : bool, optional
|
|
If False, treats binary variables (if present) as continuous. This
|
|
is the default. Else if True, treats binary variables as
|
|
changing from 0 to 1. Note that any variable that is either 0 or 1
|
|
is treated as binary. Each binary variable is treated separately
|
|
for now.
|
|
count : bool, optional
|
|
If False, treats count variables (if present) as continuous. This
|
|
is the default. Else if True, the marginal effect is the
|
|
change in probabilities when each observation is increased by one.
|
|
|
|
Returns
|
|
-------
|
|
effects : ndarray
|
|
the marginal effect corresponding to the input options
|
|
|
|
Notes
|
|
-----
|
|
When using after Poisson, returns the expected number of events
|
|
per period, assuming that the model is loglinear.
|
|
"""
|
|
self._reset() # always reset the cache when this is called
|
|
#TODO: if at is not all or overall, we can also put atexog values
|
|
# in summary table head
|
|
method = method.lower()
|
|
at = at.lower()
|
|
_check_margeff_args(at, method)
|
|
self.margeff_options = dict(method=method, at=at)
|
|
results = self.results
|
|
model = results.model
|
|
params = results.params
|
|
exog = model.exog.copy() # copy because values are changed
|
|
effects_idx, const_idx = _get_const_index(exog)
|
|
|
|
if dummy:
|
|
_check_discrete_args(at, method)
|
|
dummy_idx, dummy = _get_dummy_index(exog, const_idx)
|
|
else:
|
|
dummy_idx = None
|
|
|
|
if count:
|
|
_check_discrete_args(at, method)
|
|
count_idx, count = _get_count_index(exog, const_idx)
|
|
else:
|
|
count_idx = None
|
|
|
|
# attach dummy_idx and cout_idx
|
|
self.dummy_idx = dummy_idx
|
|
self.count_idx = count_idx
|
|
|
|
# get the exogenous variables
|
|
exog = _get_margeff_exog(exog, at, atexog, effects_idx)
|
|
|
|
# get base marginal effects, handled by sub-classes
|
|
effects = model._derivative_exog(params, exog, method,
|
|
dummy_idx, count_idx)
|
|
|
|
J = getattr(model, 'J', 1)
|
|
effects_idx = np.tile(effects_idx, J) # adjust for multi-equation.
|
|
|
|
effects = _effects_at(effects, at)
|
|
|
|
if at == 'all':
|
|
if J > 1:
|
|
K = model.K - np.any(~effects_idx) # subtract constant
|
|
self.margeff = effects[:, effects_idx].reshape(-1, K, J,
|
|
order='F')
|
|
else:
|
|
self.margeff = effects[:, effects_idx]
|
|
else:
|
|
# Set standard error of the marginal effects by Delta method.
|
|
margeff_cov, margeff_se = margeff_cov_with_se(model, params, exog,
|
|
results.cov_params(), at,
|
|
model._derivative_exog,
|
|
dummy_idx, count_idx,
|
|
method, J)
|
|
|
|
# reshape for multi-equation
|
|
if J > 1:
|
|
K = model.K - np.any(~effects_idx) # subtract constant
|
|
self.margeff = effects[effects_idx].reshape(K, J, order='F')
|
|
self.margeff_se = margeff_se[effects_idx].reshape(K, J,
|
|
order='F')
|
|
self.margeff_cov = margeff_cov[effects_idx][:, effects_idx]
|
|
else:
|
|
# do not care about at constant
|
|
# hack truncate effects_idx again if necessary
|
|
# if eyex, then effects is truncated to be without extra params
|
|
effects_idx = effects_idx[:len(effects)]
|
|
self.margeff_cov = margeff_cov[effects_idx][:, effects_idx]
|
|
self.margeff_se = margeff_se[effects_idx]
|
|
self.margeff = effects[effects_idx]
|