Source code for statsmodels.genmod.generalized_estimating_equations

"""
Procedures for fitting marginal regression models to dependent data
using Generalized Estimating Equations.

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.
"""
from __future__ import division
from statsmodels.compat.python import range, lzip, zip

import numpy as np
from scipy import stats
import pandas as pd
import patsy

from statsmodels.tools.decorators import (cache_readonly,
                                          resettable_cache)
import statsmodels.base.model as base
# used for wrapper:
import statsmodels.regression.linear_model as lm
import statsmodels.base.wrapper as wrap

from statsmodels.genmod import families
from statsmodels.genmod import cov_struct as cov_structs

import statsmodels.genmod.families.varfuncs as varfuncs
from statsmodels.genmod.families.links import Link

from statsmodels.tools.sm_exceptions import (ConvergenceWarning,
                                             DomainWarning,
                                             IterationLimitWarning,
                                             ValueWarning)
import warnings

from statsmodels.graphics._regressionplots_doc import (
    _plot_added_variable_doc,
    _plot_partial_residuals_doc,
    _plot_ceres_residuals_doc)


class ParameterConstraint(object):
    """
    A class for managing linear equality constraints for a parameter
    vector.
    """

    def __init__(self, lhs, rhs, exog):
        """
        Parameters
        ----------
        lhs : ndarray
           A q x p matrix which is the left hand side of the
           constraint lhs * param = rhs.  The number of constraints is
           q >= 1 and p is the dimension of the parameter vector.
        rhs : ndarray
          A 1-dimensional vector of length q which is the right hand
          side of the constraint equation.
        exog : ndarray
          The n x p exognenous data for the full model.
        """

        # In case a row or column vector is passed (patsy linear
        # constraints passes a column vector).
        rhs = np.atleast_1d(rhs.squeeze())

        if rhs.ndim > 1:
            raise ValueError("The right hand side of the constraint "
                             "must be a vector.")

        if len(rhs) != lhs.shape[0]:
            raise ValueError("The number of rows of the left hand "
                             "side constraint matrix L must equal "
                             "the length of the right hand side "
                             "constraint vector R.")

        self.lhs = lhs
        self.rhs = rhs

        # The columns of lhs0 are an orthogonal basis for the
        # orthogonal complement to row(lhs), the columns of lhs1 are
        # an orthogonal basis for row(lhs).  The columns of lhsf =
        # [lhs0, lhs1] are mutually orthogonal.
        lhs_u, lhs_s, lhs_vt = np.linalg.svd(lhs.T, full_matrices=1)
        self.lhs0 = lhs_u[:, len(lhs_s):]
        self.lhs1 = lhs_u[:, 0:len(lhs_s)]
        self.lhsf = np.hstack((self.lhs0, self.lhs1))

        # param0 is one solution to the underdetermined system
        # L * param = R.
        self.param0 = np.dot(self.lhs1, np.dot(lhs_vt, self.rhs) /
                             lhs_s)

        self._offset_increment = np.dot(exog, self.param0)

        self.orig_exog = exog
        self.exog_fulltrans = np.dot(exog, self.lhsf)

    def offset_increment(self):
        """
        Returns a vector that should be added to the offset vector to
        accommodate the constraint.

        Parameters
        ----------
        exog : array-like
           The exogeneous data for the model.
        """

        return self._offset_increment

    def reduced_exog(self):
        """
        Returns a linearly transformed exog matrix whose columns span
        the constrained model space.

        Parameters
        ----------
        exog : array-like
           The exogeneous data for the model.
        """
        return self.exog_fulltrans[:, 0:self.lhs0.shape[1]]

    def restore_exog(self):
        """
        Returns the full exog matrix before it was reduced to
        satisfy the constraint.
        """
        return self.orig_exog

    def unpack_param(self, params):
        """
        Converts the parameter vector `params` from reduced to full
        coordinates.
        """

        return self.param0 + np.dot(self.lhs0, params)

    def unpack_cov(self, bcov):
        """
        Converts the covariance matrix `bcov` from reduced to full
        coordinates.
        """

        return np.dot(self.lhs0, np.dot(bcov, self.lhs0.T))


_gee_init_doc = """
    Marginal regression model fit using Generalized Estimating Equations.

    GEE can be used to fit Generalized Linear Models (GLMs) when the
    data have a grouped structure, and the observations are possibly
    correlated within groups but not between groups.

    Parameters
    ----------
    endog : array-like
        1d array of endogenous values (i.e. responses, outcomes,
        dependent variables, or 'Y' values).
    exog : array-like
        2d array of exogeneous values (i.e. covariates, predictors,
        independent variables, regressors, or 'X' values). A `nobs x
        k` array where `nobs` is the number of observations and `k` is
        the number of regressors. An intercept is not included by
        default and should be added by the user. See
        `statsmodels.tools.add_constant`.
    groups : array-like
        A 1d array of length `nobs` containing the group labels.
    time : array-like
        A 2d array of time (or other index) values, used by some
        dependence structures to define similarity relationships among
        observations within a cluster.
    family : family class instance
%(family_doc)s
    cov_struct : CovStruct class instance
        The default is Independence.  To specify an exchangeable
        structure use cov_struct = Exchangeable().  See
        statsmodels.genmod.cov_struct.CovStruct for more
        information.
    offset : array-like
        An offset to be included in the fit.  If provided, must be
        an array whose length is the number of rows in exog.
    dep_data : array-like
        Additional data passed to the dependence structure.
    constraint : (ndarray, ndarray)
        If provided, the constraint is a tuple (L, R) such that the
        model parameters are estimated under the constraint L *
        param = R, where L is a q x p matrix and R is a
        q-dimensional vector.  If constraint is provided, a score
        test is performed to compare the constrained model to the
        unconstrained model.
    update_dep : bool
        If true, the dependence parameters are optimized, otherwise
        they are held fixed at their starting values.
    weights : array-like
        An array of weights to use in the analysis.  The weights must
        be constant within each group.  These correspond to
        probability weights (pweights) in Stata.
    %(extra_params)s

    See Also
    --------
    statsmodels.genmod.families.family
    :ref:`families`
    :ref:`links`

    Notes
    -----
    Only the following combinations make sense for family and link ::

                   + ident log logit probit cloglog pow opow nbinom loglog logc
      Gaussian     |   x    x                        x
      inv Gaussian |   x    x                        x
      binomial     |   x    x    x     x       x     x    x           x      x
      Poission     |   x    x                        x
      neg binomial |   x    x                        x          x
      gamma        |   x    x                        x

    Not all of these link functions are currently available.

    Endog and exog are references so that if the data they refer
    to are already arrays and these arrays are changed, endog and
    exog will change.

    The "robust" covariance type is the standard "sandwich estimator"
    (e.g. Liang and Zeger (1986)).  It is the default here and in most
    other packages.  The "naive" estimator gives smaller standard
    errors, but is only correct if the working correlation structure
    is correctly specified.  The "bias reduced" estimator of Mancl and
    DeRouen (Biometrics, 2001) reduces the downard bias of the robust
    estimator.

    The robust covariance provided here follows Liang and Zeger (1986)
    and agrees with R's gee implementation.  To obtain the robust
    standard errors reported in Stata, multiply by sqrt(N / (N - g)),
    where N is the total sample size, and g is the average group size.

    Examples
    --------
    %(example)s
"""

_gee_family_doc = """\
        The default is Gaussian.  To specify the binomial
        distribution use `family=sm.families.Binomial()`. Each family
        can take a link instance as an argument.  See
        statsmodels.genmod.families.family for more information."""

_gee_ordinal_family_doc = """\
        The only family supported is `Binomial`.  The default `Logit`
        link may be replaced with `probit` if desired."""

_gee_nominal_family_doc = """\
        The default value `None` uses a multinomial logit family
        specifically designed for use with GEE.  Setting this
        argument to a non-default value is not currently supported."""

_gee_fit_doc = """
    Fits a marginal regression model using generalized estimating
    equations (GEE).

    Parameters
    ----------
    maxiter : integer
        The maximum number of iterations
    ctol : float
        The convergence criterion for stopping the Gauss-Seidel
        iterations
    start_params : array-like
        A vector of starting values for the regression
        coefficients.  If None, a default is chosen.
    params_niter : integer
        The number of Gauss-Seidel updates of the mean structure
        parameters that take place prior to each update of the
        dependence structure.
    first_dep_update : integer
        No dependence structure updates occur before this
        iteration number.
    cov_type : string
        One of "robust", "naive", or "bias_reduced".
    ddof_scale : scalar or None
        The scale parameter is estimated as the sum of squared
        Pearson residuals divided by `N - ddof_scale`, where N
        is the total sample size.  If `ddof_scale` is None, the
        number of covariates (including an intercept if present)
        is used.
    scaling_factor : scalar
        The estimated covariance of the parameter estimates is
        scaled by this value.  Default is 1, Stata uses N / (N - g),
        where N is the total sample size and g is the average group
        size.

    Returns
    -------
    An instance of the GEEResults class or subclass

    Notes
    -----
    If convergence difficulties occur, increase the values of
    `first_dep_update` and/or `params_niter`.  Setting
    `first_dep_update` to a greater value (e.g. ~10-20) causes the
    algorithm to move close to the GLM solution before attempting
    to identify the dependence structure.

    For the Gaussian family, there is no benefit to setting
    `params_niter` to a value greater than 1, since the mean
    structure parameters converge in one step.
"""

_gee_results_doc = """
    Returns
    -------
    **Attributes**

    cov_params_default : ndarray
        default covariance of the parameter estimates. Is chosen among one
        of the following three based on `cov_type`
    cov_robust : ndarray
        covariance of the parameter estimates that is robust
    cov_naive : ndarray
        covariance of the parameter estimates that is not robust to
        correlation or variance misspecification
    cov_robust_bc : ndarray
        covariance of the parameter estimates that is robust and bias
        reduced
    converged : bool
        indicator for convergence of the optimization.
        True if the norm of the score is smaller than a threshold
    cov_type : string
        string indicating whether a "robust", "naive" or "bias_reduced"
        covariance is used as default
    fit_history : dict
        Contains information about the iterations.
    fittedvalues : array
        Linear predicted values for the fitted model.
        dot(exog, params)
    model : class instance
        Pointer to GEE model instance that called `fit`.
    normalized_cov_params : array
        See GEE docstring
    params : array
        The coefficients of the fitted model.  Note that
        interpretation of the coefficients often depends on the
        distribution family and the data.
    scale : float
        The estimate of the scale / dispersion for the model fit.
        See GEE.fit for more information.
    score_norm : float
        norm of the score at the end of the iterative estimation.
    bse : array
        The standard errors of the fitted GEE parameters.
"""

_gee_example = """
    Logistic regression with autoregressive working dependence:

    >>> import statsmodels.api as sm
    >>> family = sm.families.Binomial()
    >>> va = sm.cov_struct.Autoregressive()
    >>> model = sm.GEE(endog, exog, group, family=family, cov_struct=va)
    >>> result = model.fit()
    >>> print(result.summary())

    Use formulas to fit a Poisson GLM with independent working
    dependence:

    >>> import statsmodels.api as sm
    >>> fam = sm.families.Poisson()
    >>> ind = sm.cov_struct.Independence()
    >>> model = sm.GEE.from_formula("y ~ age + trt + base", "subject", \
                                 data, cov_struct=ind, family=fam)
    >>> result = model.fit()
    >>> print(result.summary())

    Equivalent, using the formula API:

    >>> import statsmodels.api as sm
    >>> import statsmodels.formula.api as smf
    >>> fam = sm.families.Poisson()
    >>> ind = sm.cov_struct.Independence()
    >>> model = smf.gee("y ~ age + trt + base", "subject", \
                    data, cov_struct=ind, family=fam)
    >>> result = model.fit()
    >>> print(result.summary())
"""

_gee_ordinal_example = """
    Fit an ordinal regression model using GEE, with "global
    odds ratio" dependence:

    >>> import statsmodels.api as sm
    >>> gor = sm.cov_struct.GlobalOddsRatio("ordinal")
    >>> model = sm.OrdinalGEE(endog, exog, groups, cov_struct=gor)
    >>> result = model.fit()
    >>> print(result.summary())

    Using formulas:

    >>> import statsmodels.formula.api as smf
    >>> model = smf.ordinal_gee("y ~ x1 + x2", groups, data,
                                    cov_struct=gor)
    >>> result = model.fit()
    >>> print(result.summary())
"""

_gee_nominal_example = """
    Fit a nominal regression model using GEE:

    >>> import statsmodels.api as sm
    >>> import statsmodels.formula.api as smf
    >>> gor = sm.cov_struct.GlobalOddsRatio("nominal")
    >>> model = sm.NominalGEE(endog, exog, groups, cov_struct=gor)
    >>> result = model.fit()
    >>> print(result.summary())

    Using formulas:

    >>> import statsmodels.api as sm
    >>> model = sm.NominalGEE.from_formula("y ~ x1 + x2", groups,
                     data, cov_struct=gor)
    >>> result = model.fit()
    >>> print(result.summary())

    Using the formula API:

    >>> import statsmodels.formula.api as smf
    >>> model = smf.nominal_gee("y ~ x1 + x2", groups, data,
                                cov_struct=gor)
    >>> result = model.fit()
    >>> print(result.summary())
"""


[docs]class GEE(base.Model): __doc__ = ( " Estimation of marginal regression models using Generalized\n" " Estimating Equations (GEE).\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_family_doc, 'example': _gee_example}) cached_means = None def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, exposure=None, dep_data=None, constraint=None, update_dep=True, weights=None, **kwargs): if family is not None: if not isinstance(family.link, tuple(family.safe_links)): import warnings msg = ("The {0} link function does not respect the " "domain of the {1} family.") warnings.warn(msg.format(family.link.__class__.__name__, family.__class__.__name__), DomainWarning) self.missing = missing self.dep_data = dep_data self.constraint = constraint self.update_dep = update_dep groups = np.array(groups) # in case groups is pandas # Pass groups, time, offset, and dep_data so they are # processed for missing data along with endog and exog. # Calling super creates self.exog, self.endog, etc. as # ndarrays and the original exog, endog, etc. are # self.data.endog, etc. super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, exposure=exposure, weights=weights, dep_data=dep_data, missing=missing, **kwargs) self._init_keys.extend(["update_dep", "constraint", "family", "cov_struct"]) # Handle the family argument if family is None: family = families.Gaussian() else: if not issubclass(family.__class__, families.Family): raise ValueError("GEE: `family` must be a genmod " "family instance") self.family = family # Handle the cov_struct argument if cov_struct is None: cov_struct = cov_structs.Independence() else: if not issubclass(cov_struct.__class__, cov_structs.CovStruct): raise ValueError("GEE: `cov_struct` must be a genmod " "cov_struct instance") self.cov_struct = cov_struct # Handle the offset and exposure self._offset_exposure = None if offset is not None: self._offset_exposure = self.offset.copy() self.offset = offset if exposure is not None: if not isinstance(self.family.link, families.links.Log): raise ValueError( "exposure can only be used with the log link function") if self._offset_exposure is not None: self._offset_exposure += np.log(exposure) else: self._offset_exposure = np.log(exposure) self.exposure = exposure # Handle the constraint self.constraint = None if constraint is not None: if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") if constraint[0].shape[1] != self.exog.shape[1]: raise ValueError( "GEE: the left hand side of the constraint must have " "the same number of columns as the exog matrix.") self.constraint = ParameterConstraint(constraint[0], constraint[1], self.exog) if self._offset_exposure is not None: self._offset_exposure += self.constraint.offset_increment() else: self._offset_exposure = ( self.constraint.offset_increment().copy()) self.exog = self.constraint.reduced_exog() # Create list of row indices for each group group_labels, ix = np.unique(self.groups, return_inverse=True) se = pd.Series(index=np.arange(len(ix))) gb = se.groupby(ix).groups dk = [(lb, np.asarray(gb[k])) for k, lb in enumerate(group_labels)] self.group_indices = dict(dk) self.group_labels = group_labels # Convert the data to the internal representation, which is a # list of arrays, corresponding to the groups. self.endog_li = self.cluster_list(self.endog) self.exog_li = self.cluster_list(self.exog) if self.weights is not None: self.weights_li = self.cluster_list(self.weights) self.weights_li = [x[0] for x in self.weights_li] self.weights_li = np.asarray(self.weights_li) self.num_group = len(self.endog_li) # Time defaults to a 1d grid with equal spacing if self.time is not None: self.time = np.asarray(self.time, np.float64) if self.time.ndim == 1: self.time = self.time[:, None] self.time_li = self.cluster_list(self.time) else: self.time_li = \ [np.arange(len(y), dtype=np.float64)[:, None] for y in self.endog_li] self.time = np.concatenate(self.time_li) if self._offset_exposure is not None: self.offset_li = self.cluster_list(self._offset_exposure) else: self.offset_li = None if constraint is not None: self.constraint.exog_fulltrans_li = \ self.cluster_list(self.constraint.exog_fulltrans) self.family = family self.cov_struct.initialize(self) # Total sample size group_ns = [len(y) for y in self.endog_li] self.nobs = sum(group_ns) # The following are column based, not on rank see #1928 self.df_model = self.exog.shape[1] - 1 # assumes constant self.df_resid = self.nobs - self.exog.shape[1] # Skip the covariance updates if all groups have a single # observation (reduces to fitting a GLM). maxgroup = max([len(x) for x in self.endog_li]) if maxgroup == 1: self.update_dep = False # Override to allow groups and time to be passed as variable # names.
[docs] @classmethod def from_formula(cls, formula, groups, data, subset=None, time=None, offset=None, exposure=None, *args, **kwargs): """ Create a GEE model instance from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model groups : array-like or string Array of grouping labels. If a string, this is the name of a variable in `data` that contains the grouping labels. data : array-like The data for the model. subset : array-like An array-like object of booleans, integers, or index values that indicate the subset of the data to used when fitting the model. time : array-like or string The time values, used for dependence structures involving distances between observations. If a string, this is the name of a variable in `data` that contains the time values. offset : array-like or string The offset values, added to the linear predictor. If a string, this is the name of a variable in `data` that contains the offset values. exposure : array-like or string The exposure values, only used if the link function is the logarithm function, in which case the log of `exposure` is added to the offset (if any). If a string, this is the name of a variable in `data` that contains the offset values. %(missing_param_doc)s args : extra arguments These are passed to the model kwargs : extra keyword arguments These are passed to the model with two exceptions. `dep_data` is processed as described below. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Optional arguments ------------------ dep_data : string or array-like Data used for estimating the dependence structure. See specific dependence structure classes (e.g. Nested) for details. If `dep_data` is a string, it is interpreted as a formula that is applied to `data`. If it is an array, it must be an array of strings corresponding to column names in `data`. Otherwise it must be an array-like with the same number of rows as data. Returns ------- model : GEE model instance Notes ------ `data` must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. This method currently does not correctly handle missing values, so missing values should be explicitly dropped from the DataFrame before calling this method. """ % {'missing_param_doc': base._missing_param_doc} groups_name = "Groups" if isinstance(groups, str): groups_name = groups groups = data[groups] if isinstance(time, str): time = data[time] if isinstance(offset, str): offset = data[offset] if isinstance(exposure, str): exposure = data[exposure] dep_data = kwargs.get("dep_data") dep_data_names = None if dep_data is not None: if isinstance(dep_data, str): dep_data = patsy.dmatrix(dep_data, data, return_type='dataframe') dep_data_names = dep_data.columns.tolist() else: dep_data_names = list(dep_data) dep_data = data[dep_data] kwargs["dep_data"] = np.asarray(dep_data) model = super(GEE, cls).from_formula(formula, data=data, subset=subset, groups=groups, time=time, offset=offset, exposure=exposure, *args, **kwargs) if dep_data_names is not None: model._dep_data_names = dep_data_names model._groups_name = groups_name return model
[docs] def cluster_list(self, array): """ Returns `array` split into subarrays corresponding to the cluster structure. """ if array.ndim == 1: return [np.array(array[self.group_indices[k]]) for k in self.group_labels] else: return [np.array(array[self.group_indices[k], :]) for k in self.group_labels]
[docs] def estimate_scale(self): """ Estimate the dispersion/scale. The scale parameter for binomial, Poisson, and multinomial families is fixed at 1, otherwise it is estimated from the data. """ if isinstance(self.family, (families.Binomial, families.Poisson, _Multinomial)): return 1. endog = self.endog_li cached_means = self.cached_means nobs = self.nobs varfunc = self.family.variance scale = 0. fsum = 0. for i in range(self.num_group): if len(endog[i]) == 0: continue expval, _ = cached_means[i] f = self.weights_li[i] if self.weights is not None else 1. sdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / sdev scale += f * np.sum(resid ** 2) fsum += f * len(endog[i]) scale /= (fsum * (nobs - self.ddof_scale) / float(nobs)) return scale
[docs] def mean_deriv(self, exog, lin_pred): """ Derivative of the expected endog with respect to the parameters. Parameters ---------- exog : array-like The exogeneous data at which the derivative is computed. lin_pred : array-like The values of the linear predictor. Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. Notes ----- If there is an offset or exposure, it should be added to `lin_pred` prior to calling this function. """ idl = self.family.link.inverse_deriv(lin_pred) dmat = exog * idl[:, None] return dmat
[docs] def mean_deriv_exog(self, exog, params, offset_exposure=None): """ Derivative of the expected endog with respect to exog. Parameters ---------- exog : array-like Values of the independent variables at which the derivative is calculated. params : array-like Parameter values at which the derivative is calculated. offset_exposure : array-like, optional Combined offset and exposure. Returns ------- The derivative of the expected endog with respect to exog. """ lin_pred = np.dot(exog, params) if offset_exposure is not None: lin_pred += offset_exposure idl = self.family.link.inverse_deriv(lin_pred) dmat = np.outer(idl, params) return dmat
def _update_mean_params(self): """ Returns ------- update : array-like The update vector such that params + update is the next iterate when solving the score equations. score : array-like The current value of the score equations, not incorporating the scale parameter. If desired, multiply this vector by the scale parameter to incorporate the scale. """ endog = self.endog_li exog = self.exog_li cached_means = self.cached_means varfunc = self.family.variance bmat, score = 0, 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) rslt = self.cov_struct.covariance_matrix_solve(expval, i, sdev, (dmat, resid)) if rslt is None: return None, None vinv_d, vinv_resid = tuple(rslt) f = self.weights_li[i] if self.weights is not None else 1. bmat += f * np.dot(dmat.T, vinv_d) score += f * np.dot(dmat.T, vinv_resid) update = np.linalg.solve(bmat, score) self._fit_history["cov_adjust"].append( self.cov_struct.cov_adjust) return update, score
[docs] def update_cached_means(self, mean_params): """ cached_means should always contain the most recent calculation of the group-wise mean vectors. This function should be called every time the regression parameters are changed, to keep the cached means up to date. """ endog = self.endog_li exog = self.exog_li offset = self.offset_li linkinv = self.family.link.inverse self.cached_means = [] for i in range(self.num_group): if len(endog[i]) == 0: continue lpr = np.dot(exog[i], mean_params) if offset is not None: lpr += offset[i] expval = linkinv(lpr) self.cached_means.append((expval, lpr))
def _covmat(self): """ Returns the sampling covariance matrix of the regression parameters and related quantities. Returns ------- cov_robust : array-like The robust, or sandwich estimate of the covariance, which is meaningful even if the working covariance structure is incorrectly specified. cov_naive : array-like The model-based estimate of the covariance, which is meaningful if the covariance structure is correctly specified. cmat : array-like The center matrix of the sandwich expression, used in obtaining score test results. """ endog = self.endog_li exog = self.exog_li varfunc = self.family.variance cached_means = self.cached_means # Calculate the naive (model-based) and robust (sandwich) # covariances. bmat, cmat = 0, 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (dmat, resid)) if rslt is None: return None, None, None, None vinv_d, vinv_resid = tuple(rslt) f = self.weights_li[i] if self.weights is not None else 1. bmat += f * np.dot(dmat.T, vinv_d) dvinv_resid = f * np.dot(dmat.T, vinv_resid) cmat += np.outer(dvinv_resid, dvinv_resid) scale = self.estimate_scale() bmati = np.linalg.inv(bmat) cov_naive = bmati * scale cov_robust = np.dot(bmati, np.dot(cmat, bmati)) cov_naive *= self.scaling_factor cov_robust *= self.scaling_factor return cov_robust, cov_naive, cmat # Calculate the bias-corrected sandwich estimate of Mancl and # DeRouen. def _bc_covmat(self, cov_naive): cov_naive = cov_naive / self.scaling_factor endog = self.endog_li exog = self.exog_li varfunc = self.family.variance cached_means = self.cached_means scale = self.estimate_scale() bcm = 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (dmat,)) if rslt is None: return None vinv_d = rslt[0] vinv_d /= scale hmat = np.dot(vinv_d, cov_naive) hmat = np.dot(hmat, dmat.T).T f = self.weights_li[i] if self.weights is not None else 1. aresid = np.linalg.solve(np.eye(len(resid)) - hmat, resid) rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (aresid,)) if rslt is None: return None srt = rslt[0] srt = f * np.dot(dmat.T, srt) / scale bcm += np.outer(srt, srt) cov_robust_bc = np.dot(cov_naive, np.dot(bcm, cov_naive)) cov_robust_bc *= self.scaling_factor return cov_robust_bc
[docs] def predict(self, params, exog=None, offset=None, exposure=None, linear=False): """ Return predicted values for a marginal regression model fit using GEE. Parameters ---------- params : array-like Parameters / coefficients of a marginal regression model. exog : array-like, optional Design / exogenous data. If exog is None, model exog is used. offset : array-like, optional Offset for exog if provided. If offset is None, model offset is used. exposure : array-like, optional Exposure for exog, if exposure is None, model exposure is used. Only allowed if link function is the logarithm. linear : bool If True, returns the linear predicted values. If False, returns the value of the inverse of the model's link function at the linear predicted values. Returns ------- An array of fitted values Notes ----- Using log(V) as the offset is equivalent to using V as the exposure. If exposure U and offset V are both provided, then log(U) + V is added to the linear predictor. """ # TODO: many paths through this, not well covered in tests if exposure is not None: if not isinstance(self.family.link, families.links.Log): raise ValueError( "exposure can only be used with the log link function") # This is the combined offset and exposure _offset = 0. # Using model exog if exog is None: exog = self.exog if not isinstance(self.family.link, families.links.Log): # Don't need to worry about exposure if offset is None: if self._offset_exposure is not None: _offset = self._offset_exposure.copy() else: _offset = offset else: if offset is None and exposure is None: if self._offset_exposure is not None: _offset = self._offset_exposure elif offset is None and exposure is not None: _offset = np.log(exposure) if hasattr(self, "offset"): _offset = _offset + self.offset elif offset is not None and exposure is None: _offset = offset if hasattr(self, "exposure"): _offset = offset + np.log(self.exposure) else: _offset = offset + np.log(exposure) # exog is provided: this is simpler than above because we # never use model exog or exposure if exog is provided. else: if offset is not None: _offset = _offset + offset if exposure is not None: _offset += np.log(exposure) lin_pred = _offset + np.dot(exog, params) if not linear: return self.family.link.inverse(lin_pred) return lin_pred
def _starting_params(self): # TODO: use GLM to get Poisson starting values return np.zeros(self.exog.shape[1])
[docs] def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust', ddof_scale=None, scaling_factor=1.): # Docstring attached below # Subtract this number from the total sample size when # normalizing the scale parameter estimate. if ddof_scale is None: self.ddof_scale = self.exog.shape[1] else: if not ddof_scale >= 0: raise ValueError( "ddof_scale must be a non-negative number or None") self.ddof_scale = ddof_scale self.scaling_factor = scaling_factor self._fit_history = {'params': [], 'score': [], 'dep_params': [], 'cov_adjust': []} if self.weights is not None and cov_type == 'naive': raise ValueError("when using weights, cov_type may not be naive") if start_params is None: mean_params = self._starting_params() else: start_params = np.asarray(start_params) mean_params = start_params.copy() self.update_cached_means(mean_params) del_params = -1. num_assoc_updates = 0 for itr in range(maxiter): update, score = self._update_mean_params() if update is None: warnings.warn("Singular matrix encountered in GEE update", ConvergenceWarning) break mean_params += update self.update_cached_means(mean_params) # L2 norm of the change in mean structure parameters at # this iteration. del_params = np.sqrt(np.sum(score ** 2)) self._fit_history['params'].append(mean_params.copy()) self._fit_history['score'].append(score) self._fit_history['dep_params'].append( self.cov_struct.dep_params) # Don't exit until the association parameters have been # updated at least once. if (del_params < ctol and (num_assoc_updates > 0 or self.update_dep is False)): break # Update the dependence structure if (self.update_dep and (itr % params_niter) == 0 and (itr >= first_dep_update)): self._update_assoc(mean_params) num_assoc_updates += 1 if del_params >= ctol: warnings.warn("Iteration limit reached prior to convergence", IterationLimitWarning) if mean_params is None: warnings.warn("Unable to estimate GEE parameters.", ConvergenceWarning) return None bcov, ncov, _ = self._covmat() if bcov is None: warnings.warn("Estimated covariance structure for GEE " "estimates is singular", ConvergenceWarning) return None bc_cov = None if cov_type == "bias_reduced": bc_cov = self._bc_covmat(ncov) if self.constraint is not None: x = mean_params.copy() mean_params, bcov = self._handle_constraint(mean_params, bcov) if mean_params is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None y, ncov = self._handle_constraint(x, ncov) if y is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None if bc_cov is not None: y, bc_cov = self._handle_constraint(x, bc_cov) if x is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None scale = self.estimate_scale() # kwargs to add to results instance, need to be available in __init__ res_kwds = dict(cov_type=cov_type, cov_robust=bcov, cov_naive=ncov, cov_robust_bc=bc_cov) # The superclass constructor will multiply the covariance # matrix argument bcov by scale, which we don't want, so we # divide bcov by the scale parameter here results = GEEResults(self, mean_params, bcov / scale, scale, cov_type=cov_type, use_t=False, attr_kwds=res_kwds) # attributes not needed during results__init__ results.fit_history = self._fit_history delattr(self, "_fit_history") results.score_norm = del_params results.converged = (del_params < ctol) results.cov_struct = self.cov_struct results.params_niter = params_niter results.first_dep_update = first_dep_update results.ctol = ctol results.maxiter = maxiter # These will be copied over to subclasses when upgrading. results._props = ["cov_type", "use_t", "cov_params_default", "cov_robust", "cov_naive", "cov_robust_bc", "fit_history", "score_norm", "converged", "cov_struct", "params_niter", "first_dep_update", "ctol", "maxiter"] return GEEResultsWrapper(results)
fit.__doc__ = _gee_fit_doc def _handle_constraint(self, mean_params, bcov): """ Expand the parameter estimate `mean_params` and covariance matrix `bcov` to the coordinate system of the unconstrained model. Parameters ---------- mean_params : array-like A parameter vector estimate for the reduced model. bcov : array-like The covariance matrix of mean_params. Returns ------- mean_params : array-like The input parameter vector mean_params, expanded to the coordinate system of the full model bcov : array-like The input covariance matrix bcov, expanded to the coordinate system of the full model """ # The number of variables in the full model red_p = len(mean_params) full_p = self.constraint.lhs.shape[1] mean_params0 = np.r_[mean_params, np.zeros(full_p - red_p)] # Get the score vector under the full model. save_exog_li = self.exog_li self.exog_li = self.constraint.exog_fulltrans_li import copy save_cached_means = copy.deepcopy(self.cached_means) self.update_cached_means(mean_params0) _, score = self._update_mean_params() if score is None: warnings.warn("Singular matrix encountered in GEE score test", ConvergenceWarning) return None, None _, ncov1, cmat = self._covmat() scale = self.estimate_scale() cmat = cmat / scale ** 2 score2 = score[red_p:] / scale amat = np.linalg.inv(ncov1) bmat_11 = cmat[0:red_p, 0:red_p] bmat_22 = cmat[red_p:, red_p:] bmat_12 = cmat[0:red_p, red_p:] amat_11 = amat[0:red_p, 0:red_p] amat_12 = amat[0:red_p, red_p:] score_cov = bmat_22 - np.dot(amat_12.T, np.linalg.solve(amat_11, bmat_12)) score_cov -= np.dot(bmat_12.T, np.linalg.solve(amat_11, amat_12)) score_cov += np.dot(amat_12.T, np.dot(np.linalg.solve(amat_11, bmat_11), np.linalg.solve(amat_11, amat_12))) from scipy.stats.distributions import chi2 score_statistic = np.dot(score2, np.linalg.solve(score_cov, score2)) score_df = len(score2) score_pvalue = 1 - chi2.cdf(score_statistic, score_df) self.score_test_results = {"statistic": score_statistic, "df": score_df, "p-value": score_pvalue} mean_params = self.constraint.unpack_param(mean_params) bcov = self.constraint.unpack_cov(bcov) self.exog_li = save_exog_li self.cached_means = save_cached_means self.exog = self.constraint.restore_exog() return mean_params, bcov def _update_assoc(self, params): """ Update the association parameters """ self.cov_struct.update(params) def _derivative_exog(self, params, exog=None, transform='dydx', dummy_idx=None, count_idx=None): """ For computing marginal effects, returns dF(XB) / dX where F(.) is the fitted mean. transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. """ # This form should be appropriate for group 1 probit, logit, # logistic, cloglog, heckprob, xtprobit. offset_exposure = None if exog is None: exog = self.exog offset_exposure = self._offset_exposure margeff = self.mean_deriv_exog(exog, params, offset_exposure) if 'ex' in transform: margeff *= exog if 'ey' in transform: margeff /= self.predict(params, exog)[:, None] if count_idx is not None: from statsmodels.discrete.discrete_margins import ( _get_count_effects) margeff = _get_count_effects(margeff, exog, count_idx, transform, self, params) if dummy_idx is not None: from statsmodels.discrete.discrete_margins import ( _get_dummy_effects) margeff = _get_dummy_effects(margeff, exog, dummy_idx, transform, self, params) return margeff
[docs] def qic(self, params, scale, cov_params): """ Returns quasi-information criteria and quasi-likelihood values. Parameters ---------- params : array-like The GEE estimates of the regression parameters. scale : scalar Estimated scale parameter cov_params : array-like An estimate of the covariance matrix for the model parameters. Conventionally this is the robust covariance matrix. Returns ------- ql : scalar The quasi-likelihood value qic : scalar A QIC that can be used to compare the mean and covariance structures of the model. qicu : scalar A simplified QIC that can be used to compare mean structures but not covariance structures Notes ----- The quasi-likelihood used here is obtained by numerically evaluating Wedderburn's integral representation of the quasi-likelihood function. This approach is valid for all families and links. Many other packages use analytical expressions for quasi-likelihoods that are valid in special cases where the link function is canonical. These analytical expressions may omit additive constants that only depend on the data. Therefore, the numerical values of our QL and QIC values will differ from the values reported by other packages. However only the differences between two QIC values calculated for different models using the same data are meaningful. Our QIC should produce the same QIC differences as other software. When using the QIC for models with unknown scale parameter, use a common estimate of the scale parameter for all models being compared. References ---------- .. [*] W. Pan (2001). Akaike's information criterion in generalized estimating equations. Biometrics (57) 1. """ varfunc = self.family.variance means = [] omega = 0.0 # omega^-1 is the model-based covariance assuming independence for i in range(self.num_group): expval, lpr = self.cached_means[i] means.append(expval) dmat = self.mean_deriv(self.exog_li[i], lpr) omega += np.dot(dmat.T, dmat) / scale means = np.concatenate(means) # The quasi-likelihood, use change of variables so the integration is # from -1 to 1. du = means - self.endog nstep = 10000 qv = np.empty(nstep) xv = np.linspace(-0.99999, 1, nstep) for i, g in enumerate(xv): u = self.endog + (g + 1) * du / 2.0 vu = varfunc(u) qv[i] = -np.sum(du**2 * (g + 1) / vu) qv /= (4 * scale) from scipy.integrate import trapz ql = trapz(qv, dx=xv[1] - xv[0]) qicu = -2 * ql + 2 * self.exog.shape[1] qic = -2 * ql + 2 * np.trace(np.dot(omega, cov_params)) return ql, qic, qicu
[docs]class GEEResults(base.LikelihoodModelResults): __doc__ = ( "This class summarizes the fit of a marginal regression model " "using GEE.\n" + _gee_results_doc) def __init__(self, model, params, cov_params, scale, cov_type='robust', use_t=False, **kwds): super(GEEResults, self).__init__( model, params, normalized_cov_params=cov_params, scale=scale) # not added by super self.df_resid = model.df_resid self.df_model = model.df_model self.family = model.family attr_kwds = kwds.pop('attr_kwds', {}) self.__dict__.update(attr_kwds) # we don't do this if the cov_type has already been set # subclasses can set it through attr_kwds if not (hasattr(self, 'cov_type') and hasattr(self, 'cov_params_default')): self.cov_type = cov_type # keep alias covariance_type = self.cov_type.lower() allowed_covariances = ["robust", "naive", "bias_reduced"] if covariance_type not in allowed_covariances: msg = ("GEE: `cov_type` must be one of " + ", ".join(allowed_covariances)) raise ValueError(msg) if cov_type == "robust": cov = self.cov_robust elif cov_type == "naive": cov = self.cov_naive elif cov_type == "bias_reduced": cov = self.cov_robust_bc self.cov_params_default = cov else: if self.cov_type != cov_type: raise ValueError('cov_type in argument is different from ' 'already attached cov_type')
[docs] def standard_errors(self, cov_type="robust"): """ This is a convenience function that returns the standard errors for any covariance type. The value of `bse` is the standard errors for whichever covariance type is specified as an argument to `fit` (defaults to "robust"). Parameters ---------- cov_type : string One of "robust", "naive", or "bias_reduced". Determines the covariance used to compute standard errors. Defaults to "robust". """ # Check covariance_type covariance_type = cov_type.lower() allowed_covariances = ["robust", "naive", "bias_reduced"] if covariance_type not in allowed_covariances: msg = ("GEE: `covariance_type` must be one of " + ", ".join(allowed_covariances)) raise ValueError(msg) if covariance_type == "robust": return np.sqrt(np.diag(self.cov_robust)) elif covariance_type == "naive": return np.sqrt(np.diag(self.cov_naive)) elif covariance_type == "bias_reduced": if self.cov_robust_bc is None: raise ValueError( "GEE: `bias_reduced` covariance not available") return np.sqrt(np.diag(self.cov_robust_bc))
# Need to override to allow for different covariance types.
[docs] @cache_readonly def bse(self): return self.standard_errors(self.cov_type)
[docs] @cache_readonly def resid(self): """ Returns the residuals, the endogeneous data minus the fitted values from the model. """ return self.model.endog - self.fittedvalues
[docs] @cache_readonly def resid_split(self): """ Returns the residuals, the endogeneous data minus the fitted values from the model. The residuals are returned as a list of arrays containing the residuals for each cluster. """ sresid = [] for v in self.model.group_labels: ii = self.model.group_indices[v] sresid.append(self.resid[ii]) return sresid
[docs] @cache_readonly def resid_centered(self): """ Returns the residuals centered within each group. """ cresid = self.resid.copy() for v in self.model.group_labels: ii = self.model.group_indices[v] cresid[ii] -= cresid[ii].mean() return cresid
[docs] @cache_readonly def resid_centered_split(self): """ Returns the residuals centered within each group. The residuals are returned as a list of arrays containing the centered residuals for each cluster. """ sresid = [] for v in self.model.group_labels: ii = self.model.group_indices[v] sresid.append(self.centered_resid[ii]) return sresid
[docs] def qic(self, scale=None): """ Returns the QIC and QICu information criteria. For families with a scale parameter (e.g. Gaussian), provide as the scale argument the estimated scale from the largest model under consideration. """ if scale is None: scale = self.scale _, qic, qicu = self.model.qic(self.params, scale, self.cov_params()) return qic, qicu
# FIXME: alias to be removed, temporary backwards compatibility split_resid = resid_split centered_resid = resid_centered split_centered_resid = resid_centered_split
[docs] @cache_readonly def resid_response(self): return self.model.endog - self.fittedvalues
[docs] @cache_readonly def resid_pearson(self): val = self.model.endog - self.fittedvalues val = val / np.sqrt(self.family.variance(self.fittedvalues)) return val
[docs] @cache_readonly def resid_working(self): val = self.resid_response val = val * self.family.link.deriv(self.fittedvalues) return val
[docs] @cache_readonly def resid_anscombe(self): return self.family.resid_anscombe(self.model.endog, self.fittedvalues)
[docs] @cache_readonly def resid_deviance(self): return self.family.resid_dev(self.model.endog, self.fittedvalues)
[docs] @cache_readonly def fittedvalues(self): """ Returns the fitted values from the model. """ return self.model.family.link.inverse(np.dot(self.model.exog, self.params))
[docs] def plot_added_variable(self, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None, ax=None): # Docstring attached below from statsmodels.graphics.regressionplots import plot_added_variable fig = plot_added_variable(self, focus_exog, resid_type=resid_type, use_glm_weights=use_glm_weights, fit_kwargs=fit_kwargs, ax=ax) return fig
plot_added_variable.__doc__ = _plot_added_variable_doc % { 'extra_params_doc': ''}
[docs] def plot_partial_residuals(self, focus_exog, ax=None): # Docstring attached below from statsmodels.graphics.regressionplots import plot_partial_residuals return plot_partial_residuals(self, focus_exog, ax=ax)
plot_partial_residuals.__doc__ = _plot_partial_residuals_doc % { 'extra_params_doc': ''}
[docs] def plot_ceres_residuals(self, focus_exog, frac=0.66, cond_means=None, ax=None): # Docstring attached below from statsmodels.graphics.regressionplots import plot_ceres_residuals return plot_ceres_residuals(self, focus_exog, frac, cond_means=cond_means, ax=ax)
plot_ceres_residuals.__doc__ = _plot_ceres_residuals_doc % { 'extra_params_doc': ''}
[docs] def conf_int(self, alpha=.05, cols=None, cov_type=None): """ Returns confidence intervals for the fitted parameters. Parameters ---------- alpha : float, optional The `alpha` level for the confidence interval. i.e., The default `alpha` = .05 returns a 95% confidence interval. cols : array-like, optional `cols` specifies which confidence intervals to return cov_type : string The covariance type used for computing standard errors; must be one of 'robust', 'naive', and 'bias reduced'. See `GEE` for details. Notes ----- The confidence interval is based on the Gaussian distribution. """ # super doesn't allow to specify cov_type and method is not # implemented, # FIXME: remove this method here if cov_type is None: bse = self.bse else: bse = self.standard_errors(cov_type=cov_type) params = self.params dist = stats.norm q = dist.ppf(1 - alpha / 2) if cols is None: lower = self.params - q * bse upper = self.params + q * bse else: cols = np.asarray(cols) lower = params[cols] - q * bse[cols] upper = params[cols] + q * bse[cols] return np.asarray(lzip(lower, upper))
[docs] def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the GEE regression results Parameters ----------- yname : string, optional Default is `y` xname : list of strings, optional Default is `var_##` for ## in p the number of regressors title : string, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals cov_type : string The covariance type used to compute the standard errors; one of 'robust' (the usual robust sandwich-type covariance estimate), 'naive' (ignores dependence), and 'bias reduced' (the Mancl/DeRouen estimate). Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Generalized']), ('', ['Estimating Equations']), ('Family:', [self.model.family.__class__.__name__]), ('Dependence structure:', [self.model.cov_struct.__class__.__name__]), ('Date:', None), ('Covariance type: ', [self.cov_type, ]) ] NY = [len(y) for y in self.model.endog_li] top_right = [('No. Observations:', [sum(NY)]), ('No. clusters:', [len(self.model.endog_li)]), ('Min. cluster size:', [min(NY)]), ('Max. cluster size:', [max(NY)]), ('Mean cluster size:', ["%.1f" % np.mean(NY)]), ('Num. iterations:', ['%d' % len(self.fit_history['params'])]), ('Scale:', ["%.3f" % self.scale]), ('Time:', None), ] # The skew of the residuals skew1 = stats.skew(self.resid) kurt1 = stats.kurtosis(self.resid) skew2 = stats.skew(self.centered_resid) kurt2 = stats.kurtosis(self.centered_resid) diagn_left = [('Skew:', ["%12.4f" % skew1]), ('Centered skew:', ["%12.4f" % skew2])] diagn_right = [('Kurtosis:', ["%12.4f" % kurt1]), ('Centered kurtosis:', ["%12.4f" % kurt2]) ] if title is None: title = self.model.__class__.__name__ + ' ' +\ "Regression Results" # Override the exog variable names if xname is provided as an # argument. if xname is None: xname = self.model.exog_names if yname is None: yname = self.model.endog_names # Create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=False) smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, yname=yname, xname=xname, title="") return smry
[docs] 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 semielasticity -- dy/d(lnx) - 'eydx' - estimate semeilasticity -- 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. """ if self.model.constraint is not None: warnings.warn("marginal effects ignore constraints", ValueWarning) return GEEMargins(self, (at, method, atexog, dummy, count))
[docs] def plot_isotropic_dependence(self, ax=None, xpoints=10, min_n=50): """ Create a plot of the pairwise products of within-group residuals against the corresponding time differences. This plot can be used to assess the possible form of an isotropic covariance structure. Parameters ---------- ax : Matplotlib axes instance An axes on which to draw the graph. If None, new figure and axes objects are created xpoints : scalar or array-like If scalar, the number of points equally spaced points on the time difference axis used to define bins for calculating local means. If an array, the specific points that define the bins. min_n : integer The minimum sample size in a bin for the mean residual product to be included on the plot. """ from statsmodels.graphics import utils as gutils resid = self.model.cluster_list(self.resid) time = self.model.cluster_list(self.model.time) # All within-group pairwise time distances (xdt) and the # corresponding products of scaled residuals (xre). xre, xdt = [], [] for re, ti in zip(resid, time): ix = np.tril_indices(re.shape[0], 0) re = re[ix[0]] * re[ix[1]] / self.scale ** 2 xre.append(re) dists = np.sqrt(((ti[ix[0], :] - ti[ix[1], :]) ** 2).sum(1)) xdt.append(dists) xre = np.concatenate(xre) xdt = np.concatenate(xdt) if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # Convert to a correlation ii = np.flatnonzero(xdt == 0) v0 = np.mean(xre[ii]) xre /= v0 # Use the simple average to smooth, since fancier smoothers # that trim and downweight outliers give biased results (we # need the actual mean of a skewed distribution). if np.isscalar(xpoints): xpoints = np.linspace(0, max(xdt), xpoints) dg = np.digitize(xdt, xpoints) dgu = np.unique(dg) hist = np.asarray([np.sum(dg == k) for k in dgu]) ii = np.flatnonzero(hist >= min_n) dgu = dgu[ii] dgy = np.asarray([np.mean(xre[dg == k]) for k in dgu]) dgx = np.asarray([np.mean(xdt[dg == k]) for k in dgu]) ax.plot(dgx, dgy, '-', color='orange', lw=5) ax.set_xlabel("Time difference") ax.set_ylabel("Product of scaled residuals") return fig
[docs] def sensitivity_params(self, dep_params_first, dep_params_last, num_steps): """ Refits the GEE model using a sequence of values for the dependence parameters. Parameters ---------- dep_params_first : array-like The first dep_params in the sequence dep_params_last : array-like The last dep_params in the sequence num_steps : int The number of dep_params in the sequence Returns ------- results : array-like The GEEResults objects resulting from the fits. """ model = self.model import copy cov_struct = copy.deepcopy(self.model.cov_struct) # We are fixing the dependence structure in each run. update_dep = model.update_dep model.update_dep = False dep_params = [] results = [] for x in np.linspace(0, 1, num_steps): dp = x * dep_params_last + (1 - x) * dep_params_first dep_params.append(dp) model.cov_struct = copy.deepcopy(cov_struct) model.cov_struct.dep_params = dp rslt = model.fit(start_params=self.params, ctol=self.ctol, params_niter=self.params_niter, first_dep_update=self.first_dep_update, cov_type=self.cov_type) results.append(rslt) model.update_dep = update_dep return results
# FIXME: alias to be removed, temporary backwards compatibility params_sensitivity = sensitivity_params
class GEEResultsWrapper(lm.RegressionResultsWrapper): _attrs = { 'centered_resid': 'rows', } _wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs, _attrs) wrap.populate_wrapper(GEEResultsWrapper, GEEResults) class OrdinalGEE(GEE): __doc__ = ( " Estimation of ordinal response marginal regression models\n" " using Generalized Estimating Equations (GEE).\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_ordinal_family_doc, 'example': _gee_ordinal_example}) def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, dep_data=None, constraint=None, **kwargs): if family is None: family = families.Binomial() else: if not isinstance(family, families.Binomial): raise ValueError("ordinal GEE must use a Binomial family") if cov_struct is None: cov_struct = cov_structs.OrdinalIndependence() endog, exog, groups, time, offset = self.setup_ordinal( endog, exog, groups, time, offset) super(OrdinalGEE, self).__init__(endog, exog, groups, time, family, cov_struct, missing, offset, dep_data, constraint) def setup_ordinal(self, endog, exog, groups, time, offset): """ Restructure ordinal data as binary indicators so that they can be analysed using Generalized Estimating Equations. """ self.endog_orig = endog.copy() self.exog_orig = exog.copy() self.groups_orig = groups.copy() if offset is not None: self.offset_orig = offset.copy() else: self.offset_orig = None offset = np.zeros(len(endog)) if time is not None: self.time_orig = time.copy() else: self.time_orig = None time = np.zeros((len(endog), 1)) exog = np.asarray(exog) endog = np.asarray(endog) groups = np.asarray(groups) time = np.asarray(time) offset = np.asarray(offset) # The unique outcomes, except the greatest one. self.endog_values = np.unique(endog) endog_cuts = self.endog_values[0:-1] ncut = len(endog_cuts) nrows = ncut * len(endog) exog_out = np.zeros((nrows, exog.shape[1]), dtype=np.float64) endog_out = np.zeros(nrows, dtype=np.float64) intercepts = np.zeros((nrows, ncut), dtype=np.float64) groups_out = np.zeros(nrows, dtype=groups.dtype) time_out = np.zeros((nrows, time.shape[1]), dtype=np.float64) offset_out = np.zeros(nrows, dtype=np.float64) jrow = 0 zipper = zip(exog, endog, groups, time, offset) for (exog_row, endog_value, group_value, time_value, offset_value) in zipper: # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): exog_out[jrow, :] = exog_row endog_out[jrow] = (int(endog_value > thresh)) intercepts[jrow, thresh_ix] = 1 groups_out[jrow] = group_value time_out[jrow] = time_value offset_out[jrow] = offset_value jrow += 1 exog_out = np.concatenate((intercepts, exog_out), axis=1) # exog column names, including intercepts xnames = ["I(y>%.1f)" % v for v in endog_cuts] if type(self.exog_orig) == pd.DataFrame: xnames.extend(self.exog_orig.columns) else: xnames.extend(["x%d" % k for k in range(1, exog.shape[1] + 1)]) exog_out = pd.DataFrame(exog_out, columns=xnames) # Preserve the endog name if there is one if type(self.endog_orig) == pd.Series: endog_out = pd.Series(endog_out, name=self.endog_orig.name) return endog_out, exog_out, groups_out, time_out, offset_out def _starting_params(self): model = GEE(self.endog, self.exog, self.groups, time=self.time, family=families.Binomial(), offset=self.offset, exposure=self.exposure) result = model.fit() return result.params def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust'): rslt = super(OrdinalGEE, self).fit(maxiter, ctol, start_params, params_niter, first_dep_update, cov_type=cov_type) rslt = rslt._results # use unwrapped instance res_kwds = dict(((k, getattr(rslt, k)) for k in rslt._props)) # Convert the GEEResults to an OrdinalGEEResults ord_rslt = OrdinalGEEResults(self, rslt.params, rslt.cov_params() / rslt.scale, rslt.scale, cov_type=cov_type, attr_kwds=res_kwds) # for k in rslt._props: # setattr(ord_rslt, k, getattr(rslt, k)) return OrdinalGEEResultsWrapper(ord_rslt) fit.__doc__ = _gee_fit_doc class OrdinalGEEResults(GEEResults): __doc__ = ( "This class summarizes the fit of a marginal regression model" "for an ordinal response using GEE.\n" + _gee_results_doc) def plot_distribution(self, ax=None, exog_values=None): """ Plot the fitted probabilities of endog in an ordinal model, for specifed values of the predictors. Parameters ---------- ax : Matplotlib axes instance An axes on which to draw the graph. If None, new figure and axes objects are created exog_values : array-like A list of dictionaries, with each dictionary mapping variable names to values at which the variable is held fixed. The values P(endog=y | exog) are plotted for all possible values of y, at the given exog value. Variables not included in a dictionary are held fixed at the mean value. Example: -------- We have a model with covariates 'age' and 'sex', and wish to plot the probabilities P(endog=y | exog) for males (sex=0) and for females (sex=1), as separate paths on the plot. Since 'age' is not included below in the map, it is held fixed at its mean value. >>> ev = [{"sex": 1}, {"sex": 0}] >>> rslt.distribution_plot(exog_values=ev) """ from statsmodels.graphics import utils as gutils if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # If no covariate patterns are specified, create one with all # variables set to their mean values. if exog_values is None: exog_values = [{}, ] exog_means = self.model.exog.mean(0) ix_icept = [i for i, x in enumerate(self.model.exog_names) if x.startswith("I(")] for ev in exog_values: for k in ev.keys(): if k not in self.model.exog_names: raise ValueError("%s is not a variable in the model" % k) # Get the fitted probability for each level, at the given # covariate values. pr = [] for j in ix_icept: xp = np.zeros_like(self.params) xp[j] = 1. for i, vn in enumerate(self.model.exog_names): if i in ix_icept: continue # User-specified value if vn in ev: xp[i] = ev[vn] # Mean value else: xp[i] = exog_means[i] p = 1 / (1 + np.exp(-np.dot(xp, self.params))) pr.append(p) pr.insert(0, 1) pr.append(0) pr = np.asarray(pr) prd = -np.diff(pr) ax.plot(self.model.endog_values, prd, 'o-') ax.set_xlabel("Response value") ax.set_ylabel("Probability") ax.set_ylim(0, 1) return fig class OrdinalGEEResultsWrapper(GEEResultsWrapper): pass wrap.populate_wrapper(OrdinalGEEResultsWrapper, OrdinalGEEResults) class NominalGEE(GEE): __doc__ = ( " Estimation of nominal response marginal regression models\n" " using Generalized Estimating Equations (GEE).\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_nominal_family_doc, 'example': _gee_nominal_example}) def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, dep_data=None, constraint=None, **kwargs): endog, exog, groups, time, offset = self.setup_nominal( endog, exog, groups, time, offset) if family is None: family = _Multinomial(self.ncut + 1) if cov_struct is None: cov_struct = cov_structs.NominalIndependence() super(NominalGEE, self).__init__( endog, exog, groups, time, family, cov_struct, missing, offset, dep_data, constraint) def _starting_params(self): model = GEE(self.endog, self.exog, self.groups, time=self.time, family=families.Binomial(), offset=self.offset, exposure=self.exposure) result = model.fit() return result.params def setup_nominal(self, endog, exog, groups, time, offset): """ Restructure nominal data as binary indicators so that they can be analysed using Generalized Estimating Equations. """ self.endog_orig = endog.copy() self.exog_orig = exog.copy() self.groups_orig = groups.copy() if offset is not None: self.offset_orig = offset.copy() else: self.offset_orig = None offset = np.zeros(len(endog)) if time is not None: self.time_orig = time.copy() else: self.time_orig = None time = np.zeros((len(endog), 1)) exog = np.asarray(exog) endog = np.asarray(endog) groups = np.asarray(groups) time = np.asarray(time) offset = np.asarray(offset) # The unique outcomes, except the greatest one. self.endog_values = np.unique(endog) endog_cuts = self.endog_values[0:-1] ncut = len(endog_cuts) self.ncut = ncut nrows = len(endog_cuts) * exog.shape[0] ncols = len(endog_cuts) * exog.shape[1] exog_out = np.zeros((nrows, ncols), dtype=np.float64) endog_out = np.zeros(nrows, dtype=np.float64) groups_out = np.zeros(nrows, dtype=np.float64) time_out = np.zeros((nrows, time.shape[1]), dtype=np.float64) offset_out = np.zeros(nrows, dtype=np.float64) jrow = 0 zipper = zip(exog, endog, groups, time, offset) for (exog_row, endog_value, group_value, time_value, offset_value) in zipper: # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): u = np.zeros(len(endog_cuts), dtype=np.float64) u[thresh_ix] = 1 exog_out[jrow, :] = np.kron(u, exog_row) endog_out[jrow] = (int(endog_value == thresh)) groups_out[jrow] = group_value time_out[jrow] = time_value offset_out[jrow] = offset_value jrow += 1 # exog names if isinstance(self.exog_orig, pd.DataFrame): xnames_in = self.exog_orig.columns else: xnames_in = ["x%d" % k for k in range(1, exog.shape[1] + 1)] xnames = [] for tr in endog_cuts: xnames.extend(["%s[%.1f]" % (v, tr) for v in xnames_in]) exog_out = pd.DataFrame(exog_out, columns=xnames) exog_out = pd.DataFrame(exog_out, columns=xnames) # Preserve endog name if there is one if isinstance(self.endog_orig, pd.Series): endog_out = pd.Series(endog_out, name=self.endog_orig.name) return endog_out, exog_out, groups_out, time_out, offset_out def mean_deriv(self, exog, lin_pred): """ Derivative of the expected endog with respect to the parameters. Parameters ---------- exog : array-like The exogeneous data at which the derivative is computed, number of rows must be a multiple of `ncut`. lin_pred : array-like The values of the linear predictor, length must be multiple of `ncut`. Returns ------- The derivative of the expected endog with respect to the parameters. """ expval = np.exp(lin_pred) # Reshape so that each row contains all the indicators # corresponding to one multinomial observation. expval_m = np.reshape(expval, (len(expval) // self.ncut, self.ncut)) # The normalizing constant for the multinomial probabilities. denom = 1 + expval_m.sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) # The multinomial probabilities mprob = expval / denom # First term of the derivative: denom * expval' / denom^2 = # expval' / denom. dmat = mprob[:, None] * exog # Second term of the derivative: -expval * denom' / denom^2 ddenom = expval[:, None] * exog dmat -= mprob[:, None] * ddenom / denom[:, None] return dmat def mean_deriv_exog(self, exog, params, offset_exposure=None): """ Derivative of the expected endog with respect to exog for the multinomial model, used in analyzing marginal effects. Parameters ---------- exog : array-like The exogeneous data at which the derivative is computed, number of rows must be a multiple of `ncut`. lpr : array-like The linear predictor values, length must be multiple of `ncut`. Returns ------- The value of the derivative of the expected endog with respect to exog. Notes ----- offset_exposure must be set at None for the multinoial family. """ if offset_exposure is not None: warnings.warn("Offset/exposure ignored for the multinomial family", ValueWarning) lpr = np.dot(exog, params) expval = np.exp(lpr) expval_m = np.reshape(expval, (len(expval) // self.ncut, self.ncut)) denom = 1 + expval_m.sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) bmat0 = np.outer(np.ones(exog.shape[0]), params) # Masking matrix qmat = [] for j in range(self.ncut): ee = np.zeros(self.ncut, dtype=np.float64) ee[j] = 1 qmat.append(np.kron(ee, np.ones(len(params) // self.ncut))) qmat = np.array(qmat) qmat = np.kron(np.ones((exog.shape[0] // self.ncut, 1)), qmat) bmat = bmat0 * qmat dmat = expval[:, None] * bmat / denom[:, None] expval_mb = np.kron(expval_m, np.ones((self.ncut, 1))) expval_mb = np.kron(expval_mb, np.ones((1, self.ncut))) dmat -= expval[:, None] * (bmat * expval_mb) / denom[:, None] ** 2 return dmat def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust'): rslt = super(NominalGEE, self).fit(maxiter, ctol, start_params, params_niter, first_dep_update, cov_type=cov_type) if rslt is None: warnings.warn("GEE updates did not converge", ConvergenceWarning) return None rslt = rslt._results # use unwrapped instance res_kwds = dict(((k, getattr(rslt, k)) for k in rslt._props)) # Convert the GEEResults to a NominalGEEResults nom_rslt = NominalGEEResults(self, rslt.params, rslt.cov_params() / rslt.scale, rslt.scale, cov_type=cov_type, attr_kwds=res_kwds) # for k in rslt._props: # setattr(nom_rslt, k, getattr(rslt, k)) return NominalGEEResultsWrapper(nom_rslt) fit.__doc__ = _gee_fit_doc class NominalGEEResults(GEEResults): __doc__ = ( "This class summarizes the fit of a marginal regression model" "for a nominal response using GEE.\n" + _gee_results_doc) def plot_distribution(self, ax=None, exog_values=None): """ Plot the fitted probabilities of endog in an nominal model, for specifed values of the predictors. Parameters ---------- ax : Matplotlib axes instance An axes on which to draw the graph. If None, new figure and axes objects are created exog_values : array-like A list of dictionaries, with each dictionary mapping variable names to values at which the variable is held fixed. The values P(endog=y | exog) are plotted for all possible values of y, at the given exog value. Variables not included in a dictionary are held fixed at the mean value. Example: -------- We have a model with covariates 'age' and 'sex', and wish to plot the probabilities P(endog=y | exog) for males (sex=0) and for females (sex=1), as separate paths on the plot. Since 'age' is not included below in the map, it is held fixed at its mean value. >>> ex = [{"sex": 1}, {"sex": 0}] >>> rslt.distribution_plot(exog_values=ex) """ from statsmodels.graphics import utils as gutils if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # If no covariate patterns are specified, create one with all # variables set to their mean values. if exog_values is None: exog_values = [{}, ] link = self.model.family.link.inverse ncut = self.model.family.ncut k = int(self.model.exog.shape[1] / ncut) exog_means = self.model.exog.mean(0)[0:k] exog_names = self.model.exog_names[0:k] exog_names = [x.split("[")[0] for x in exog_names] params = np.reshape(self.params, (ncut, len(self.params) // ncut)) for ev in exog_values: exog = exog_means.copy() for k in ev.keys(): if k not in exog_names: raise ValueError("%s is not a variable in the model" % k) ii = exog_names.index(k) exog[ii] = ev[k] lpr = np.dot(params, exog) pr = link(lpr) pr = np.r_[pr, 1 - pr.sum()] ax.plot(self.model.endog_values, pr, 'o-') ax.set_xlabel("Response value") ax.set_ylabel("Probability") ax.set_xticks(self.model.endog_values) ax.set_xticklabels(self.model.endog_values) ax.set_ylim(0, 1) return fig class NominalGEEResultsWrapper(GEEResultsWrapper): pass wrap.populate_wrapper(NominalGEEResultsWrapper, NominalGEEResults) class _MultinomialLogit(Link): """ The multinomial logit transform, only for use with GEE. Notes ----- The data are assumed coded as binary indicators, where each observed multinomial value y is coded as I(y == S[0]), ..., I(y == S[-1]), where S is the set of possible response labels, excluding the largest one. Thererefore functions in this class should only be called using vector argument whose length is a multiple of |S| = ncut, which is an argument to be provided when initializing the class. call and derivative use a private method _clean to trim p by 1e-10 so that p is in (0, 1) """ def __init__(self, ncut): self.ncut = ncut def inverse(self, lpr): """ Inverse of the multinomial logit transform, which gives the expected values of the data as a function of the linear predictors. Parameters ---------- lpr : array-like (length must be divisible by `ncut`) The linear predictors Returns ------- prob : array Probabilities, or expected values """ expval = np.exp(lpr) denom = 1 + np.reshape(expval, (len(expval) // self.ncut, self.ncut)).sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) prob = expval / denom return prob class _Multinomial(families.Family): """ Pseudo-link function for fitting nominal multinomial models with GEE. Not for use outside the GEE class. """ links = [_MultinomialLogit, ] variance = varfuncs.binary safe_links = [_MultinomialLogit, ] def __init__(self, nlevels): """ Parameters ---------- nlevels : integer The number of distinct categories for the multinomial distribution. """ self.initialize(nlevels) def initialize(self, nlevels): self.ncut = nlevels - 1 self.link = _MultinomialLogit(self.ncut) from statsmodels.discrete.discrete_margins import ( _get_margeff_exog, _check_margeff_args, _effects_at, margeff_cov_with_se, _check_at_is_all, _transform_names, _check_discrete_args, _get_dummy_index, _get_count_index)
[docs]class GEEMargins(object): """ Estimated marginal effects for a regression model fit with GEE. Parameters ---------- results : GEEResults instance The results instance of a fitted discrete choice model args : tuple Args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. kwargs : dict Keyword args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. """ def __init__(self, results, args, kwargs={}): self._cache = resettable_cache() self.results = results self.get_margeff(*args, **kwargs) def _reset(self): self._cache = resettable_cache()
[docs] @cache_readonly def tvalues(self): _check_at_is_all(self.margeff_options) return self.margeff / self.margeff_se
[docs] def summary_frame(self, alpha=.05): """ Returns a DataFrame summarizing the marginal effects. Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- frame : DataFrames A DataFrame summarizing the marginal effects. """ _check_at_is_all(self.margeff_options) from pandas import DataFrame names = [_transform_names[self.margeff_options['method']], 'Std. Err.', 'z', 'Pr(>|z|)', 'Conf. Int. Low', 'Cont. Int. Hi.'] ind = self.results.model.exog.var(0) != 0 # True if not a constant exog_names = self.results.model.exog_names var_names = [name for i, name in enumerate(exog_names) if ind[i]] table = np.column_stack((self.margeff, self.margeff_se, self.tvalues, self.pvalues, self.conf_int(alpha))) return DataFrame(table, columns=names, index=var_names)
[docs] @cache_readonly def pvalues(self): _check_at_is_all(self.margeff_options) return stats.norm.sf(np.abs(self.tvalues)) * 2
[docs] def conf_int(self, alpha=.05): """ Returns the confidence intervals of the marginal effects Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. 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 = stats.norm.ppf(1 - alpha / 2) lower = self.margeff - q * me_se upper = self.margeff + q * me_se return np.asarray(lzip(lower, upper))
[docs] 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() const_idx = model.data.const_idx if const_idx is not None: exog_names.pop(const_idx) 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|', '[%3.1f%% Conf. Int.]' % (100 - alpha * 100)] tble.insert_header_row(0, header) # from IPython.core.debugger import Pdb; Pdb().set_trace() 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|', '[%3.1f%% Conf. Int.]' % (100 - alpha * 100)] table.insert_header_row(0, header) smry.tables.append(table) return smry
[docs] def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): 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 = exog.var(0) != 0 const_idx = model.data.const_idx 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 # 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) effects = _effects_at(effects, at) if at == 'all': 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, 1) # don't care about at constant self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] self.margeff_se = margeff_se[effects_idx] self.margeff = effects[effects_idx]