from statsmodels.compat.python import iterkeys, itervalues, zip, range
from statsmodels.stats.correlation_tools import cov_nearest
import numpy as np
from scipy import linalg as spl
from statsmodels.tools.sm_exceptions import (ConvergenceWarning,
IterationLimitWarning)
import warnings
[docs]class CovStruct(object):
"""
A base class for correlation and covariance structures of grouped
data.
Each implementation of this class takes the residuals from a
regression model that has been fitted to grouped data, and uses
them to estimate the within-group dependence structure of the
random errors in the model.
The state of the covariance structure is represented through the
value of the class variable `dep_params`. The default state of a
newly-created instance should correspond to the identity
correlation matrix.
"""
def __init__(self, cov_nearest_method="clipped"):
# Parameters describing the dependency structure
self.dep_params = None
# Keep track of the number of times that the covariance was
# adjusted.
self.cov_adjust = []
# Method for projecting the covariance matrix if it not SPD.
self.cov_nearest_method = cov_nearest_method
[docs] def initialize(self, model):
"""
Called by GEE, used by implementations that need additional
setup prior to running `fit`.
Parameters
----------
model : GEE class
A reference to the parent GEE class instance.
"""
self.model = model
[docs] def update(self, params):
"""
Updates the association parameter values based on the current
regression coefficients.
Parameters
----------
params : array-like
Working values for the regression parameters.
"""
raise NotImplementedError
[docs] def covariance_matrix(self, endog_expval, index):
"""
Returns the working covariance or correlation matrix for a
given cluster of data.
Parameters
----------
endog_expval: array-like
The expected values of endog for the cluster for which the
covariance or correlation matrix will be returned
index: integer
The index of the cluster for which the covariane or
correlation matrix will be returned
Returns
-------
M: matrix
The covariance or correlation matrix of endog
is_cor: bool
True if M is a correlation matrix, False if M is a
covariance matrix
"""
raise NotImplementedError
[docs] def covariance_matrix_solve(self, expval, index, stdev, rhs):
"""
Solves matrix equations of the form `covmat * soln = rhs` and
returns the values of `soln`, where `covmat` is the covariance
matrix represented by this class.
Parameters
----------
expval: array-like
The expected value of endog for each observed value in the
group.
index: integer
The group index.
stdev : array-like
The standard deviation of endog for each observation in
the group.
rhs : list/tuple of array-like
A set of right-hand sides; each defines a matrix equation
to be solved.
Returns
-------
soln : list/tuple of array-like
The solutions to the matrix equations.
Notes
-----
Returns None if the solver fails.
Some dependence structures do not use `expval` and/or `index`
to determine the correlation matrix. Some families
(e.g. binomial) do not use the `stdev` parameter when forming
the covariance matrix.
If the covariance matrix is singular or not SPD, it is
projected to the nearest such matrix. These projection events
are recorded in the fit_history member of the GEE model.
Systems of linear equations with the covariance matrix as the
left hand side (LHS) are solved for different right hand sides
(RHS); the LHS is only factorized once to save time.
This is a default implementation, it can be reimplemented in
subclasses to optimize the linear algebra according to the
struture of the covariance matrix.
"""
vmat, is_cor = self.covariance_matrix(expval, index)
if is_cor:
vmat *= np.outer(stdev, stdev)
# Factor the covariance matrix. If the factorization fails,
# attempt to condition it into a factorizable matrix.
threshold = 1e-2
success = False
cov_adjust = 0
for itr in range(20):
try:
vco = spl.cho_factor(vmat)
success = True
break
except np.linalg.LinAlgError:
vmat = cov_nearest(vmat, method=self.cov_nearest_method,
threshold=threshold)
threshold *= 2
cov_adjust += 1
self.cov_adjust.append(cov_adjust)
# Last resort if we still can't factor the covariance matrix.
if success == False:
warnings.warn("Unable to condition covariance matrix to an SPD matrix using cov_nearest",
ConvergenceWarning)
vmat = np.diag(np.diag(vmat))
vco = spl.cho_factor(vmat)
soln = [spl.cho_solve(vco, x) for x in rhs]
return soln
[docs] def summary(self):
"""
Returns a text summary of the current estimate of the
dependence structure.
"""
raise NotImplementedError
[docs]class Independence(CovStruct):
"""
An independence working dependence structure.
"""
# Nothing to update
[docs] def update(self, params):
return
[docs] def covariance_matrix(self, expval, index):
dim = len(expval)
return np.eye(dim, dtype=np.float64), True
[docs] def covariance_matrix_solve(self, expval, index, stdev, rhs):
v = stdev**2
rslt = []
for x in rhs:
if x.ndim == 1:
rslt.append(x / v)
else:
rslt.append(x / v[:, None])
return rslt
update.__doc__ = CovStruct.update.__doc__
covariance_matrix.__doc__ = CovStruct.covariance_matrix.__doc__
covariance_matrix_solve.__doc__ = CovStruct.covariance_matrix_solve.__doc__
[docs] def summary(self):
return "Observations within a cluster are modeled as being independent."
[docs]class Exchangeable(CovStruct):
"""
An exchangeable working dependence structure.
"""
def __init__(self):
super(Exchangeable, self).__init__()
# The correlation between any two values in the same cluster
self.dep_params = 0.
[docs] def update(self, params):
endog = self.model.endog_li
nobs = self.model.nobs
dim = len(params)
varfunc = self.model.family.variance
cached_means = self.model.cached_means
residsq_sum, scale, nterm = 0, 0, 0
for i in range(self.model.num_group):
expval, _ = cached_means[i]
stdev = np.sqrt(varfunc(expval))
resid = (endog[i] - expval) / stdev
ngrp = len(resid)
residsq = np.outer(resid, resid)
scale += np.trace(residsq)
residsq = np.tril(residsq, -1)
residsq_sum += residsq.sum()
nterm += 0.5 * ngrp * (ngrp - 1)
scale /= (nobs - dim)
self.dep_params = residsq_sum / (scale * (nterm - dim))
[docs] def covariance_matrix(self, expval, index):
dim = len(expval)
dp = self.dep_params * np.ones((dim, dim), dtype=np.float64)
return dp + (1. - self.dep_params) * np.eye(dim), True
[docs] def covariance_matrix_solve(self, expval, index, stdev, rhs):
k = len(expval)
c = self.dep_params / (1. - self.dep_params)
c /= 1. + self.dep_params * (k - 1)
rslt = []
for x in rhs:
if x.ndim == 1:
x1 = x / stdev
y = x1 / (1. - self.dep_params)
y -= c * sum(x1)
y /= stdev
else:
x1 = x / stdev[:, None]
y = x1 / (1. - self.dep_params)
y -= c * x1.sum(0)
y /= stdev[:, None]
rslt.append(y)
return rslt
update.__doc__ = CovStruct.update.__doc__
covariance_matrix.__doc__ = CovStruct.covariance_matrix.__doc__
covariance_matrix_solve.__doc__ = CovStruct.covariance_matrix_solve.__doc__
[docs] def summary(self):
return ("The correlation between two observations in the " +
"same cluster is %.3f" % self.dep_params)
[docs]class Nested(CovStruct):
"""
A nested working dependence structure.
A working dependence structure that captures a nested hierarchy of
groups, each level of which contributes to the random error term
of the model.
When using this working covariance structure, `dep_data` of the
GEE instance should contain a n_obs x k matrix of 0/1 indicators,
corresponding to the k subgroups nested under the top-level
`groups` of the GEE instance. These subgroups should be nested
from left to right, so that two observations with the same value
for column j of `dep_data` should also have the same value for all
columns j' < j (this only applies to observations in the same
top-level cluster given by the `groups` argument to GEE).
Examples
--------
Suppose our data are student test scores, and the students are in
classrooms, nested in schools, nested in school districts. The
school district is the highest level of grouping, so the school
district id would be provided to GEE as `groups`, and the school
and classroom id's would be provided to the Nested class as the
`dep_data` argument, e.g.
0 0 # School 0, classroom 0, student 0
0 0 # School 0, classroom 0, student 1
0 1 # School 0, classroom 1, student 0
0 1 # School 0, classroom 1, student 1
1 0 # School 1, classroom 0, student 0
1 0 # School 1, classroom 0, student 1
1 1 # School 1, classroom 1, student 0
1 1 # School 1, classroom 1, student 1
Labels lower in the hierarchy are recycled, so that student 0 in
classroom 0 is different fro student 0 in classroom 1, etc.
Notes
-----
The calculations for this dependence structure involve all pairs
of observations within a group (that is, within the top level
`group` structure passed to GEE). Large group sizes will result
in slow iterations.
The variance components are estimated using least squares
regression of the products r*r', for standardized residuals r and
r' in the same group, on a vector of indicators defining which
variance components are shared by r and r'.
"""
[docs] def initialize(self, model):
"""
Called on the first call to update
`ilabels` is a list of n_i x n_i matrices containing integer
labels that correspond to specific correlation parameters.
Two elements of ilabels[i] with the same label share identical
variance components.
`designx` is a matrix, with each row containing dummy
variables indicating which variance components are associated
with the corresponding element of QY.
"""
super(Nested, self).initialize(model)
# A bit of processing of the nest data
id_matrix = np.asarray(self.model.dep_data)
if id_matrix.ndim == 1:
id_matrix = id_matrix[:,None]
self.id_matrix = id_matrix
endog = self.model.endog_li
designx, ilabels = [], []
# The number of layers of nesting
n_nest = self.id_matrix.shape[1]
for i in range(self.model.num_group):
ngrp = len(endog[i])
glab = self.model.group_labels[i]
rix = self.model.group_indices[glab]
# Determine the number of common variance components
# shared by each pair of observations.
ix1, ix2 = np.tril_indices(ngrp, -1)
ncm = (self.id_matrix[rix[ix1], :] ==
self.id_matrix[rix[ix2], :]).sum(1)
# This is used to construct the working correlation
# matrix.
ilabel = np.zeros((ngrp, ngrp), dtype=np.int32)
ilabel[[ix1, ix2]] = ncm + 1
ilabel[[ix2, ix1]] = ncm + 1
ilabels.append(ilabel)
# This is used to estimate the variance components.
dsx = np.zeros((len(ix1), n_nest+1), dtype=np.float64)
dsx[:,0] = 1
for k in np.unique(ncm):
ii = np.flatnonzero(ncm == k)
dsx[ii, 1:k+1] = 1
designx.append(dsx)
self.designx = np.concatenate(designx, axis=0)
self.ilabels = ilabels
svd = np.linalg.svd(self.designx, 0)
self.designx_u = svd[0]
self.designx_s = svd[1]
self.designx_v = svd[2].T
[docs] def update(self, params):
endog = self.model.endog_li
offset = self.model.offset_li
nobs = self.model.nobs
dim = len(params)
if self.designx is None:
self._compute_design(self.model)
cached_means = self.model.cached_means
varfunc = self.model.family.variance
dvmat = []
scale = 0.
for i in range(self.model.num_group):
expval, _ = cached_means[i]
stdev = np.sqrt(varfunc(expval))
resid = (endog[i] - offset[i] - expval) / stdev
ix1, ix2 = np.tril_indices(len(resid), -1)
dvmat.append(resid[ix1] * resid[ix2])
scale += np.sum(resid**2)
dvmat = np.concatenate(dvmat)
scale /= (nobs - dim)
# Use least squares regression to estimate the variance
# components
vcomp_coeff = np.dot(self.designx_v, np.dot(self.designx_u.T,
dvmat) / self.designx_s)
self.vcomp_coeff = np.clip(vcomp_coeff, 0, np.inf)
self.scale = scale
self.dep_params = self.vcomp_coeff.copy()
[docs] def covariance_matrix(self, expval, index):
dim = len(expval)
# First iteration
if self.dep_params is None:
return np.eye(dim, dtype=np.float64), True
ilabel = self.ilabels[index]
c = np.r_[self.scale, np.cumsum(self.vcomp_coeff)]
vmat = c[ilabel]
vmat /= self.scale
return vmat, True
update.__doc__ = CovStruct.update.__doc__
covariance_matrix.__doc__ = CovStruct.covariance_matrix.__doc__
[docs] def summary(self):
"""
Returns a summary string describing the state of the
dependence structure.
"""
msg = "Variance estimates\n------------------\n"
for k in range(len(self.vcomp_coeff)):
msg += "Component %d: %.3f\n" % (k+1, self.vcomp_coeff[k])
msg += "Residual: %.3f\n" % (self.scale -
np.sum(self.vcomp_coeff))
return msg
[docs]class Autoregressive(CovStruct):
"""
An autoregressive working dependence structure.
The dependence is defined in terms of the `time` component of the
parent GEE class. Time represents a potentially multidimensional
index from which distances between pairs of observations can be
determined. The correlation between two observations in the same
cluster is dep_params^distance, where `dep_params` is the
autocorrelation parameter to be estimated, and `distance` is the
distance between the two observations, calculated from their
corresponding time values. `time` is stored as an n_obs x k
matrix, where `k` represents the number of dimensions in the time
index.
The autocorrelation parameter is estimated using weighted
nonlinear least squares, regressing each value within a cluster on
each preceeding value in the same cluster.
Parameters
----------
dist_func: function from R^k x R^k to R^+, optional
A function that computes the distance between the two
observations based on their `time` values.
References
----------
B Rosner, A Munoz. Autoregressive modeling for the analysis of
longitudinal data with unequally spaced examinations. Statistics
in medicine. Vol 7, 59-71, 1988.
"""
def __init__(self, dist_func=None):
super(Autoregressive, self).__init__()
# The function for determining distances based on time
if dist_func is None:
self.dist_func = lambda x, y: np.abs(x - y).sum()
else:
self.dist_func = dist_func
self.designx = None
# The autocorrelation parameter
self.dep_params = 0.
[docs] def update(self, params):
endog = self.model.endog_li
time = self.model.time_li
# Only need to compute this once
if self.designx is not None:
designx = self.designx
else:
designx = []
for i in range(self.model.num_group):
ngrp = len(endog[i])
if ngrp == 0:
continue
# Loop over pairs of observations within a cluster
for j1 in range(ngrp):
for j2 in range(j1):
designx.append(self.dist_func(time[i][j1, :],
time[i][j2, :]))
designx = np.array(designx)
self.designx = designx
scale = self.model.estimate_scale()
varfunc = self.model.family.variance
cached_means = self.model.cached_means
# Weights
var = 1. - self.dep_params**(2*designx)
var /= 1. - self.dep_params**2
wts = 1. / var
wts /= wts.sum()
residmat = []
for i in range(self.model.num_group):
expval, _ = cached_means[i]
stdev = np.sqrt(scale * varfunc(expval))
resid = (endog[i] - expval) / stdev
ngrp = len(resid)
for j1 in range(ngrp):
for j2 in range(j1):
residmat.append([resid[j1], resid[j2]])
residmat = np.array(residmat)
# Need to minimize this
def fitfunc(a):
dif = residmat[:, 0] - (a**designx)*residmat[:, 1]
return np.dot(dif**2, wts)
# Left bracket point
b_lft, f_lft = 0., fitfunc(0.)
# Center bracket point
b_ctr, f_ctr = 0.5, fitfunc(0.5)
while f_ctr > f_lft:
b_ctr /= 2
f_ctr = fitfunc(b_ctr)
if b_ctr < 1e-8:
self.dep_params = 0
return
# Right bracket point
b_rgt, f_rgt = 0.75, fitfunc(0.75)
while f_rgt < f_ctr:
b_rgt = b_rgt + (1. - b_rgt) / 2
f_rgt = fitfunc(b_rgt)
if b_rgt > 1. - 1e-6:
raise ValueError(
"Autoregressive: unable to find right bracket")
from scipy.optimize import brent
self.dep_params = brent(fitfunc, brack=[b_lft, b_ctr, b_rgt])
[docs] def covariance_matrix(self, endog_expval, index):
ngrp = len(endog_expval)
if self.dep_params == 0:
return np.eye(ngrp, dtype=np.float64), True
idx = np.arange(ngrp)
cmat = self.dep_params**np.abs(idx[:, None] - idx[None, :])
return cmat, True
[docs] def covariance_matrix_solve(self, expval, index, stdev, rhs):
# The inverse of an AR(1) covariance matrix is tri-diagonal.
k = len(expval)
soln = []
# LHS has 1 column
if k == 1:
return [x / stdev**2 for x in rhs]
# LHS has 2 columns
if k == 2:
mat = np.array([[1, -self.dep_params], [-self.dep_params, 1]])
mat /= (1. - self.dep_params**2)
for x in rhs:
if x.ndim == 1:
x1 = x / stdev
else:
x1 = x / stdev[:, None]
x1 = np.dot(mat, x1)
if x.ndim == 1:
x1 /= stdev
else:
x1 /= stdev[:, None]
soln.append(x1)
return soln
# LHS has >= 3 columns: values c0, c1, c2 defined below give
# the inverse. c0 is on the diagonal, except for the first
# and last position. c1 is on the first and last position of
# the diagonal. c2 is on the sub/super diagonal.
c0 = (1. + self.dep_params**2) / (1. - self.dep_params**2)
c1 = 1. / (1. - self.dep_params**2)
c2 = -self.dep_params / (1. - self.dep_params**2)
soln = []
for x in rhs:
flatten = False
if x.ndim == 1:
x = x[:, None]
flatten = True
x1 = x / stdev[:, None]
z0 = np.zeros((1, x.shape[1]))
rhs1 = np.concatenate((x[1:,:], z0), axis=0)
rhs2 = np.concatenate((z0, x[0:-1,:]), axis=0)
y = c0*x + c2*rhs1 + c2*rhs2
y[0, :] = c1*x[0, :] + c2*x[1, :]
y[-1, :] = c1*x[-1, :] + c2*x[-2, :]
y /= stdev[:, None]
if flatten:
y = np.squeeze(y)
soln.append(y)
return soln
update.__doc__ = CovStruct.update.__doc__
covariance_matrix.__doc__ = CovStruct.covariance_matrix.__doc__
covariance_matrix_solve.__doc__ = CovStruct.covariance_matrix_solve.__doc__
[docs] def summary(self):
return ("Autoregressive(1) dependence parameter: %.3f\n" %
self.dep_params)
[docs]class GlobalOddsRatio(CovStruct):
"""
Estimate the global odds ratio for a GEE with ordinal or nominal
data.
References
----------
PJ Heagerty and S Zeger. "Marginal Regression Models for Clustered
Ordinal Measurements". Journal of the American Statistical
Association Vol. 91, Issue 435 (1996).
Thomas Lumley. Generalized Estimating Equations for Ordinal Data:
A Note on Working Correlation Structures. Biometrics Vol. 52,
No. 1 (Mar., 1996), pp. 354-361
http://www.jstor.org/stable/2533173
Notes
-----
The following data structures are calculated in the class:
'ibd' is a list whose i^th element ibd[i] is a sequence of integer
pairs (a,b), where endog_li[i][a:b] is the subvector of binary
indicators derived from the same ordinal value.
`cpp` is a dictionary where cpp[group] is a map from cut-point
pairs (c,c') to the indices of all between-subject pairs derived
from the given cut points.
"""
def __init__(self, endog_type):
super(GlobalOddsRatio, self).__init__()
self.endog_type = endog_type
self.dep_params = 0.
[docs] def initialize(self, model):
super(GlobalOddsRatio, self).initialize(model)
self.nlevel = len(model.endog_values)
self.ncut = self.nlevel - 1
ibd = []
for v in model.endog_li:
jj = np.arange(0, len(v) + 1, self.ncut)
ibd1 = np.hstack((jj[0:-1][:, None], jj[1:][:, None]))
ibd1 = [(jj[k], jj[k + 1]) for k in range(len(jj) - 1)]
ibd.append(ibd1)
self.ibd = ibd
# Need to restrict to between-subject pairs
cpp = []
for v in model.endog_li:
# Number of subjects in this group
m = int(len(v) / self.ncut)
cpp1 = {}
# Loop over distinct subject pairs
for i1 in range(m):
for i2 in range(i1):
# Loop over cut point pairs
for k1 in range(self.ncut):
for k2 in range(k1+1):
if (k2, k1) not in cpp1:
cpp1[(k2, k1)] = []
j1 = i1*self.ncut + k1
j2 = i2*self.ncut + k2
cpp1[(k2, k1)].append([j2, j1])
for k in cpp1.keys():
cpp1[k] = np.asarray(cpp1[k])
cpp.append(cpp1)
self.cpp = cpp
# Initialize the dependence parameters
self.crude_or = self.observed_crude_oddsratio()
self.dep_params = self.crude_or
[docs] def pooled_odds_ratio(self, tables):
"""
Returns the pooled odds ratio for a list of 2x2 tables.
The pooled odds ratio is the inverse variance weighted average
of the sample odds ratios of the tables.
"""
if len(tables) == 0:
return 1.
# Get the sampled odds ratios and variances
log_oddsratio, var = [], []
for table in tables:
lor = np.log(table[1, 1]) + np.log(table[0, 0]) -\
np.log(table[0, 1]) - np.log(table[1, 0])
log_oddsratio.append(lor)
var.append((1 / table.astype(np.float64)).sum())
# Calculate the inverse variance weighted average
wts = [1 / v for v in var]
wtsum = sum(wts)
wts = [w / wtsum for w in wts]
log_pooled_or = sum([w*e for w, e in zip(wts, log_oddsratio)])
return np.exp(log_pooled_or)
[docs] def covariance_matrix(self, expected_value, index):
vmat = self.get_eyy(expected_value, index)
vmat -= np.outer(expected_value, expected_value)
return vmat, False
[docs] def observed_crude_oddsratio(self):
"""
To obtain the crude (global) odds ratio, first pool all binary
indicators corresponding to a given pair of cut points (c,c'),
then calculate the odds ratio for this 2x2 table. The crude
odds ratio is the inverse variance weighted average of these
odds ratios. Since the covariate effects are ignored, this OR
will generally be greater than the stratified OR.
"""
cpp = self.cpp
endog = self.model.endog_li
# Storage for the contingency tables for each (c,c')
tables = {}
for ii in iterkeys(cpp[0]):
tables[ii] = np.zeros((2, 2), dtype=np.float64)
# Get the observed crude OR
for i in range(len(endog)):
# The observed joint values for the current cluster
yvec = endog[i]
endog_11 = np.outer(yvec, yvec)
endog_10 = np.outer(yvec, 1. - yvec)
endog_01 = np.outer(1. - yvec, yvec)
endog_00 = np.outer(1. - yvec, 1. - yvec)
cpp1 = cpp[i]
for ky in iterkeys(cpp1):
ix = cpp1[ky]
tables[ky][1, 1] += endog_11[ix[:, 0], ix[:, 1]].sum()
tables[ky][1, 0] += endog_10[ix[:, 0], ix[:, 1]].sum()
tables[ky][0, 1] += endog_01[ix[:, 0], ix[:, 1]].sum()
tables[ky][0, 0] += endog_00[ix[:, 0], ix[:, 1]].sum()
return self.pooled_odds_ratio(list(itervalues(tables)))
[docs] def get_eyy(self, endog_expval, index):
"""
Returns a matrix V such that V[i,j] is the joint probability
that endog[i] = 1 and endog[j] = 1, based on the marginal
probabilities of endog and the global odds ratio `current_or`.
"""
current_or = self.dep_params
ibd = self.ibd[index]
# The between-observation joint probabilities
if current_or == 1.0:
vmat = np.outer(endog_expval, endog_expval)
else:
psum = endog_expval[:, None] + endog_expval[None, :]
pprod = endog_expval[:, None] * endog_expval[None, :]
pfac = np.sqrt((1. + psum * (current_or - 1.))**2 +
4 * current_or * (1. - current_or) * pprod)
vmat = 1. + psum * (current_or - 1.) - pfac
vmat /= 2. * (current_or - 1)
# Fix E[YY'] for elements that belong to same observation
for bdl in ibd:
evy = endog_expval[bdl[0]:bdl[1]]
if self.endog_type == "ordinal":
eyr = np.outer(evy, np.ones(len(evy)))
eyc = np.outer(np.ones(len(evy)), evy)
vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] = \
np.where(eyr < eyc, eyr, eyc)
else:
vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] = np.diag(evy)
return vmat
[docs] def update(self, params):
"""
Update the global odds ratio based on the current value of
params.
"""
endog = self.model.endog_li
cpp = self.cpp
cached_means = self.model.cached_means
# This will happen if all the clusters have only
# one observation
if len(cpp[0]) == 0:
return
tables = {}
for ii in cpp[0]:
tables[ii] = np.zeros((2, 2), dtype=np.float64)
for i in range(self.model.num_group):
endog_expval, _ = cached_means[i]
emat_11 = self.get_eyy(endog_expval, i)
emat_10 = endog_expval[:, None] - emat_11
emat_01 = -emat_11 + endog_expval
emat_00 = 1. - (emat_11 + emat_10 + emat_01)
cpp1 = cpp[i]
for ky in iterkeys(cpp1):
ix = cpp1[ky]
tables[ky][1, 1] += emat_11[ix[:, 0], ix[:, 1]].sum()
tables[ky][1, 0] += emat_10[ix[:, 0], ix[:, 1]].sum()
tables[ky][0, 1] += emat_01[ix[:, 0], ix[:, 1]].sum()
tables[ky][0, 0] += emat_00[ix[:, 0], ix[:, 1]].sum()
cor_expval = self.pooled_odds_ratio(list(itervalues(tables)))
self.dep_params *= self.crude_or / cor_expval
if not np.isfinite(self.dep_params):
self.dep_params = 1.
warnings.warn("dep_params became inf, resetting to 1",
ConvergenceWarning)
update.__doc__ = CovStruct.update.__doc__
covariance_matrix.__doc__ = CovStruct.covariance_matrix.__doc__
[docs] def summary(self):
return "Global odds ratio: %.3f\n" % self.dep_params
