"""
Ordinary Least Squares regression with regimes.
"""
__author__ = "Luc Anselin, Pedro V. Amaral, Daniel Arribas-Bel"
import numpy as np
import multiprocessing as mp
import pandas as pd
from . import regimes as REGI
from . import user_output as USER
from .utils import set_warn, RegressionProps_basic, spdot, RegressionPropsY, get_lags, optim_k
from .ols import BaseOLS
from .robust import hac_multi
from .output import output, _spat_diag_out, _nonspat_mid, _nonspat_top
from .skater_reg import Skater_reg
[docs]
class OLS_Regimes(BaseOLS, REGI.Regimes_Frame, RegressionPropsY):
"""
Ordinary least squares with results and diagnostics.
Parameters
----------
y : numpy.ndarray or pandas.Series
nx1 array for dependent variable
x : numpy.ndarray or pandas object
Two dimensional array with n rows and one column for each
independent (exogenous) variable, excluding the constant
regimes : list or pandas.Series
List of n values with the mapping of each
observation to a regime. Assumed to be aligned with 'x'.
w : pysal W object
Spatial weights object (required if running spatial
diagnostics)
robust : string
If 'white', then a White consistent estimator of the
variance-covariance matrix is given. If 'hac', then a
HAC consistent estimator of the variance-covariance
matrix is given. Default set to None.
gwk : pysal W object
Kernel spatial weights needed for HAC estimation. Note:
matrix must have ones along the main diagonal.
slx_lags : integer
Number of spatial lags of X to include in the model specification.
If slx_lags>0, the specification becomes of the SLX type.
Note: WX is computed using the complete weights matrix
slx_vars : either "All" (default) or list of booleans to select x variables
to be lagged
sig2n_k : boolean
If True, then use n-k to estimate sigma^2. If False, use n.
nonspat_diag : boolean
If True, then compute non-spatial diagnostics on
the regression.
spat_diag : boolean
If True, then compute Lagrange multiplier tests (requires
w). Note: see moran for further tests.
moran : boolean
If True, compute Moran's I on the residuals. Note:
requires spat_diag=True.
white_test : boolean
If True, compute White's specification robust test.
(requires nonspat_diag=True)
vm : boolean
If True, include variance-covariance matrix in summary
results
constant_regi: string, optional
Switcher controlling the constant term setup. It may take
the following values:
* 'one': a vector of ones is appended to x and held constant across regimes
* 'many': a vector of ones is appended to x and considered different per regime (default)
cols2regi : list, 'all'
Argument indicating whether each
column of x should be considered as different per regime
or held constant across regimes (False).
If a list, k booleans indicating for each variable the
option (True if one per regime, False to be held constant).
If 'all' (default), all the variables vary by regime.
regime_err_sep : boolean
If True, a separate regression is run for each regime.
cores : boolean
Specifies if multiprocessing is to be used
Default: no multiprocessing, cores = False
Note: Multiprocessing may not work on all platforms.
name_y : string
Name of dependent variable for use in output
name_x : list of strings
Names of independent variables for use in output
name_w : string
Name of weights matrix for use in output
name_gwk : string
Name of kernel weights matrix for use in output
name_ds : string
Name of dataset for use in output
name_regimes : string
Name of regime variable for use in the output
latex : boolean
Specifies if summary is to be printed in latex format
Attributes
----------
output : dataframe
regression results pandas dataframe
summary : string
Summary of regression results and diagnostics (note: use in
conjunction with the print command)
betas : array
kx1 array of estimated coefficients
u : array
nx1 array of residuals
predy : array
nx1 array of predicted y values
n : integer
Number of observations
k : integer
Number of variables for which coefficients are estimated
(including the constant)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
y : array
nx1 array for dependent variable
x : array
Two dimensional array with n rows and one column for each
independent (exogenous) variable, including the constant
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
robust : string
Adjustment for robust standard errors
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
mean_y : float
Mean of dependent variable
std_y : float
Standard deviation of dependent variable
vm : array
Variance covariance matrix (kxk)
r2 : float
R squared
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
ar2 : float
Adjusted R squared
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
utu : float
Sum of squared residuals
sig2 : float
Sigma squared used in computations
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
sig2ML : float
Sigma squared (maximum likelihood)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
f_stat : tuple
Statistic (float), p-value (float)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
logll : float
Log likelihood
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
aic : float
Akaike information criterion
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
schwarz : float
Schwarz information criterion
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
std_err : array
1xk array of standard errors of the betas
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
t_stat : list of tuples
t statistic; each tuple contains the pair (statistic,
p-value), where each is a float
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
mulColli : float
Multicollinearity condition number
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
jarque_bera : dictionary
'jb': Jarque-Bera statistic (float); 'pvalue': p-value
(float); 'df': degrees of freedom (int)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
breusch_pagan : dictionary
'bp': Breusch-Pagan statistic (float); 'pvalue': p-value
(float); 'df': degrees of freedom (int)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
koenker_bassett: dictionary
'kb': Koenker-Bassett statistic (float); 'pvalue': p-value (float);
'df': degrees of freedom (int). Only available in dictionary
'multi' when multiple regressions (see 'multi' below for details).
white : dictionary
'wh': White statistic (float); 'pvalue': p-value (float);
'df': degrees of freedom (int).
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
lm_error : tuple
Lagrange multiplier test for spatial error model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
lm_lag : tuple
Lagrange multiplier test for spatial lag model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
rlm_error : tuple
Robust lagrange multiplier test for spatial error model;
tuple contains the pair (statistic, p-value), where each
is a float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
rlm_lag : tuple
Robust lagrange multiplier test for spatial lag model;
tuple contains the pair (statistic, p-value), where each
is a float. Only available in dictionary 'multi' when
multiple regressions (see 'multi' below for details)
lm_sarma : tuple
Lagrange multiplier test for spatial SARMA model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
moran_res : tuple
Moran's I for the residuals; tuple containing the triple
(Moran's I, standardized Moran's I, p-value)
name_y : string
Name of dependent variable for use in output
name_x : list of strings
Names of independent variables for use in output
name_w : string
Name of weights matrix for use in output
name_gwk : string
Name of kernel weights matrix for use in output
name_ds : string
Name of dataset for use in output
name_regimes : string
Name of regime variable for use in the output
title : string
Name of the regression method used.
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
sig2n : float
Sigma squared (computed with n in the denominator)
sig2n_k : float
Sigma squared (computed with n-k in the denominator)
xtx : float
:math:`X'X`. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
xtxi : float
:math:`(X'X)^{-1}`. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
regimes : list
List of n values with the mapping of each observation to
a regime. Assumed to be aligned with 'x'.
constant_regi : string
Ignored if regimes=False. Constant option for regimes.
Switcher controlling the constant term setup. It may take
the following values:
* 'one': a vector of ones is appended to x and held constant across regimes.
* 'many': a vector of ones is appended to x and considered different per regime.
cols2regi : list
Ignored if regimes=False. Argument indicating whether each
column of x should be considered as different per regime
or held constant across regimes (False).
If a list, k booleans indicating for each variable the
option (True if one per regime, False to be held constant).
If 'all', all the variables vary by regime.
regime_err_sep: boolean
If True, a separate regression is run for each regime.
kr : int
Number of variables/columns to be "regimized" or subject
to change by regime. These will result in one parameter
estimate by regime for each variable (i.e. nr parameters per
variable)
kf : int
Number of variables/columns to be considered fixed or
global across regimes and hence only obtain one parameter
estimate.
nr : int
Number of different regimes in the 'regimes' list.
multi : dictionary
Only available when multiple regressions are estimated,
i.e. when regime_err_sep=True and no variable is fixed
across regimes.
Contains all attributes of each individual regression.
Examples
--------
>>> import numpy as np
>>> import libpysal
>>> from spreg import OLS_Regimes
Open data on NCOVR US County Homicides (3085 areas) using libpysal.io.open().
This is the DBF associated with the NAT shapefile. Note that
libpysal.io.open() also reads data in CSV format; since the actual class
requires data to be passed in as numpy arrays, the user can read their
data in using any method.
>>> db = libpysal.io.open(libpysal.examples.get_path("NAT.dbf"),'r')
Extract the HR90 column (homicide rates in 1990) from the DBF file and make it
the dependent variable for the regression. Note that PySAL requires this to be
an numpy array of shape (n, 1) as opposed to the also common shape of (n, )
that other packages accept.
>>> y_var = 'HR90'
>>> y = db.by_col(y_var)
>>> y = np.array(y)
Extract UE90 (unemployment rate) and PS90 (population structure) vectors from
the DBF to be used as independent variables in the regression. Other variables
can be inserted by adding their names to x_var, such as x_var = ['Var1','Var2','...]
Note that PySAL requires this to be an nxj numpy array, where j is the
number of independent variables (not including a constant). By default
this model adds a vector of ones to the independent variables passed in.
>>> x_var = ['PS90','UE90']
>>> x = np.array([db.by_col(name) for name in x_var]).T
The different regimes in this data are given according to the North and
South dummy (SOUTH).
>>> r_var = 'SOUTH'
>>> regimes = db.by_col(r_var)
We can now run the regression and then have a summary of the output
by typing: olsr.summary
>>> olsr = OLS_Regimes(y, x, regimes, nonspat_diag=False, name_y=y_var, name_x=['PS90','UE90'], name_regimes=r_var, name_ds='NAT')
>>> print(olsr.summary)
REGRESSION RESULTS
------------------
<BLANKLINE>
SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 0
---------------------------------------------------------------
Data set : NAT
Weights matrix : None
Dependent Variable : 0_HR90 Number of Observations: 1673
Mean dependent var : 3.3416 Number of Variables : 3
S.D. dependent var : 4.6795 Degrees of Freedom : 1670
R-squared : 0.1271
Adjusted R-squared : 0.1260
<BLANKLINE>
------------------------------------------------------------------------------------
Variable Coefficient Std.Error t-Statistic Probability
------------------------------------------------------------------------------------
0_CONSTANT 0.39643 0.24816 1.59745 0.11035
0_PS90 0.65583 0.09663 6.78728 0.00000
0_UE90 0.48704 0.03629 13.42213 0.00000
------------------------------------------------------------------------------------
Regimes variable: SOUTH
<BLANKLINE>
SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 1
---------------------------------------------------------------
Data set : NAT
Weights matrix : None
Dependent Variable : 1_HR90 Number of Observations: 1412
Mean dependent var : 9.5493 Number of Variables : 3
S.D. dependent var : 7.0389 Degrees of Freedom : 1409
R-squared : 0.0661
Adjusted R-squared : 0.0647
<BLANKLINE>
------------------------------------------------------------------------------------
Variable Coefficient Std.Error t-Statistic Probability
------------------------------------------------------------------------------------
1_CONSTANT 5.59835 0.46895 11.93816 0.00000
1_PS90 1.16210 0.21667 5.36338 0.00000
1_UE90 0.53164 0.05946 8.94164 0.00000
------------------------------------------------------------------------------------
Regimes variable: SOUTH
------------------------------------------------------------------------------------
<BLANKLINE>
GLOBAL DIAGNOSTICS
<BLANKLINE>
REGIMES DIAGNOSTICS - CHOW TEST
VARIABLE DF VALUE PROB
CONSTANT 1 96.129 0.0000
PS90 1 4.554 0.0328
UE90 1 0.410 0.5220
Global test 3 680.960 0.0000
================================ END OF REPORT =====================================
"""
[docs]
def __init__(
self,
y,
x,
regimes,
w=None,
robust=None,
gwk=None,
slx_lags=0,
slx_vars = "all",
sig2n_k=True,
nonspat_diag=True,
spat_diag=False,
moran=False,
white_test=False,
vm=False,
constant_regi="many",
cols2regi="all",
regime_err_sep=True,
cores=False,
name_y=None,
name_x=None,
name_regimes=None,
name_w=None,
name_gwk=None,
name_ds=None,
latex=False,
**kwargs,
):
n = USER.check_arrays(y, x)
y, name_y = USER.check_y(y, n, name_y)
USER.check_robust(robust, gwk)
if robust == "hac":
if regime_err_sep:
set_warn(
self,
"Error by regimes is not available for HAC estimation. The error by regimes has been disabled for this model.",
)
regime_err_sep = False
spat_diag, warn = USER.check_spat_diag(spat_diag=spat_diag, w=w, robust=robust, slx_lags=slx_lags)
set_warn(self, warn)
if robust in ["hac", "white"] and white_test:
set_warn(
self,
"White test not available when standard errors are estimated by HAC or White correction.",
)
white_test = False
x_constant, name_x, warn = USER.check_constant(x, name_x, just_rem=True)
set_warn(self, warn)
name_x = USER.set_name_x(name_x, x_constant, constant=True)
if spat_diag or moran or slx_lags > 0:
w = USER.check_weights(w, y, slx_lags=slx_lags, w_required=True, allow_wk=True)
else:
w = USER.check_weights(w, y, slx_lags=slx_lags, allow_wk=True)
if slx_lags > 0:
x_constant,name_x = USER.flex_wx(w,x=x_constant,name_x=name_x,constant=False,
slx_lags=slx_lags,slx_vars=slx_vars)
set_warn(self,"WX is computed using the complete W, i.e. not trimmed by regimes.")
self.slx_lags = slx_lags
self.name_x_r = USER.set_name_x(name_x, x_constant)
self.constant_regi = constant_regi
self.cols2regi = cols2regi
self.name_w = USER.set_name_w(name_w, w)
self.name_gwk = USER.set_name_w(name_gwk, gwk)
self.name_ds = USER.set_name_ds(name_ds)
self.name_y = USER.set_name_y(name_y)
regimes, name_regimes = USER.check_reg_list(regimes, name_regimes, n)
self.name_regimes = USER.set_name_ds(name_regimes)
self.n = n
cols2regi = REGI.check_cols2regi(
constant_regi, cols2regi, x_constant, add_cons=False
)
self.regimes_set = REGI._get_regimes_set(regimes)
self.regimes = regimes
USER.check_regimes(self.regimes_set, self.n, x_constant.shape[1])
self.regime_err_sep = regime_err_sep
if (
regime_err_sep == True
and set(cols2regi) == set([True])
and constant_regi == "many"
):
self.y = y
regi_ids = dict(
(r, list(np.where(np.array(regimes) == r)[0])) for r in self.regimes_set
)
self._ols_regimes_multi(
x_constant,
w,
regi_ids,
cores,
gwk,
slx_lags,
sig2n_k,
robust,
nonspat_diag,
spat_diag,
vm,
name_x,
moran,
white_test,
latex
)
else:
x, self.name_x, xtype, x_rlist = REGI.Regimes_Frame.__init__(
self, x_constant, regimes, constant_regi, cols2regi, name_x, rlist=True
)
self.output = pd.DataFrame(self.name_x,
columns=['var_names'])
self.output['var_type'] = xtype
self.output['regime'] = x_rlist
self.output['equation'] = 0
BaseOLS.__init__(self, y=y, x=x, robust=robust, gwk=gwk, sig2n_k=sig2n_k)
if regime_err_sep == True and robust == None:
y2, x2 = REGI._get_weighted_var(
regimes, self.regimes_set, sig2n_k, self.u, y, x
)
ols2 = BaseOLS(y=y2, x=x2, sig2n_k=sig2n_k)
RegressionProps_basic(self, betas=ols2.betas, vm=ols2.vm)
self.title = (
"ORDINARY LEAST SQUARES - REGIMES (Group-wise heteroskedasticity)"
)
if slx_lags > 0:
self.title = "ORDINARY LEAST SQUARES WITH SLX - REGIMES (Group-wise heteroskedasticity)"
nonspat_diag = None
set_warn(
self,
"Residuals treated as homoskedastic for the purpose of diagnostics.",
)
else:
if slx_lags == 0:
self.title = "ORDINARY LEAST SQUARES - REGIMES"
else:
self.title = "ORDINARY LEAST SQUARES WITH SLX - REGIMES"
self.robust = USER.set_robust(robust)
self.chow = REGI.Chow(self)
self.other_mid, other_end = ("", "") # strings where function-specific diag. are stored
if nonspat_diag:
self.other_mid += _nonspat_mid(self, white_test=white_test)
top_diag = _nonspat_top(self)
try:
self.other_top += top_diag
except:
self.other_top = top_diag
if spat_diag:
other_end += _spat_diag_out(self, w, 'ols', moran=moran) #Must decide what to do with W.
output(reg=self, vm=vm, robust=robust, other_end=other_end, latex=latex)
def _ols_regimes_multi(
self,
x,
w,
regi_ids,
cores,
gwk,
slx_lags,
sig2n_k,
robust,
nonspat_diag,
spat_diag,
vm,
name_x,
moran,
white_test,
latex
):
results_p = {}
"""
for r in self.regimes_set:
if system() == 'Windows':
is_win = True
results_p[r] = _work(*(self.y,x,w,regi_ids,r,robust,sig2n_k,self.name_ds,self.name_y,name_x,self.name_w,self.name_regimes))
else:
pool = mp.Pool(cores)
results_p[r] = pool.apply_async(_work,args=(self.y,x,w,regi_ids,r,robust,sig2n_k,self.name_ds,self.name_y,name_x,self.name_w,self.name_regimes))
is_win = False
"""
x_constant, name_x = REGI.check_const_regi(self, x, name_x, regi_ids)
self.name_x_r = name_x
for r in self.regimes_set:
if cores:
pool = mp.Pool(None)
results_p[r] = pool.apply_async(
_work,
args=(
self.y,
x_constant,
w,
regi_ids,
r,
robust,
sig2n_k,
self.name_ds,
self.name_y,
name_x,
self.name_w,
self.name_regimes,
slx_lags
),
)
else:
results_p[r] = _work(
*(
self.y,
x_constant,
w,
regi_ids,
r,
robust,
sig2n_k,
self.name_ds,
self.name_y,
name_x,
self.name_w,
self.name_regimes,
slx_lags
)
)
self.kryd = 0
self.kr = x_constant.shape[1]
self.kf = 0
self.nr = len(self.regimes_set)
self.vm = np.zeros((self.nr * self.kr, self.nr * self.kr), float)
self.betas = np.zeros((self.nr * self.kr, 1), float)
self.u = np.zeros((self.n, 1), float)
self.predy = np.zeros((self.n, 1), float)
"""
if not is_win:
pool.close()
pool.join()
"""
if cores:
pool.close()
pool.join()
results = {}
self.name_y, self.name_x = [], []
counter = 0
self.output = pd.DataFrame(columns=['var_names', 'var_type', 'regime', 'equation'])
for r in self.regimes_set:
"""
if is_win:
results[r] = results_p[r]
else:
results[r] = results_p[r].get()
"""
if not cores:
results[r] = results_p[r]
else:
results[r] = results_p[r].get()
self.vm[
(counter * self.kr): ((counter + 1) * self.kr),
(counter * self.kr): ((counter + 1) * self.kr),
] = results[r].vm
self.betas[
(counter * self.kr): ((counter + 1) * self.kr),
] = results[r].betas
self.u[
regi_ids[r],
] = results[r].u
self.predy[
regi_ids[r],
] = results[r].predy
self.name_y += results[r].name_y
self.name_x += results[r].name_x
self.output = pd.concat([self.output, pd.DataFrame({'var_names': results[r].name_x,
'var_type': ['o']+['x']*(len(results[r].name_x)-1),
'regime': r, 'equation': r})], ignore_index=True)
try:
results[r].other_top = self.other_top
except:
results[r].other_top = ""
results[r].other_mid = ""
if nonspat_diag:
results[r].other_mid += _nonspat_mid(results[r], white_test=white_test)
results[r].other_top += _nonspat_top(results[r])
counter += 1
self.multi = results
self.hac_var = x_constant[:, 1:]
if robust == "hac":
hac_multi(self, gwk)
self.chow = REGI.Chow(self)
other_end = ""
if spat_diag:
self._get_spat_diag_props(x_constant, sig2n_k)
other_end += _spat_diag_out(self, w, 'ols', moran=moran) #Need to consider W
output(reg=self, vm=vm, robust=robust, other_end=other_end, latex=latex)
def _get_spat_diag_props(self, x, sig2n_k):
self.k = self.kr
self._cache = {}
self.x = REGI.regimeX_setup(
x, self.regimes, [True] * x.shape[1], self.regimes_set
)
self.xtx = spdot(self.x.T, self.x)
self.xtxi = np.linalg.inv(self.xtx)
def _work(
y, x, w, regi_ids, r, robust, sig2n_k, name_ds, name_y, name_x, name_w, name_regimes, slx_lags
):
y_r = y[regi_ids[r]]
x_r = x[regi_ids[r]]
# x_constant,name_x,warn = USER.check_constant(x_r, name_x)
# name_x = USER.set_name_x(name_x, x_constant)
if robust == "hac":
robust = None
model = BaseOLS(y_r, x_r, robust=robust, sig2n_k=sig2n_k)
if slx_lags == 0:
model.title = "ORDINARY LEAST SQUARES ESTIMATION - REGIME %s" % r
else:
model.title = "ORDINARY LEAST SQUARES ESTIMATION WITH SLX - REGIME %s" % r
model.robust = USER.set_robust(robust)
model.name_ds = name_ds
model.name_y = "%s_%s" % (str(r), name_y)
model.name_x = ["%s_%s" % (str(r), i) for i in name_x]
model.name_w = name_w
model.name_regimes = name_regimes
if w:
w_r, warn = REGI.w_regime(w, regi_ids[r], r, transform=True)
set_warn(model, warn)
model.w = w_r
return model
[docs]
class OLS_Endog_Regimes(OLS_Regimes):
"""
Ordinary least squares with endogenous regimes. Based on the function skater_reg as shown in :cite:`Anselin2021`.
Parameters
----------
y : numpy.ndarray or pandas.Series
nx1 array for dependent variable
x : numpy.ndarray or pandas object
Two dimensional array with n rows and one column for each
independent (exogenous) variable, excluding the constant
w : pysal W object
Spatial weights object (required if running spatial
diagnostics)
n_clusters : int
Number of clusters to be used in the endogenous regimes.
If None (default), the number of clusters will be chosen
according to the function utils.optim_k using a method
adapted from Mojena (1977)'s Rule Two
quorum : int
Minimum number of observations in a cluster to be considered
Must be at least larger than the number of variables in x
Default value is 30 or 10*k, whichever is larger.
trace : boolean
Sets whether to store intermediate results of the clustering
Hard-coded to True if n_clusters is None
name_y : string
Name of dependent variable for use in output
name_x : list of strings
Names of independent variables for use in output
name_w : string
Name of weights matrix for use in output
name_ds : string
Name of dataset for use in output
latex : boolean
Specifies if summary is to be printed in latex format
**kwargs : additional keyword arguments depending on the specific model
Attributes
----------
output : dataframe
regression results pandas dataframe
summary : string
Summary of regression results and diagnostics (note: use in
conjunction with the print command)
betas : array
kx1 array of estimated coefficients
u : array
nx1 array of residuals
predy : array
nx1 array of predicted y values
n : integer
Number of observations
k : integer
Number of variables for which coefficients are estimated
(including the constant)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
y : array
nx1 array for dependent variable
x : array
Two dimensional array with n rows and one column for each
independent (exogenous) variable, including the constant
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
robust : string
Adjustment for robust standard errors
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
mean_y : float
Mean of dependent variable
std_y : float
Standard deviation of dependent variable
vm : array
Variance covariance matrix (kxk)
r2 : float
R squared
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
ar2 : float
Adjusted R squared
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
utu : float
Sum of squared residuals
sig2 : float
Sigma squared used in computations
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
sig2ML : float
Sigma squared (maximum likelihood)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
f_stat : tuple
Statistic (float), p-value (float)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
logll : float
Log likelihood
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
aic : float
Akaike information criterion
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
schwarz : float
Schwarz information criterion
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
std_err : array
1xk array of standard errors of the betas
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
t_stat : list of tuples
t statistic; each tuple contains the pair (statistic,
p-value), where each is a float
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
mulColli : float
Multicollinearity condition number
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
jarque_bera : dictionary
'jb': Jarque-Bera statistic (float); 'pvalue': p-value
(float); 'df': degrees of freedom (int)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
breusch_pagan : dictionary
'bp': Breusch-Pagan statistic (float); 'pvalue': p-value
(float); 'df': degrees of freedom (int)
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
koenker_bassett: dictionary
'kb': Koenker-Bassett statistic (float); 'pvalue': p-value (float);
'df': degrees of freedom (int). Only available in dictionary
'multi' when multiple regressions (see 'multi' below for details).
white : dictionary
'wh': White statistic (float); 'pvalue': p-value (float);
'df': degrees of freedom (int).
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
lm_error : tuple
Lagrange multiplier test for spatial error model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
lm_lag : tuple
Lagrange multiplier test for spatial lag model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
rlm_error : tuple
Robust lagrange multiplier test for spatial error model;
tuple contains the pair (statistic, p-value), where each
is a float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
rlm_lag : tuple
Robust lagrange multiplier test for spatial lag model;
tuple contains the pair (statistic, p-value), where each
is a float. Only available in dictionary 'multi' when
multiple regressions (see 'multi' below for details)
lm_sarma : tuple
Lagrange multiplier test for spatial SARMA model; tuple
contains the pair (statistic, p-value), where each is a
float. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
moran_res : tuple
Moran's I for the residuals; tuple containing the triple
(Moran's I, standardized Moran's I, p-value)
name_y : string
Name of dependent variable for use in output
name_x : list of strings
Names of independent variables for use in output
name_w : string
Name of weights matrix for use in output
name_gwk : string
Name of kernel weights matrix for use in output
name_ds : string
Name of dataset for use in output
name_regimes : string
Name of regime variable for use in the output
title : string
Name of the regression method used.
Only available in dictionary 'multi' when multiple regressions
(see 'multi' below for details)
sig2n : float
Sigma squared (computed with n in the denominator)
sig2n_k : float
Sigma squared (computed with n-k in the denominator)
xtx : float
:math:`X'X`. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
xtxi : float
:math:`(X'X)^{-1}`. Only available in dictionary 'multi' when multiple
regressions (see 'multi' below for details)
regimes : list
List of n values with the mapping of each observation to
a regime. Assumed to be aligned with 'x'.
constant_regi : string
Ignored if regimes=False. Constant option for regimes.
Switcher controlling the constant term setup. It may take
the following values:
* 'one': a vector of ones is appended to x and held constant across regimes.
* 'many': a vector of ones is appended to x and considered different per regime.
cols2regi : list
Ignored if regimes=False. Argument indicating whether each
column of x should be considered as different per regime
or held constant across regimes (False).
If a list, k booleans indicating for each variable the
option (True if one per regime, False to be held constant).
If 'all', all the variables vary by regime.
regime_err_sep: boolean
If True, a separate regression is run for each regime.
kr : int
Number of variables/columns to be "regimized" or subject
to change by regime. These will result in one parameter
estimate by regime for each variable (i.e. nr parameters per
variable)
kf : int
Number of variables/columns to be considered fixed or
global across regimes and hence only obtain one parameter
estimate.
nr : int
Number of different regimes in the 'regimes' list.
multi : dictionary
Only available when multiple regressions are estimated,
i.e. when regime_err_sep=True and no variable is fixed
across regimes.
Contains all attributes of each individual regression.
SSR : list
list with the total sum of squared residuals for the model
considering all regimes for each of steps of number of regimes
considered, starting with the solution with 2 regimes.
clusters : int
Number of clusters considered in the endogenous regimes
_trace : list
List of dictionaries with the clustering results for each
number of clusters tested. Only available if n_clusters is
None or trace=True.
Examples
--------
>>> import libpysal
>>> import numpy as np
>>> np.set_printoptions(legacy='1.25') #to avoid printing issues with numpy floats
>>> import geopandas as gpd
>>> from spreg import OLS_Endog_Regimes
Open data on Baltimore house sales price and characteristics in Baltimore
from libpysal examples using geopandas.
>>> db = gpd.read_file(libpysal.examples.get_path('baltim.shp'))
We will create a weights matrix based on contiguity.
>>> w = libpysal.weights.Queen.from_dataframe(db, use_index=True)
>>> w.transform = "r"
For this example, we will use the 'PRICE' column as the dependent variable and
the 'NROOM', 'AGE', and 'SQFT' columns as independent variables.
At this point, we will let the model choose the number of clusters.
>>> olsr = OLS_Endog_Regimes(y=db['PRICE'], x=db[['NROOM','AGE','SQFT']], w=w, name_w="baltim_q.gal")
The function `print(olsr.summary)` can be used to visualize the results of the regression.
Alternatively, we can check individual attributes:
>>> olsr.betas
array([[26.24209866],
[ 2.40329959],
[-0.24183707],
[ 0.45714794],
[19.84817747],
[ 5.12117483],
[-0.65466516],
[ 1.10034154]])
>>> olsr.SSR
[68840.74965798721, 62741.55717492997]
>>> olsr.clusters
array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0,
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0,
1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], dtype=int32)
We will now set the number of clusters to 2 and run the regression again.
>>> olsr = OLS_Endog_Regimes(y=db['PRICE'], x=db[['NROOM','AGE','SQFT']], w=w, n_clusters=2, name_w="baltim_q.gal")
The function `print(olsr.summary)` can be used to visualize the results of the regression.
Alternatively, we can check individual attributes as before:
>>> olsr.betas
array([[26.24209866],
[ 2.40329959],
[-0.24183707],
[ 0.45714794],
[19.84817747],
[ 5.12117483],
[-0.65466516],
[ 1.10034154]])
>>> olsr.SSR
[68840.74965798721]
>>> olsr.clusters
array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0,
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0,
1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], dtype=int32)
"""
[docs]
def __init__(
self, y, x, w, n_clusters=None, quorum=-1, trace=True, name_y=None, name_x=None,
constant_regi='many', cols2regi='all', regime_err_sep=True, **kwargs):
n = USER.check_arrays(y, x)
y, name_y = USER.check_y(y, n, name_y)
w = USER.check_weights(w, y, w_required=True)
x_constant, name_x, warn = USER.check_constant(x, name_x, just_rem=True)
set_warn(self, warn)
warn = USER.check_regi_args(constant_regi, cols2regi, regime_err_sep)
set_warn(self, warn)
# Standardize the variables
x_std = (x_constant - np.mean(x_constant, axis=0)) / np.std(x_constant, axis=0)
if quorum < 0:
quorum = np.max([(x_constant.shape[1]+1)*10, 30])
if not n_clusters:
n_clusters_opt = x_constant.shape[0]*0.70//quorum
if n_clusters_opt < 2:
raise ValueError(
"The combination of the values of `N` and `quorum` is not compatible with regimes estimation.")
sk_reg_results = Skater_reg().fit(n_clusters_opt, w, x_std, {'reg':BaseOLS,'y':y,'x':x_constant}, quorum=quorum, trace=True)
n_clusters = optim_k([sk_reg_results._trace[i][1][2] for i in range(1, len(sk_reg_results._trace))])
self.clusters = sk_reg_results._trace[n_clusters-1][0]
self.score = sk_reg_results._trace[n_clusters-1][1][2]
else:
try:
# Call the Skater_reg method based on OLS
sk_reg_results = Skater_reg().fit(n_clusters, w, x_std, {'reg':BaseOLS,'y':y,'x':x_constant}, quorum=quorum, trace=trace)
self.clusters = sk_reg_results.current_labels_
self.score = sk_reg_results._trace[-1][1][2]
except Exception as e:
if str(e) == "one or more input arrays have more columns than rows":
raise ValueError("One or more input ended up with more variables than observations. Please check your setting for `quorum`.")
else:
print("An error occurred:", e)
self._trace = sk_reg_results._trace
self.SSR = [self._trace[i][1][2] for i in range(1, len(self._trace))]
OLS_Regimes.__init__(self, y, x_constant, regimes=self.clusters, w=w, name_regimes='Skater_reg', name_y=name_y, name_x=name_x,
constant_regi='many', cols2regi='all', regime_err_sep=True, **kwargs)
def _test():
import doctest
start_suppress = np.get_printoptions()["suppress"]
np.set_printoptions(suppress=True)
doctest.testmod()
np.set_printoptions(suppress=start_suppress)
if __name__ == "__main__":
_test()
import numpy as np
import libpysal
from spreg import OLS_Regimes
db = libpysal.io.open(libpysal.examples.get_path("NAT.dbf"), "r")
y_var = "HR90"
y = np.array(db.by_col(y_var)).reshape(-1,1)
x_var = ['PS90','UE90']
x = np.array([db.by_col(name) for name in x_var]).T
r_var = "SOUTH"
regimes = db.by_col(r_var)
w = libpysal.weights.Rook.from_shapefile(libpysal.examples.get_path("NAT.shp"))
w.transform = "r"
olsr = OLS_Regimes(
y,
x,
regimes,
w=w,
constant_regi="many",
nonspat_diag=True,
spat_diag=True,
name_y=y_var,
name_x=x_var,
name_ds="NAT",
name_regimes=r_var,
regime_err_sep=True,
cols2regi=[True, True],
sig2n_k=False,
white_test=True,
#robust="white"
)
print(olsr.output)
print(olsr.summary)