spreg.OLS_Regimes¶

class
spreg.
OLS_Regimes
(y, x, regimes, w=None, robust=None, gwk=None, 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)[source]¶ Ordinary least squares with results and diagnostics.
 Parameters
 yarray
nx1 array for dependent variable
 xarray
Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant
 regimeslist
List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.
 wpysal W object
Spatial weights object (required if running spatial diagnostics)
 robuststring
If ‘white’, then a White consistent estimator of the variancecovariance matrix is given. If ‘hac’, then a HAC consistent estimator of the variancecovariance matrix is given. Default set to None.
 gwkpysal W object
Kernel spatial weights needed for HAC estimation. Note: matrix must have ones along the main diagonal.
 sig2n_kboolean
If True, then use nk to estimate sigma^2. If False, use n.
 nonspat_diagboolean
If True, then compute nonspatial diagnostics on the regression.
 spat_diagboolean
If True, then compute Lagrange multiplier tests (requires w). Note: see moran for further tests.
 moranboolean
If True, compute Moran’s I on the residuals. Note: requires spat_diag=True.
 white_testboolean
If True, compute White’s specification robust test. (requires nonspat_diag=True)
 vmboolean
If True, include variancecovariance 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)
 cols2regilist, ‘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_sepboolean
If True, a separate regression is run for each regime.
 coresboolean
Specifies if multiprocessing is to be used Default: no multiprocessing, cores = False Note: Multiprocessing may not work on all platforms.
 name_ystring
Name of dependent variable for use in output
 name_xlist of strings
Names of independent variables for use in output
 name_wstring
Name of weights matrix for use in output
 name_gwkstring
Name of kernel weights matrix for use in output
 name_dsstring
Name of dataset for use in output
 name_regimesstring
Name of regime variable for use in the output
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).reshape(len(y), 1)
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 Alternatively, we can just check the betas and standard errors of the parameters:
>>> olsr = OLS_Regimes(y, x, regimes, nonspat_diag=False, name_y=y_var, name_x=['PS90','UE90'], name_regimes=r_var, name_ds='NAT') >>> olsr.betas array([[0.39642899], [0.65583299], [0.48703937], [5.59835 ], [1.16210453], [0.53163886]]) >>> np.sqrt(olsr.vm.diagonal()) array([0.24816345, 0.09662678, 0.03628629, 0.46894564, 0.21667395, 0.05945651]) >>> olsr.cols2regi 'all'
 Attributes
 summarystring
Summary of regression results and diagnostics (note: use in conjunction with the print command)
 betasarray
kx1 array of estimated coefficients
 uarray
nx1 array of residuals
 predyarray
nx1 array of predicted y values
 ninteger
Number of observations
 kinteger
Number of variables for which coefficients are estimated (including the constant) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 yarray
nx1 array for dependent variable
 xarray
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)
 robuststring
Adjustment for robust standard errors Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 mean_yfloat
Mean of dependent variable
 std_yfloat
Standard deviation of dependent variable
 vmarray
Variance covariance matrix (kxk)
 r2float
R squared Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 ar2float
Adjusted R squared Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 utufloat
Sum of squared residuals
 sig2float
Sigma squared used in computations Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 sig2MLfloat
Sigma squared (maximum likelihood) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 f_stattuple
Statistic (float), pvalue (float) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 logllfloat
Log likelihood Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 aicfloat
Akaike information criterion Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 schwarzfloat
Schwarz information criterion Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 std_errarray
1xk array of standard errors of the betas Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 t_statlist of tuples
t statistic; each tuple contains the pair (statistic, pvalue), where each is a float Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 mulCollifloat
Multicollinearity condition number Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 jarque_beradictionary
‘jb’: JarqueBera statistic (float); ‘pvalue’: pvalue (float); ‘df’: degrees of freedom (int) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 breusch_pagandictionary
‘bp’: BreuschPagan statistic (float); ‘pvalue’: pvalue (float); ‘df’: degrees of freedom (int) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 koenker_bassett: dictionary
‘kb’: KoenkerBassett statistic (float); ‘pvalue’: pvalue (float); ‘df’: degrees of freedom (int). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details).
 whitedictionary
‘wh’: White statistic (float); ‘pvalue’: pvalue (float); ‘df’: degrees of freedom (int). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 lm_errortuple
Lagrange multiplier test for spatial error model; tuple contains the pair (statistic, pvalue), where each is a float. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 lm_lagtuple
Lagrange multiplier test for spatial lag model; tuple contains the pair (statistic, pvalue), where each is a float. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 rlm_errortuple
Robust lagrange multiplier test for spatial error model; tuple contains the pair (statistic, pvalue), where each is a float. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 rlm_lagtuple
Robust lagrange multiplier test for spatial lag model; tuple contains the pair (statistic, pvalue), where each is a float. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 lm_sarmatuple
Lagrange multiplier test for spatial SARMA model; tuple contains the pair (statistic, pvalue), where each is a float. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 moran_restuple
Moran’s I for the residuals; tuple containing the triple (Moran’s I, standardized Moran’s I, pvalue)
 name_ystring
Name of dependent variable for use in output
 name_xlist of strings
Names of independent variables for use in output
 name_wstring
Name of weights matrix for use in output
 name_gwkstring
Name of kernel weights matrix for use in output
 name_dsstring
Name of dataset for use in output
 name_regimesstring
Name of regime variable for use in the output
 titlestring
Name of the regression method used. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 sig2nfloat
Sigma squared (computed with n in the denominator)
 sig2n_kfloat
Sigma squared (computed with nk in the denominator)
 xtxfloat
\(X'X\). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 xtxifloat
\((X'X)^{1}\). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)
 regimeslist
List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.
 constant_registring
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.
 cols2regilist
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.
 krint
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)
 kfint
Number of variables/columns to be considered fixed or global across regimes and hence only obtain one parameter estimate.
 nrint
Number of different regimes in the ‘regimes’ list.
 multidictionary
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.

__init__
(y, x, regimes, w=None, robust=None, gwk=None, 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)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
(y, x, regimes[, w, robust, gwk, …])Initialize self.
Attributes

property
mean_y
¶

property
sig2n
¶

property
sig2n_k
¶

property
std_y
¶

property
utu
¶

property
vm
¶