# 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 variance-covariance matrix is given. If ‘hac’, then a HAC consistent estimator of the variance-covariance 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 n-k to estimate sigma^2. If False, use n.

nonspat_diagboolean

If True, then compute non-spatial 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 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)

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), p-value (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, p-value), 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)

‘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_pagandictionary

‘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).

whitedictionary

‘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_errortuple

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_lagtuple

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_errortuple

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_lagtuple

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_sarmatuple

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_restuple

Moran’s I for the residuals; tuple containing the triple (Moran’s I, standardized Moran’s I, p-value)

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 n-k 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