spreg.OLS_Regimes¶

class spreg.OLS_Regimes(y, x, regimes, w=None, robust=None, gwk=None, slx_lags=0, 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)[source]¶

Ordinary least squares with results and diagnostics.

Parameters:

ynumpy.ndarray or pandas.Series

nx1 array for dependent variable

xnumpy.ndarray or pandas object

Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant

regimeslist or pandas.Series

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)

robuststr

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.

slx_lagsinteger

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

sig2n_kbool

If True, then use n-k to estimate sigma^2. If False, use n.

nonspat_diagbool

If True, then compute non-spatial diagnostics on the regression.

spat_diagbool

If True, then compute Lagrange multiplier tests (requires w). Note: see moran for further tests.

moranbool

If True, compute Moran’s I on the residuals. Note: requires spat_diag=True.

white_testbool

If True, compute White’s specification robust test. (requires nonspat_diag=True)

vmbool

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_sepbool

If True, a separate regression is run for each regime.

coresbool

Specifies if multiprocessing is to be used Default: no multiprocessing, cores = False Note: Multiprocessing may not work on all platforms.

name_ystr

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_wstr

Name of weights matrix for use in output

name_gwkstr

Name of kernel weights matrix for use in output

name_dsstr

Name of dataset for use in output

name_regimesstr

Name of regime variable for use in the output

latexbool

Specifies if summary is to be printed in latex format

Attributes:

outputdataframe

regression results pandas dataframe

summarystr

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)

robuststr

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)

jarque_beradictionary

‘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_ystr

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_wstr

Name of weights matrix for use in output

name_gwkstr

Name of kernel weights matrix for use in output

name_dsstr

Name of dataset for use in output

name_regimesstr

Name of regime variable for use in the output

titlestr

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_registr

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.

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
------------------

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

------------------------------------------------------------------------------------
            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

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

------------------------------------------------------------------------------------
            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
------------------------------------------------------------------------------------

GLOBAL DIAGNOSTICS

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 =====================================

__init__(y, x, regimes, w=None, robust=None, gwk=None, slx_lags=0, 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)[source]¶

Methods

__init__(y, x, regimes[, w, robust, gwk, ...])

Attributes

`mean_y`
`sig2n`
`sig2n_k`
`std_y`
`utu`
`vm`

property mean_y¶

property sig2n¶

property sig2n_k¶

property std_y¶

property utu¶

property vm¶