pysal.model.spreg.OLS_Regimes¶

class pysal.model.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:

Parameters:	y : array nx1 array for dependent variable x : array Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant regimes : list 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. 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: [‘one’, ‘many’] 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

y : array

nx1 array for dependent variable

x : array

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

regimes : list

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.

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: [‘one’, ‘many’]

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

Examples

>>> import numpy as np
>>> import pysal.lib

Open data on NCOVR US County Homicides (3085 areas) using pysal.lib.io.open(). This is the DBF associated with the NAT shapefile. Note that pysal.lib.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 = pysal.lib.io.open(pysal.lib.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:

Attributes:	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 X’X Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) xtxi : float (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: [‘one’, ‘many’] 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, ‘all’ 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

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

X’X Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

xtxi : float

(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: [‘one’, ‘many’]

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, ‘all’

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

__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

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