spreg.TSLS_Regimes¶

class spreg.TSLS_Regimes(y, x, yend, q, regimes, w=None, robust=None, gwk=None, slx_lags=0, sig2n_k=True, spat_diag=False, vm=False, constant_regi='many', cols2regi='all', regime_err_sep=True, name_y=None, name_x=None, cores=False, name_yend=None, name_q=None, name_regimes=None, name_w=None, name_gwk=None, name_ds=None, summ=True, latex=False)[source]¶

Two stage least squares (2SLS) with regimes.

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

yendarray

Two dimensional array with n rows and one column for each endogenous variable

qarray

Two dimensional array with n rows and one column for each external exogenous variable to use as instruments (note: this should not contain any variables from x)

regimeslist

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.

constant_regi: string

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_sep: boolean

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

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. If ‘ogmm’, then Optimal GMM is used to estimate betas and the variance-covariance matrix. 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.

vmbool

If True, include variance-covariance matrix in summary

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_yendlist of strings

Names of endogenous variables for use in output

name_qlist of strings

Names of instruments for use in output

name_regimesstr

Name of regimes variable 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

latexbool

Specifies if summary is to be printed in latex format

Examples

We first need to import the needed modules, namely numpy to convert the data we read into arrays that spreg understands and pysal to perform all the analysis.

>>> import numpy as np
>>> import libpysal
>>> from libpysal.examples import load_example
>>> from libpysal.weights import Rook

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.

>>> nat = load_example('Natregimes')
>>> db = libpysal.io.open(nat.get_path('natregimes.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 = np.array([db.by_col(y_var)]).reshape(3085,1)

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

In this case we consider RD90 (resource deprivation) as an endogenous regressor. We tell the model that this is so by passing it in a different parameter from the exogenous variables (x).

>>> yd_var = ['RD90']
>>> yd = np.array([db.by_col(name) for name in yd_var]).T

Because we have endogenous variables, to obtain a correct estimate of the model, we need to instrument for RD90. We use FP89 (families below poverty) for this and hence put it in the instruments parameter, ‘q’.

>>> q_var = ['FP89']
>>> q = np.array([db.by_col(name) for name in q_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)

Since we want to perform tests for spatial dependence, we need to specify the spatial weights matrix that includes the spatial configuration of the observations into the error component of the model. To do that, we can open an already existing gal file or create a new one. In this case, we will create one from NAT.shp.

>>> w = Rook.from_shapefile(nat.get_path("natregimes.shp"))

Unless there is a good reason not to do it, the weights have to be row-standardized so every row of the matrix sums to one. Among other things, this allows to interpret the spatial lag of a variable as the average value of the neighboring observations. In PySAL, this can be easily performed in the following way:

>>> w.transform = 'r'

We can now run the regression and then have a summary of the output by typing: model.summary Alternatively, we can just check the betas and standard errors of the parameters:

>>> from spreg import TSLS_Regimes
>>> tslsr = TSLS_Regimes(y, x, yd, q, regimes, w=w, constant_regi='many', spat_diag=False, name_y=y_var, name_x=x_var, name_yend=yd_var, name_q=q_var, name_regimes=r_var, name_ds='NAT', name_w='NAT.shp')

>>> tslsr.betas
array([[ 3.66973562],
       [ 1.06950466],
       [ 0.14680946],
       [ 2.45864196],
       [ 9.55873243],
       [ 1.94666348],
       [-0.30810214],
       [ 3.68718119]])

>>> np.sqrt(tslsr.vm.diagonal())
array([0.38389901, 0.09963973, 0.04672091, 0.22725012, 0.49181223,
       0.19630774, 0.07784587, 0.25529011])

>>> print(tslsr.summary)
REGRESSION RESULTS
------------------

SUMMARY OF OUTPUT: TWO STAGE LEAST SQUARES ESTIMATION - REGIME 0
----------------------------------------------------------------
Data set            :         NAT
Weights matrix      :     NAT.shp
Dependent Variable  :      0_HR90                Number of Observations:        1673
Mean dependent var  :      3.3416                Number of Variables   :           4
S.D. dependent var  :      4.6795                Degrees of Freedom    :        1669
Pseudo R-squared    :      0.2092

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     z-Statistic     Probability
------------------------------------------------------------------------------------
          0_CONSTANT       3.6697356       0.3838990       9.5591172       0.0000000
              0_PS90       1.0695047       0.0996397      10.7337170       0.0000000
              0_UE90       0.1468095       0.0467209       3.1422643       0.0016765
              0_RD90       2.4586420       0.2272501      10.8191009       0.0000000
------------------------------------------------------------------------------------
Instrumented: 0_RD90
Instruments: 0_FP89
Regimes variable: SOUTH

SUMMARY OF OUTPUT: TWO STAGE LEAST SQUARES ESTIMATION - REGIME 1
----------------------------------------------------------------
Data set            :         NAT
Weights matrix      :     NAT.shp
Dependent Variable  :      1_HR90                Number of Observations:        1412
Mean dependent var  :      9.5493                Number of Variables   :           4
S.D. dependent var  :      7.0389                Degrees of Freedom    :        1408
Pseudo R-squared    :      0.2987

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     z-Statistic     Probability
------------------------------------------------------------------------------------
          1_CONSTANT       9.5587324       0.4918122      19.4357356       0.0000000
              1_PS90       1.9466635       0.1963077       9.9163867       0.0000000
              1_UE90      -0.3081021       0.0778459      -3.9578483       0.0000756
              1_RD90       3.6871812       0.2552901      14.4431026       0.0000000
------------------------------------------------------------------------------------
Instrumented: 1_RD90
Instruments: 1_FP89
Regimes variable: SOUTH
------------------------------------------------------------------------------------
GLOBAL DIAGNOSTICS

REGIMES DIAGNOSTICS - CHOW TEST
                 VARIABLE        DF        VALUE           PROB
                 CONSTANT         1          89.093           0.0000
                     PS90         1          15.876           0.0001
                     UE90         1          25.106           0.0000
                     RD90         1          12.920           0.0003
              Global test         4         201.237           0.0000
================================ END OF REPORT =====================================

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

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)

yendarray

Two dimensional array with n rows and one column for each endogenous variable Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

qarray

Two dimensional array with n rows and one column for each external exogenous variable used as instruments Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

vmarray

Variance covariance matrix (kxk)

regimeslist

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.

constant_regi: [False, ‘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 (default).

cols2regilist, ‘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.

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