pysal.model.spreg.GM_Combo_Hom_Regimes

class pysal.model.spreg.GM_Combo_Hom_Regimes(y, x, regimes, yend=None, q=None, w=None, w_lags=1, lag_q=True, cores=False, max_iter=1, epsilon=1e-05, A1='het', constant_regi='many', cols2regi='all', regime_err_sep=False, regime_lag_sep=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None, name_regimes=None)[source]

GMM method for a spatial lag and error model with homoskedasticity, regimes and endogenous variables, with results and diagnostics; based on Drukker et al. (2013) [Drukker2013], following Anselin (2011) [Anselin2011].

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

yend : array

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

q : array

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)

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 (always needed)

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.

regime_lag_sep : boolean

If True, the spatial parameter for spatial lag is also computed according to different regimes. If False (default), the spatial parameter is fixed accross regimes.

w_lags : integer

Orders of W to include as instruments for the spatially lagged dependent variable. For example, w_lags=1, then instruments are WX; if w_lags=2, then WX, WWX; and so on.

lag_q : boolean

If True, then include spatial lags of the additional instruments (q).

max_iter : int

Maximum number of iterations of steps 2a and 2b from Arraiz et al. Note: epsilon provides an additional stop condition.

epsilon : float

Minimum change in lambda required to stop iterations of steps 2a and 2b from Arraiz et al. Note: max_iter provides an additional stop condition.

A1 : string

If A1=’het’, then the matrix A1 is defined as in Arraiz et al. If A1=’hom’, then as in Anselin (2011). If A1=’hom_sc’, then as in Drukker, Egger and Prucha (2010) and Drukker, Prucha and Raciborski (2010).

vm : boolean

If True, include variance-covariance matrix in summary results

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_yend : list of strings

Names of endogenous variables for use in output

name_q : list of strings

Names of instruments for use in output

name_w : string

Name of 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

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 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 = 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

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 run a spatial combo model, we need to specify the spatial weights matrix that includes the spatial configuration of the observations. 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 = pysal.lib.weights.Rook.from_shapefile(pysal.lib.examples.get_path("NAT.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 are all set with the preliminaries, we are good to run the model. In this case, we will need the variables and the weights matrix. If we want to have the names of the variables printed in the output summary, we will have to pass them in as well, although this is optional.

Example only with spatial lag

The Combo class runs an SARAR model, that is a spatial lag+error model. In this case we will run a simple version of that, where we have the spatial effects as well as exogenous variables. Since it is a spatial model, we have to pass in the weights matrix. If we want to have the names of the variables printed in the output summary, we will have to pass them in as well, although this is optional. We can have a summary of the output by typing: model.summary Alternatively, we can check the betas:

>>> reg = GM_Combo_Hom_Regimes(y, x, regimes, w=w, A1='hom_sc', name_y=y_var, name_x=x_var, name_regimes=r_var, name_ds='NAT')
>>> print reg.name_z
['0_CONSTANT', '0_PS90', '0_UE90', '1_CONSTANT', '1_PS90', '1_UE90', '_Global_W_HR90', 'lambda']
>>> print np.around(reg.betas,4)
[[ 1.4607]
 [ 0.9579]
 [ 0.5658]
 [ 9.1129]
 [ 1.1339]
 [ 0.6517]
 [-0.4583]
 [ 0.6634]]

This class also allows the user to run a spatial lag+error model with the extra feature of including non-spatial endogenous regressors. This means that, in addition to the spatial lag and error, we consider some of the variables on the right-hand side of the equation as endogenous and we instrument for this. In this case we consider RD90 (resource deprivation) as an endogenous regressor. We use FP89 (families below poverty) for this and hence put it in the instruments parameter, ‘q’.

>>> yd_var = ['RD90']
>>> yd = np.array([db.by_col(name) for name in yd_var]).T
>>> q_var = ['FP89']
>>> q = np.array([db.by_col(name) for name in q_var]).T

And then we can run and explore the model analogously to the previous combo:

>>> reg = GM_Combo_Hom_Regimes(y, x, regimes, yd, q, w=w, A1='hom_sc', name_y=y_var, name_x=x_var, name_yend=yd_var, name_q=q_var, name_regimes=r_var, name_ds='NAT')
>>> print reg.name_z
['0_CONSTANT', '0_PS90', '0_UE90', '1_CONSTANT', '1_PS90', '1_UE90', '0_RD90', '1_RD90', '_Global_W_HR90', 'lambda']
>>> print reg.betas
[[ 3.4196478 ]
 [ 1.04065595]
 [ 0.16630304]
 [ 8.86570777]
 [ 1.85134286]
 [-0.24921597]
 [ 2.43007651]
 [ 3.61656899]
 [ 0.03315061]
 [ 0.22636055]]
>>> print np.sqrt(reg.vm.diagonal())
[ 0.53989913  0.13506086  0.06143434  0.77049956  0.18089997  0.07246848
  0.29218837  0.25378655  0.06184801  0.06323236]
>>> print 'lambda: ', np.around(reg.betas[-1], 4)
lambda:  [ 0.2264]
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

e_filtered : array

nx1 array of spatially filtered residuals

e_pred : array

nx1 array of residuals (using reduced form)

predy : array

nx1 array of predicted y values

predy_e : array

nx1 array of predicted y values (using reduced form)

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)

yend : array

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)

q : array

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)

z : array

nxk array of variables (combination of x and yend) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

h : array

nxl array of instruments (combination of x and q) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

iter_stop : string

Stop criterion reached during iteration of steps 2a and 2b from Arraiz et al. Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

iteration : integer

Number of iterations of steps 2a and 2b from Arraiz et al. 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)

pr2 : float

Pseudo R squared (squared correlation between y and ypred) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

pr2_e : float

Pseudo R squared (squared correlation between y and ypred_e (using reduced form)) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

sig2 : float

Sigma squared used in computations (based on filtered residuals) 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)

z_stat : list of tuples

z 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)

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_yend : list of strings

Names of endogenous variables for use in output

name_z : list of strings

Names of exogenous and endogenous variables for use in output

name_q : list of strings

Names of external instruments

name_h : list of strings

Names of all instruments used in ouput

name_w : string

Name of weights matrix for use in output

name_ds : string

Name of dataset for use in output

name_regimes : string

Name of regimes variable for use in output

title : string

Name of the regression method used

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.

regime_lag_sep : boolean

If True, the spatial parameter for spatial lag is also computed according to different regimes. If False (default), the spatial parameter is fixed accross regimes.

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, yend=None, q=None, w=None, w_lags=1, lag_q=True, cores=False, max_iter=1, epsilon=1e-05, A1='het', constant_regi='many', cols2regi='all', regime_err_sep=False, regime_lag_sep=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None, name_regimes=None)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(y, x, regimes[, yend, q, w, …]) Initialize self.

Attributes

mean_y
std_y