pysal.model.spreg.GM_Endog_Error_Hom_Regimes¶

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

GMM method for a spatial error model with homoskedasticity, regimes and endogenous variables. 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 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 Always False, kept for consistency, ignored. 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). 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


For the endogenous models, we add the endogenous variable RD90 (resource deprivation) and we decide to instrument for it with FP89 (families below poverty):

>>> yd_var = ['RD90']
>>> yend = 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


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 error model, 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 = 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 (exogenous and endogenous), the instruments 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.

>>> reg = GM_Endog_Error_Hom_Regimes(y, x, yend, q, regimes, 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.dbf')


Once we have run the model, we can explore a little bit the output. The regression object we have created has many attributes so take your time to discover them. This class offers an error model that assumes homoskedasticity but that unlike the models from spreg.error_sp, it allows for inference on the spatial parameter. Hence, we find the same number of betas as of standard errors, which we calculate taking the square root of the diagonal of the variance-covariance matrix. Alternatively, we can have a summary of the output by typing: model.summary

>>> print reg.name_z
['0_CONSTANT', '0_PS90', '0_UE90', '1_CONSTANT', '1_PS90', '1_UE90', '0_RD90', '1_RD90', 'lambda']

>>> print np.around(reg.betas,4)
[[ 3.5973]
[ 1.0652]
[ 0.1582]
[ 9.198 ]
[ 1.8809]
[-0.2489]
[ 2.4616]
[ 3.5796]
[ 0.2541]]

>>> print np.around(np.sqrt(reg.vm.diagonal()),4)
[ 0.5204  0.1371  0.0629  0.4721  0.1824  0.0725  0.2992  0.2395  0.024 ]

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 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) 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) sig2 : float Sigma squared used in computations 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) hth : float H’H 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. 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, yend, q, regimes, w, constant_regi='many', cols2regi='all', regime_err_sep=False, regime_lag_sep=False, max_iter=1, epsilon=1e-05, A1='het', cores=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None, name_regimes=None, summ=True, add_lag=False)[source]

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

Methods

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

Attributes

 mean_y std_y