spreg.GMM_Error

class spreg.GMM_Error(y, x, w, yend=None, q=None, estimator='het', add_wy=False, slx_lags=0, slx_vars='All', vm=False, name_y=None, name_x=None, name_w=None, name_yend=None, name_q=None, name_ds=None, latex=False, hard_bound=False, spat_diag=False, **kwargs)[source]

Wrapper function to call any of the GMM methods for a spatial error model available in spreg

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

wpysal W object

Spatial weights object (always needed)

yendnumpy.ndarray or pandas object

Two dimensional array with n rows and one column for each endogenous variable (if any)

qnumpy.ndarray or pandas object

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

estimatorstr

Choice of estimator to be used. Options are: ‘het’, which is robust to heteroskedasticity, ‘hom’, which assumes homoskedasticity, and ‘kp98’, which does not provide inference on the spatial parameter for the error term.

add_wybool

If True, then a spatial lag of the dependent variable is included.

slx_lagsinteger

Number of spatial lags of X to include in the model specification. If slx_lags>0, the specification becomes of the SLX-Error or GNSM type.

slx_varseither “All” (default) or list of booleans to select x variables

to be lagged

vmbool

If True, include variance-covariance matrix in summary results

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_yendlist of strings

Names of endogenous variables for use in output

name_qlist of strings

Names of instruments for use in output

name_dsstr

Name of dataset for use in output

latexbool

Specifies if summary is to be printed in latex format

hard_boundbool

If true, raises an exception if the estimated spatial autoregressive parameter is outside the maximum/minimum bounds.

spat_diagbool, ignored, included for compatibility with other models
**kwargskeywords

Additional arguments to pass on to the estimators. See the specific functions for details on what can be used.

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

e_filteredarray

nx1 array of spatially filtered residuals

predyarray

nx1 array of predicted y values

ninteger

Number of observations

kinteger

Number of variables for which coefficients are estimated (including the constant)

yarray

nx1 array for dependent variable

xarray

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

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

pr2float

Pseudo R squared (squared correlation between y and ypred)

vmarray

Variance covariance matrix (kxk)

sig2float

Sigma squared used in computations

std_errarray

1xk array of standard errors of the betas

z_statlist of tuples

z statistic; each tuple contains the pair (statistic, p-value), where each is a float

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_dsstr

Name of dataset for use in output

titlestr

Name of the regression method used

name_yendlist of strings (optional)

Names of endogenous variables for use in output

name_zlist of strings (optional)

Names of exogenous and endogenous variables for use in output

name_qlist of strings (optional)

Names of external instruments

name_hlist of strings (optional)

Names of all instruments used in ouput

Examples

We first need to import the needed modules, namely numpy to convert the data we read into arrays that spreg understands and libpysal to handle the weights and file management.

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

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

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. 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 = libpysal.weights.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'

The GMM_Error class can run error models and SARAR models, that is a spatial lag+error model. In this example we will run a simple version of the latter, 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.

>>> from spreg import GMM_Error
>>> model = GMM_Error(y, x, w=w, add_wy=True, name_y=y_var, name_x=x_var, name_ds='NAT')

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.

>>> print(model.output)
  var_names coefficients   std_err    zt_stat      prob
0  CONSTANT     2.176007  1.115807   1.950165  0.051156
1      PS90     1.108054  0.207964   5.328096       0.0
2      UE90     0.664362  0.061294   10.83893       0.0
3    W_HR90    -0.066539  0.154395  -0.430964  0.666494
4    lambda     0.765087   0.04268  17.926245       0.0

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:

>>> model = GMM_Error(y, x, yend=yd, q=q, w=w, add_wy=True, name_y=y_var, name_x=x_var, name_yend=yd_var, name_q=q_var, name_ds='NAT')
>>> print(model.output)
  var_names coefficients   std_err    zt_stat      prob
0  CONSTANT      5.44035  0.560476   9.706652       0.0
1      PS90     1.427042    0.1821   7.836572       0.0
2      UE90    -0.075224  0.050031  -1.503544  0.132699
3      RD90     3.316266  0.261269  12.692924       0.0
4    W_HR90     0.200314  0.057433   3.487777  0.000487
5    lambda     0.136933  0.070098   1.953457  0.050765

The class also allows for estimating a GNS model by adding spatial lags of the exogenous variables, using the argument slx_lags:

>>> model = GMM_Error(y, x, w=w, add_wy=True, slx_lags=1, name_y=y_var, name_x=x_var, name_ds='NAT')
>>> print(model.output)
  var_names coefficients   std_err   zt_stat      prob
0  CONSTANT    -0.554756  0.551765  -1.00542  0.314695
1      PS90      1.09369  0.225895  4.841583  0.000001
2      UE90     0.697393  0.082744  8.428291       0.0
3    W_PS90    -1.533378  0.396651 -3.865811  0.000111
4    W_UE90    -1.107944   0.33523 -3.305028   0.00095
5    W_HR90     1.529277  0.389354  3.927728  0.000086
6    lambda    -0.917928  0.079569 -11.53625       0.0
__init__(y, x, w, yend=None, q=None, estimator='het', add_wy=False, slx_lags=0, slx_vars='All', vm=False, name_y=None, name_x=None, name_w=None, name_yend=None, name_q=None, name_ds=None, latex=False, hard_bound=False, spat_diag=False, **kwargs)[source]

Methods

__init__(y, x, w[, yend, q, estimator, ...])

Attributes

mean_y

std_y

property mean_y
property std_y