spreg.GM_Combo_Het¶

class spreg.GM_Combo_Het(y, x, yend=None, q=None, w=None, w_lags=1, slx_lags=0, slx_vars='All', lag_q=True, max_iter=1, epsilon=1e-05, step1c=False, inv_method='power_exp', vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None, latex=False, hard_bound=False)[source]¶

GMM method for a spatial lag and error model with heteroskedasticity and endogenous variables, with results and diagnostics; based on [ADKP10], following [Ans11].

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
yendnumpy.ndarray or pandas object: Two dimensional array with n rows and one column for each endogenous variable
qnumpy.ndarray or pandas object: 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)
wpysal W object: Spatial weights object (always needed)
w_lagsinteger: 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.
slx_lagsinteger: Number of spatial lags of X to include in the model specification. If slx_lags>0, the specification becomes of the General Nesting Spatial Model (GNSM) type.
slx_varseither “All” (default) or list of booleans to select x variables: to be lagged
lag_qbool: If True, then include spatial lags of the additional instruments (q).
max_iterint: Maximum number of iterations of steps 2a and 2b from [ADKP10]. Note: epsilon provides an additional stop condition.
epsilonfloat: Minimum change in lambda required to stop iterations of steps 2a and 2b from [ADKP10]. Note: max_iter provides an additional stop condition.
step1cbool: If True, then include Step 1c from [ADKP10].
inv_methodstr: If “power_exp”, then compute inverse using the power expansion. If “true_inv”, then compute the true inverse. Note that true_inv will fail for large n.
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_yendlist of strings: Names of endogenous variables for use in output
name_qlist of strings: Names of instruments for use in output
name_wstr: Name of 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
hard_boundbool: If true, raises an exception if the estimated spatial autoregressive parameter is outside the maximum/minimum bounds.
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
e_predarray: nx1 array of residuals (using reduced form)
predyarray: nx1 array of predicted y values
predy_earray: nx1 array of predicted y values (using reduced form)
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
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 used as instruments
zarray: nxk array of variables (combination of x and yend)
harray: nxl array of instruments (combination of x and q)
iter_stopstr: Stop criterion reached during iteration of steps 2a and 2b from [ADKP10].
iterationinteger: Number of iterations of steps 2a and 2b from [ADKP10].
mean_yfloat: Mean of dependent variable
std_yfloat: Standard deviation of dependent variable
vmarray: Variance covariance matrix (kxk)
pr2float: Pseudo R squared (squared correlation between y and ypred)
pr2_efloat: Pseudo R squared (squared correlation between y and ypred_e (using reduced form))
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_yendlist of strings: Names of endogenous variables for use in output
name_zlist of strings: Names of exogenous and endogenous variables for use in output
name_qlist of strings: Names of external instruments
name_hlist of strings: Names of all instruments used in ouput
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
hthfloat: \(H'H\)

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 spreg import GM_Combo_Het

Open data on Columbus neighborhood crime (49 areas) using libpysal.io.open(). This is the DBF associated with the Columbus 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.

>>> db = libpysal.io.open(libpysal.examples.get_path('columbus.dbf'),'r')

Extract the HOVAL column (home values) 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 = np.array(db.by_col("HOVAL"))
>>> y = np.reshape(y, (49,1))

Extract INC (income) vector from the DBF to be used as independent variables in the regression. 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 class adds a vector of ones to the independent variables passed in.

>>> X = []
>>> X.append(db.by_col("INC"))
>>> X = np.array(X).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 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 columbus.shp.

>>> w = libpysal.weights.Rook.from_shapefile(libpysal.examples.get_path("columbus.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, his 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 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.

>>> reg = GM_Combo_Het(y, X, w=w, step1c=True, name_y='hoval', name_x=['income'], name_ds='columbus')

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 explicitly accounts for heteroskedasticity and 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:

>>> print(reg.name_z)
['CONSTANT', 'income', 'W_hoval', 'lambda']
>>> print(np.around(np.hstack((reg.betas,np.sqrt(reg.vm.diagonal()).reshape(4,1))),4))
[[ 9.9753 14.1435]
 [ 1.5742  0.374 ]
 [ 0.1535  0.3978]
 [ 0.2103  0.3924]]

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. As an example, we will include CRIME (crime rates) as endogenous and will instrument with DISCBD (distance to the CSB). We first need to read in the variables:

>>> yd = []
>>> yd.append(db.by_col("CRIME"))
>>> yd = np.array(yd).T
>>> q = []
>>> q.append(db.by_col("DISCBD"))
>>> q = np.array(q).T

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

>>> reg = GM_Combo_Het(y, X, yd, q, w=w, step1c=True, name_x=['inc'], name_y='hoval', name_yend=['crime'], name_q=['discbd'], name_ds='columbus')
>>> print(reg.name_z)
['CONSTANT', 'inc', 'crime', 'W_hoval', 'lambda']
>>> print(np.round(reg.betas,4))
[[113.9129]
 [ -0.3482]
 [ -1.3566]
 [ -0.5766]
 [  0.6561]]

__init__(y, x, yend=None, q=None, w=None, w_lags=1, slx_lags=0, slx_vars='All', lag_q=True, max_iter=1, epsilon=1e-05, step1c=False, inv_method='power_exp', vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None, latex=False, hard_bound=False)[source]¶

Methods

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

Attributes

`mean_y`
`std_y`

property mean_y¶

property std_y¶