spreg.ML_LagRE

class spreg.ML_LagRE(y, x, w, slx_lags=0, slx_vars='all', time_effects=False, epsilon=1e-07, spat_impacts='simple', vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, latex=False)

ML estimation of the random effects spatial lag model with all results and diagnostics [Elh03].

Parameters:

ynumpy.ndarray or pandas object

nxt or (nxt)x1 array for dependent variable

xnumpy.ndarray or pandas object

nx(txk) or (nxt)xk array for independent (exogenous) variables, excluding the constant

wpysal W object

Spatial weights object

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.

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

to be lagged

time_effectsbool

If True, then include time dummies in the model specification (first omitted). Default: False

spat_impactsstr or list

Include average direct impact (ADI), average indirect impact (AII),

and average total impact (ATI) in summary results. Options are ‘simple’, ‘full’, ‘power’, ‘all’ or None. See sputils.spmultiplier for more information.

epsilonfloat

tolerance criterion in mimimize_scalar function and inverse_product

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_dsstr

Name of dataset for use in output

Attributes:

betasarray

(k+2)x1 array of estimated coefficients (rho and phi last)

rhofloat

estimate of spatial autoregressive coefficient

phifloat

estimate of weight attached to the cross-sectional component phi^2 = sig2 / (t*sig2_u + sig2)

uarray

(nxt)x1 array of residuals

predyarray

(nxt)x1 array of predicted y values

ninteger

Total number of observations

tinteger

Number of time periods

kinteger

Number of variables for which coefficients are estimated (excluding the phi)

yarray

(nxt)x1 array for dependent variable

xarray

Two dimensional array with nxt rows and one column for each independent (exogenous) variable

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

vmarray

Variance covariance matrix (k+2 x k+2)

vm1array

Variance covariance matrix (k+3 x k+3) includes sigma2

sig2float

Sigma squared used in computations

logllfloat

maximized log-likelihood (including constant terms)

predy_earray

predicted values from reduced form

e_predarray

prediction errors using reduced form predicted values

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))

utufloat

Sum of squared residuals

std_errarray

1x(k+1) 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

Examples

>>> import libpysal
>>> import geopandas as gpd
>>> from spreg import ML_LagRE

In this example, we will use data on NCOVR US County Homicides (3085 areas) included in libpysal.

>>> libpysal.examples.load_example('NCOVR')
>>> db = gpd.read_file(libpysal.examples.get_path("NAT.shp"))
>>> name_ds = "NCOVR.shp"

Extract the HR (homicide rates) data in the 70’s, 80’s and 90’s from the dataframe and make it the dependent variable for the regression. Note that the data can also be passed in the long format instead of wide format (i.e. a vector with n*t rows and a single column for the dependent variable and a matrix of dimension n*txk for the independent variables).

>>> y_name = ['HR70','HR80','HR90']
>>> y = db[y_name]

Extract RD and PS in the same time periods from the dataframe to be used as independent variables in the regression. IMPORTANT: The data must be organized in a way that all time periods of a given variable are side-by-side and in the correct time order. That is: x[:, 0:T] refers to T periods of k1, x[:, T+1:2T] refers to k2, etc. By default a vector of ones will be added to the independent variables passed in.

>>> x_names = ['RD70','RD80','RD90','PS70','PS80','PS90']
>>> x = db[x_names]

Since we are running a spatial 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.Queen.from_dataframe(db, use_index=True)
>>> w.transform = 'r'
>>> name_w = "NCOVR.gal"

We are all set with the preliminaries, we are good to run the model.

>>> reg = ML_LagRE(y, x, w)

Once we have run the model, we can explore a little bit the output with the command print(reg.summary).

__init__(y, x, w, slx_lags=0, slx_vars='all', time_effects=False, epsilon=1e-07, spat_impacts='simple', vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, latex=False)

Methods

__init__(y, x, w[, slx_lags, slx_vars, ...])
lag_c_loglik_sp(rho, n, t, e0, e1, I, Wsp)
phi_c_loglik(phi, rho, beta, bigy, bigx, n, ...)

Attributes

mean_y
sig2n
sig2n_k
std_y
utu
vm

lag_c_loglik_sp(rho, n, t, e0, e1, I, Wsp)

property mean_y

phi_c_loglik(phi, rho, beta, bigy, bigx, n, t, W_nt)

property sig2n

property sig2n_k

property std_y

property utu

property vm