spreg.ML_Lag

class spreg.ML_Lag(y, x, w, method='full', epsilon=1e-07, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None)[source]

ML estimation of the spatial lag model with all results and diagnostics; [Ans88]

Parameters
yarray

nx1 array for dependent variable

xarray

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

wpysal W object

Spatial weights object

methodstring

if ‘full’, brute force calculation (full matrix expressions) if ‘ord’, Ord eigenvalue method

epsilonfloat

tolerance criterion in mimimize_scalar function and inverse_product

vmboolean

if True, include variance-covariance matrix in summary results

name_ystring

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_wstring

Name of weights matrix for use in output

name_dsstring

Name of dataset for use in output

Examples

>>> import numpy as np
>>> import libpysal
>>> from libpysal.examples import load_example
>>> from libpysal.weights import Queen
>>> from spreg import ML_Error_Regimes
>>> import geopandas as gpd
>>> from spreg import ML_Lag
>>> np.set_printoptions(suppress=True) #prevent scientific format
>>> baltimore = load_example('Baltimore')
>>> db = libpysal.io.open(baltimore.get_path("baltim.dbf"),'r')
>>> df = gpd.read_file(baltimore.get_path("baltim.shp"))
>>> ds_name = "baltim.dbf"
>>> y_name = "PRICE"
>>> y = np.array(db.by_col(y_name)).T
>>> y.shape = (len(y),1)
>>> x_names = ["NROOM","NBATH","PATIO","FIREPL","AC","GAR","AGE","LOTSZ","SQFT"]
>>> x = np.array([db.by_col(var) for var in x_names]).T
>>> w = Queen.from_dataframe(df)
>>> w_name = "baltim_q.gal"
>>> w.transform = 'r'
>>> mllag = ML_Lag(y,x,w,name_y=y_name,name_x=x_names,               name_w=w_name,name_ds=ds_name) 
>>> np.around(mllag.betas, decimals=4) 
array([[ 4.3675],
       [ 0.7502],
       [ 5.6116],
       [ 7.0497],
       [ 7.7246],
       [ 6.1231],
       [ 4.6375],
       [-0.1107],
       [ 0.0679],
       [ 0.0794],
       [ 0.4259]])
>>> "{0:.6f}".format(mllag.rho) 
'0.425885'
>>> "{0:.6f}".format(mllag.mean_y) 
'44.307180'
>>> "{0:.6f}".format(mllag.std_y) 
'23.606077'
>>> np.around(np.diag(mllag.vm1), decimals=4) 
array([  23.8716,    1.1222,    3.0593,    7.3416,    5.6695,    5.4698,
          2.8684,    0.0026,    0.0002,    0.0266,    0.0032,  220.1292])
>>> np.around(np.diag(mllag.vm), decimals=4) 
array([ 23.8716,   1.1222,   3.0593,   7.3416,   5.6695,   5.4698,
         2.8684,   0.0026,   0.0002,   0.0266,   0.0032])
>>> "{0:.6f}".format(mllag.sig2) 
'151.458698'
>>> "{0:.6f}".format(mllag.logll) 
'-832.937174'
>>> "{0:.6f}".format(mllag.aic) 
'1687.874348'
>>> "{0:.6f}".format(mllag.schwarz) 
'1724.744787'
>>> "{0:.6f}".format(mllag.pr2) 
'0.727081'
>>> "{0:.4f}".format(mllag.pr2_e) 
'0.7062'
>>> "{0:.4f}".format(mllag.utu) 
'31957.7853'
>>> np.around(mllag.std_err, decimals=4) 
array([ 4.8859,  1.0593,  1.7491,  2.7095,  2.3811,  2.3388,  1.6936,
        0.0508,  0.0146,  0.1631,  0.057 ])
>>> np.around(mllag.z_stat, decimals=4) 
array([[ 0.8939,  0.3714],
       [ 0.7082,  0.4788],
       [ 3.2083,  0.0013],
       [ 2.6018,  0.0093],
       [ 3.2442,  0.0012],
       [ 2.6181,  0.0088],
       [ 2.7382,  0.0062],
       [-2.178 ,  0.0294],
       [ 4.6487,  0.    ],
       [ 0.4866,  0.6266],
       [ 7.4775,  0.    ]])
>>> mllag.name_y 
'PRICE'
>>> mllag.name_x 
['CONSTANT', 'NROOM', 'NBATH', 'PATIO', 'FIREPL', 'AC', 'GAR', 'AGE', 'LOTSZ', 'SQFT', 'W_PRICE']
>>> mllag.name_w 
'baltim_q.gal'
>>> mllag.name_ds 
'baltim.dbf'
>>> mllag.title 
'MAXIMUM LIKELIHOOD SPATIAL LAG (METHOD = FULL)'
>>> mllag = ML_Lag(y,x,w,method='ord',name_y=y_name,name_x=x_names,               name_w=w_name,name_ds=ds_name) 
>>> np.around(mllag.betas, decimals=4) 
array([[ 4.3675],
       [ 0.7502],
       [ 5.6116],
       [ 7.0497],
       [ 7.7246],
       [ 6.1231],
       [ 4.6375],
       [-0.1107],
       [ 0.0679],
       [ 0.0794],
       [ 0.4259]])
>>> "{0:.6f}".format(mllag.rho) 
'0.425885'
>>> "{0:.6f}".format(mllag.mean_y) 
'44.307180'
>>> "{0:.6f}".format(mllag.std_y) 
'23.606077'
>>> np.around(np.diag(mllag.vm1), decimals=4) 
array([  23.8716,    1.1222,    3.0593,    7.3416,    5.6695,    5.4698,
          2.8684,    0.0026,    0.0002,    0.0266,    0.0032,  220.1292])
>>> np.around(np.diag(mllag.vm), decimals=4) 
array([ 23.8716,   1.1222,   3.0593,   7.3416,   5.6695,   5.4698,
         2.8684,   0.0026,   0.0002,   0.0266,   0.0032])
>>> "{0:.6f}".format(mllag.sig2) 
'151.458698'
>>> "{0:.6f}".format(mllag.logll) 
'-832.937174'
>>> "{0:.6f}".format(mllag.aic) 
'1687.874348'
>>> "{0:.6f}".format(mllag.schwarz) 
'1724.744787'
>>> "{0:.6f}".format(mllag.pr2) 
'0.727081'
>>> "{0:.6f}".format(mllag.pr2_e) 
'0.706198'
>>> "{0:.4f}".format(mllag.utu) 
'31957.7853'
>>> np.around(mllag.std_err, decimals=4) 
array([ 4.8859,  1.0593,  1.7491,  2.7095,  2.3811,  2.3388,  1.6936,
        0.0508,  0.0146,  0.1631,  0.057 ])
>>> np.around(mllag.z_stat, decimals=4) 
array([[ 0.8939,  0.3714],
       [ 0.7082,  0.4788],
       [ 3.2083,  0.0013],
       [ 2.6018,  0.0093],
       [ 3.2442,  0.0012],
       [ 2.6181,  0.0088],
       [ 2.7382,  0.0062],
       [-2.178 ,  0.0294],
       [ 4.6487,  0.    ],
       [ 0.4866,  0.6266],
       [ 7.4775,  0.    ]])
>>> mllag.name_y 
'PRICE'
>>> mllag.name_x 
['CONSTANT', 'NROOM', 'NBATH', 'PATIO', 'FIREPL', 'AC', 'GAR', 'AGE', 'LOTSZ', 'SQFT', 'W_PRICE']
>>> mllag.name_w 
'baltim_q.gal'
>>> mllag.name_ds 
'baltim.dbf'
>>> mllag.title 
'MAXIMUM LIKELIHOOD SPATIAL LAG (METHOD = ORD)'
Attributes
betasarray

(k+1)x1 array of estimated coefficients (rho first)

rhofloat

estimate of spatial autoregressive coefficient

uarray

nx1 array of residuals

predyarray

nx1 array of predicted y values

ninteger

Number of observations

kinteger

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

yarray

nx1 array for dependent variable

xarray

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

methodstring

log Jacobian method if ‘full’: brute force (full matrix computations)

epsilonfloat

tolerance criterion used in minimize_scalar function and inverse_product

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

vmarray

Variance covariance matrix (k+1 x k+1), all coefficients

vm1array

Variance covariance matrix (k+2 x k+2), includes sig2

sig2float

Sigma squared used in computations

logllfloat

maximized log-likelihood (including constant terms)

aicfloat

Akaike information criterion

schwarzfloat

Schwarz criterion

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

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_ystring

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_wstring

Name of weights matrix for use in output

name_dsstring

Name of dataset for use in output

titlestring

Name of the regression method used

__init__(y, x, w, method='full', epsilon=1e-07, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None)[source]

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

Methods

__init__(y, x, w[, method, epsilon, vm, …])

Initialize self.

Attributes

mean_y

sig2n

sig2n_k

std_y

utu

vm

property mean_y
property sig2n
property sig2n_k
property std_y
property utu
property vm