spreg.ML_Lag

class spreg.ML_Lag(y, x, w, slx_lags=0, slx_vars='All', regimes=None, method='full', epsilon=1e-07, spat_impacts='simple', vm=False, spat_diag=True, name_y=None, name_x=None, name_w=None, name_ds=None, latex=False, **kwargs)

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

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

slx_lagsinteger

Number of spatial lags of X to include in the model specification. If slx_lags>0, the specification becomes of the Spatial Durbin type.

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

to be lagged

regimeslist or pandas.Series

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’. For other regimes-specific arguments, see ML_Lag_Regimes

methodstr

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

epsilonfloat

tolerance criterion in mimimize_scalar function and inverse_product

spat_diagbool

If True, then compute Common Factor Hypothesis test when applicable

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.

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

latexbool

Specifies if summary is to be printed in latex format

Attributes:

outputdataframe

regression results pandas dataframe

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

methodstr

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

cfh_testtuple

Common Factor Hypothesis test; tuple contains the pair (statistic, p-value). Only when it applies (see specific documentation).

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

sp_multipliers: dict

Dictionary of spatial multipliers (if spat_impacts is not None)

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 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)'

__init__(y, x, w, slx_lags=0, slx_vars='All', regimes=None, method='full', epsilon=1e-07, spat_impacts='simple', vm=False, spat_diag=True, name_y=None, name_x=None, name_w=None, name_ds=None, latex=False, **kwargs)

Methods

__init__(y, x, w[, slx_lags, slx_vars, ...])

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