spreg.ML_Lag¶

class spreg.ML_Lag(y, x, w, slx_lags=0, slx_vars='All', 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)[source]¶

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

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', 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)[source]¶

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¶