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
-
property
mean_y
¶
-
property
sig2n
¶
-
property
sig2n_k
¶
-
property
std_y
¶
-
property
utu
¶
-
property
vm
¶