# pysal.model.spreg.ML_Lag_Regimes¶

class pysal.model.spreg.ML_Lag_Regimes(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_lag_sep=False, regime_err_sep=False, cores=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None)[source]

ML estimation of the spatial lag model with regimes (note no consistency checks, diagnostics or constants added); Anselin (1988) [Anselin1988]

Parameters: y : array nx1 array for dependent variable x : array Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant regimes : list List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’. constant_regi: [‘one’, ‘many’] Switcher controlling the constant term setup. It may take the following values: ‘one’: a vector of ones is appended to x and held constant across regimes ‘many’: a vector of ones is appended to x and considered different per regime (default) cols2regi : list, ‘all’ Argument indicating whether each column of x should be considered as different per regime or held constant across regimes (False). If a list, k booleans indicating for each variable the option (True if one per regime, False to be held constant). If ‘all’ (default), all the variables vary by regime. w : Sparse matrix Spatial weights sparse matrix method : string if ‘full’, brute force calculation (full matrix expressions) if ‘ord’, Ord eigenvalue method if ‘LU’, LU sparse matrix decomposition epsilon : float tolerance criterion in mimimize_scalar function and inverse_product regime_lag_sep: boolean If True, the spatial parameter for spatial lag is also computed according to different regimes. If False (default), the spatial parameter is fixed accross regimes. cores : boolean Specifies if multiprocessing is to be used Default: no multiprocessing, cores = False Note: Multiprocessing may not work on all platforms. spat_diag : boolean if True, include spatial diagnostics (not implemented yet) vm : boolean if True, include variance-covariance matrix in summary results name_y : string Name of dependent variable for use in output name_x : list of strings Names of independent variables for use in output name_w : string Name of weights matrix for use in output name_ds : string Name of dataset for use in output name_regimes : string Name of regimes variable for use in output summary : string Summary of regression results and diagnostics (note: use in conjunction with the print command) betas : array (k+1)x1 array of estimated coefficients (rho first) rho : float estimate of spatial autoregressive coefficient Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) u : array nx1 array of residuals predy : array nx1 array of predicted y values n : integer Number of observations k : integer Number of variables for which coefficients are estimated (including the constant, excluding the rho) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) y : array nx1 array for dependent variable x : array Two dimensional array with n rows and one column for each independent (exogenous) variable, including the constant Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) method : string log Jacobian method if ‘full’: brute force (full matrix computations) if ‘ord’, Ord eigenvalue method if ‘LU’, LU sparse matrix decomposition epsilon : float tolerance criterion used in minimize_scalar function and inverse_product mean_y : float Mean of dependent variable std_y : float Standard deviation of dependent variable vm : array Variance covariance matrix (k+1 x k+1), all coefficients vm1 : array Variance covariance matrix (k+2 x k+2), includes sig2 Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) sig2 : float Sigma squared used in computations Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) logll : float maximized log-likelihood (including constant terms) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) aic : float Akaike information criterion Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) schwarz : float Schwarz criterion Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) predy_e : array predicted values from reduced form e_pred : array prediction errors using reduced form predicted values pr2 : float Pseudo R squared (squared correlation between y and ypred) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) pr2_e : float Pseudo R squared (squared correlation between y and ypred_e (using reduced form)) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) std_err : array 1xk array of standard errors of the betas Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) z_stat : list of tuples z statistic; each tuple contains the pair (statistic, p-value), where each is a float Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) name_y : string Name of dependent variable for use in output name_x : list of strings Names of independent variables for use in output name_w : string Name of weights matrix for use in output name_ds : string Name of dataset for use in output name_regimes : string Name of regimes variable for use in output title : string Name of the regression method used Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details) regimes : list List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’. constant_regi: [‘one’, ‘many’] Ignored if regimes=False. Constant option for regimes. Switcher controlling the constant term setup. It may take the following values: ‘one’: a vector of ones is appended to x and held constant across regimes ‘many’: a vector of ones is appended to x and considered different per regime cols2regi : list, ‘all’ Ignored if regimes=False. Argument indicating whether each column of x should be considered as different per regime or held constant across regimes (False). If a list, k booleans indicating for each variable the option (True if one per regime, False to be held constant). If ‘all’, all the variables vary by regime. regime_lag_sep : boolean If True, the spatial parameter for spatial lag is also computed according to different regimes. If False (default), the spatial parameter is fixed accross regimes. regime_err_sep : boolean always set to False - kept for compatibility with other regime models kr : int Number of variables/columns to be “regimized” or subject to change by regime. These will result in one parameter estimate by regime for each variable (i.e. nr parameters per variable) kf : int Number of variables/columns to be considered fixed or global across regimes and hence only obtain one parameter estimate nr : int Number of different regimes in the ‘regimes’ list multi : dictionary Only available when multiple regressions are estimated, i.e. when regime_err_sep=True and no variable is fixed across regimes. Contains all attributes of each individual regression Examples ________ Open data baltim.dbf using pysal and create the variables matrices and weights matrix. >>> import numpy as np >>> import pysal.lib >>> from pysal.lib import examples >>> db = pysal.lib.io.open(examples.get_path(“baltim.dbf”),’r’) >>> ds_name = “baltim.dbf” >>> y_name = “PRICE” >>> y = np.array(db.by_col(y_name)).T >>> y.shape = (len(y),1) >>> x_names = [“NROOM”,”AGE”,”SQFT”] >>> x = np.array([db.by_col(var) for var in x_names]).T >>> ww = ps.open(ps.examples.get_path(“baltim_q.gal”)) >>> w = ww.read() >>> ww.close() >>> w_name = “baltim_q.gal” >>> w.transform = ‘r’ Since in this example we are interested in checking whether the results vary by regimes, we use CITCOU to define whether the location is in the city or outside the city (in the county): >>> regimes = db.by_col(“CITCOU”) Now we can run the regression with all parameters: >>> mllag = ML_Lag_Regimes(y,x,regimes,w=w,name_y=y_name,name_x=x_names, name_w=w_name,name_ds=ds_name,name_regimes=”CITCOU”) >>> np.around(mllag.betas, decimals=4) array([[-15.0059], [ 4.496 ], [ -0.0318], [ 0.35 ], [ -4.5404], [ 3.9219], [ -0.1702], [ 0.8194], [ 0.5385]]) >>> “{0:.6f}”.format(mllag.rho) ‘0.538503’ >>> “{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([ 47.42 , 2.3953, 0.0051, 0.0648, 69.6765, 3.2066, 0.0116, 0.0486, 0.004 , 390.7274]) >>> np.around(np.diag(mllag.vm), decimals=4) array([ 47.42 , 2.3953, 0.0051, 0.0648, 69.6765, 3.2066, 0.0116, 0.0486, 0.004 ]) >>> “{0:.6f}”.format(mllag.sig2) ‘200.044334’ >>> “{0:.6f}”.format(mllag.logll) ‘-864.985056’ >>> “{0:.6f}”.format(mllag.aic) ‘1747.970112’ >>> “{0:.6f}”.format(mllag.schwarz) ‘1778.136835’ >>> mllag.title ‘MAXIMUM LIKELIHOOD SPATIAL LAG - REGIMES (METHOD = full)’

Methods

 ML_Lag_Regimes_Multi
__init__(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_lag_sep=False, regime_err_sep=False, cores=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None)[source]

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

Methods

 ML_Lag_Regimes_Multi(y, x, w_i, w, regi_ids, …) __init__(y, x, regimes[, w, constant_regi, …]) Initialize self.

Attributes

 mean_y sig2n sig2n_k std_y utu vm