Several changes

This commit incorporates several developments into spreg.

Main changes:
- Refactoring of the output. The way the results from the models are printed to the users has been completely refactored. The new function is simpler and generic. It is based on pandas to create an 'output' attribute to the regression object that contains the most important information on the estimates from the model.
- Addition of slx_lags to all cross-section models. An attribute slx_lags was added to all cross-section models to allow for the direct estimation of SLX models.
- Creation of wrapper functions for the error models. Both error_sp and error_sp_regimes now have wrapper functions that allow for easy estimation of error models based on the kp98, hom or het estimators. The wrapper functions also allow specifications with extra endogenous variables or spatial lag of the dependent variable.
- Several minor updates of fixes were also developed in this commit.

Despite the major changes, this commit does not break any previous code. This update was developed in a private branch by Luc Anselin and Pedro Amaral.

spreg/diagnostics_sp.py

@@ -18,7 +18,6 @@
 
 
 class LMtests:
-
     """
     Lagrange Multiplier tests. Implemented as presented in :cite:`Anselin1996a`
 
@@ -142,7 +141,6 @@ def __init__(self, ols, w, tests=["all"]):
 
 
 class MoranRes:
-
     """
     Moran's I for spatial autocorrelation in residuals from OLS regression
 
@@ -396,7 +394,6 @@ def __init__(self, iv, w, case="nosp"):
 
 
 class spDcache:
-
     """
     Helper class to compute reusable pieces in the spatial diagnostics module
     ...
@@ -669,7 +666,7 @@ def get_vI(ols, w, ei, spDcache):
     B = spDcache.AB[1]
     trB = np.sum(B.diagonal()) * 4.0
     vi = (w.n ** 2 / (w.s0 ** 2 * (w.n - ols.k) * (w.n - ols.k + 2.0))) * (
-        w.s1 + 2.0 * trA2 - trB - ((2.0 * (spDcache.trA ** 2)) / (w.n - ols.k))
+            w.s1 + 2.0 * trA2 - trB - ((2.0 * (spDcache.trA ** 2)) / (w.n - ols.k))
     )
     return vi
 
@@ -716,9 +713,6 @@ def akTest(iv, w, spDcache):
     p           : float
                   P-value of the test
 
-    ToDo:
-        * Code in as Nancy
-        * Compare both
     """
     mi = get_mI(iv, w, spDcache)
     # Phi2
@@ -731,6 +725,42 @@ def akTest(iv, w, spDcache):
     return (mi, ak[0][0], pval[0][0])
 
 
+def comfac_test(lambd, beta, gamma, vm):
+    """
+    Computes the Spatial Common Factor Hypothesis test as shown in Anselin (1988, p. 226-229)
+
+    Parameters
+    ----------
+
+    lambd       : float
+                  Spatial autoregressive coefficient (as in lambd*Wy)
+    beta        : array
+                  Coefficients of the exogenous (not spatially lagged) variables, without the constant (as in X*beta)
+    gamma       : array
+                  coefficients of the spatially lagged exogenous variables (as in WX*gamma)
+    vm          : array
+                  Variance-covariance matrix of the coefficients
+                  Obs. Needs to match the order of theta' = [beta', gamma', lambda]
+
+    Returns
+    -------
+    W       : float
+              Wald statistic
+    pvalue  : float
+              P value for Wald statistic calculated as a Chi sq. distribution
+              with k-1 degrees of freedom
+
+    """
+    g = lambd * beta + gamma
+    G = np.vstack((lambd * np.eye(beta.shape[0]), np.eye(beta.shape[0]), beta.T))
+
+    GVGi = la.inv(np.dot(G.T, np.dot(vm, G)))
+    W = np.dot(g.T, np.dot(GVGi, g))[0][0]
+    df = G.shape[1]
+    pvalue = chisqprob(W, df)
+    return W, pvalue
+
+
 def _test():
     import doctest