def sur_joinrho(n_eq, bigK, bSUR, varb):
"""Test on joint significance of spatial autoregressive coefficient in SUR
Parameters
----------
n_eq : integer, number of equations
bigK : n_eq x 1 array with number of variables by equation
(includes constant term, exogenous and endogeneous and
spatial lag)
bSUR : dictionary with regression coefficients by equation, with
the spatial autoregressive term as last
varb : variance-covariance matrix for regression coefficients
Returns
-------
: tuple with test statistic, degrees of freedom, p-value
"""
bb = sur_dict2mat(bSUR)
R = np.zeros((n_eq, varb.shape[0]))
q = np.zeros((n_eq, 1))
kc = -1
for i in range(n_eq):
kc = kc + bigK[i]
R[i, kc] = 1
w, p = wald_test(bb, R, q, varb)
return (w, n_eq, p)
def sur_chow(n_eq, bigK, bSUR, varb):
"""test on constancy of regression coefficients across equations in
a SUR specification
Note: requires a previous check on constancy of number of coefficients
across equations; no other checks are carried out, so it is possible
that the results are meaningless if the variables are not listed in
the same order in each equation.
Parameters
----------
n_eq : integer, number of equations
bigK : array with the number of variables by equation (includes constant)
bSUR : dictionary with the SUR regression coefficients by equation
varb : array with the variance-covariance matrix for the SUR regression
coefficients
Returns
-------
test : a list with for each coefficient (in order) a tuple with the
value of the test statistic, the degrees of freedom, and the
p-value
"""
kr = bigK[0][0]
test = []
bb = sur_dict2mat(bSUR)
kf = 0
nr = n_eq
df = n_eq - 1
for i in range(kr):
Ri = buildR1var(i, kr, kf, 0, nr)
tt, p = wald_test(bb, Ri, np.zeros((df, 1)), varb)
test.append((tt, df, p))
return test
def sur_chow(n_eq,bigK,bSUR,varb):
"""test on constancy of regression coefficients across equations in
a SUR specification
Note: requires a previous check on constancy of number of coefficients
across equations; no other checks are carried out, so it is possible
that the results are meaningless if the variables are not listed in
the same order in each equation.
Parameters
----------
n_eq : integer, number of equations
bigK : array with the number of variables by equation (includes constant)
bSUR : dictionary with the SUR regression coefficients by equation
varb : array with the variance-covariance matrix for the SUR regression
coefficients
Returns
-------
test : a list with for each coefficient (in order) a tuple with the
value of the test statistic, the degrees of freedom, and the
p-value
"""
kr = bigK[0][0]
test = []
bb = sur_dict2mat(bSUR)
kf = 0
nr = n_eq
df = n_eq - 1
for i in range(kr):
Ri = buildR1var(i,kr,kf,0,nr)
tt,p = wald_test(bb,Ri,np.zeros((df,1)),varb)
test.append((tt,df,p))
return test
def sur_joinrho(n_eq,bigK,bSUR,varb):
"""Test on joint significance of spatial autoregressive coefficient in SUR
Parameters
----------
n_eq : integer, number of equations
bigK : n_eq x 1 array with number of variables by equation
(includes constant term, exogenous and endogeneous and
spatial lag)
bSUR : dictionary with regression coefficients by equation, with
the spatial autoregressive term as last
varb : variance-covariance matrix for regression coefficients
Returns
-------
: tuple with test statistic, degrees of freedom, p-value
"""
bb = sur_dict2mat(bSUR)
R = np.zeros((n_eq,varb.shape[0]))
q = np.zeros((n_eq,1))
kc = -1
for i in range(n_eq):
kc = kc + bigK[i]
R[i,kc] = 1
w,p = wald_test(bb,R,q,varb)
return (w,n_eq,p)
def __init__(self,bigy,bigX,w,nonspat_diag=True,spat_diag=False,vm=False,\
epsilon=0.0000001,\
name_bigy=None,name_bigX=None,name_ds=None,name_w=None):
#need checks on match between bigy, bigX dimensions
# moved init here
BaseSURerrorML.__init__(self,bigy=bigy,bigX=bigX,w=w,epsilon=epsilon)
# check on variable names for listing results
self.name_ds = USER.set_name_ds(name_ds)
self.name_w = USER.set_name_w(name_w, w)
#initialize names - should be generated by sur_stack
if name_bigy:
self.name_bigy = name_bigy
else: # need to construct y names
self.name_bigy = {}
for r in range(self.n_eq):
yn = 'dep_var_' + str(r)
self.name_bigy[r] = yn
if name_bigX:
self.name_bigX = name_bigX
else: # need to construct x names
self.name_bigX = {}
for r in range(self.n_eq):
k = self.bigX[r].shape[1] - 1
name_x = ['var_' + str(i + 1) + "_" + str(r+1) for i in range(k)]
ct = 'Constant_' + str(r+1) # NOTE: constant always included in X
name_x.insert(0, ct)
self.name_bigX[r] = name_x
#inference
self.sur_inf = sur_setp(self.bSUR,self.varb)
# adjust concentrated log lik for constant
const = -self.n2 * (self.n_eq * (1.0 + np.log(2.0*np.pi)))
self.errllik = const + self.clikerr
self.surerrllik = const + self.cliksurerr
# LR test on off-diagonal sigma
if nonspat_diag:
M = self.n_eq * (self.n_eq - 1)/2.0
likrodiag = 2.0 * (self.surerrllik - self.errllik)
plik1 = stats.chisqprob(likrodiag, M)
self.lrtest = (likrodiag,int(M),plik1)
else:
self.lrtest = None
# LR test on spatial autoregressive coefficients
if spat_diag:
liklambda = 2.0 * (self.surerrllik - self.llik)
plik2 = stats.chisqprob(liklambda, self.n_eq)
self.likrlambda = (liklambda,self.n_eq,plik2)
else:
self.likrlambda = None
# asymptotic variance for spatial coefficient
if vm:
self.vm = surerrvm(self.n,self.n_eq,w,self.lamsur,self.sig)
vlam = self.vm[:self.n_eq,:self.n_eq]
self.lamsetp = lam_setp(self.lamsur,vlam)
# test on constancy of lambdas
R = buildR(kr=1,kf=0,nr=self.n_eq)
w,p = wald_test(self.lamsur,R,np.zeros((R.shape[0],1)),vlam)
self.lamtest = (w,R.shape[0],p)
if spat_diag: # test on joint significance of lambdas
Rj = np.identity(self.n_eq)
wj,pj = wald_test(self.lamsur,Rj,np.zeros((Rj.shape[0],1)),vlam)
self.joinlam = (wj,Rj.shape[0],pj)
else:
self.joinlam = None
else:
self.vm = None
self.lamsetp = None
self.lamtest = None
self.joinlam = None
# test on constancy of regression coefficients across equations
if check_k(self.bigK): # only for equal number of variables
self.surchow = sur_chow(self.n_eq,self.bigK,self.bSUR,self.varb)
else:
self.surchow = None
# listing of results
self.title = "SEEMINGLY UNRELATED REGRESSIONS (SUR) - SPATIAL ERROR MODEL"
SUMMARY.SUR(reg=self, nonspat_diag=nonspat_diag, spat_diag=spat_diag, lambd=True)