def __init__(self, y, x, w, method='full', epsilon=0.0000001, regimes_att=None):
# set up main regression variables and spatial filters
self.y = y
if regimes_att:
self.x = x.toarray()
else:
self.x = x
self.n, self.k = self.x.shape
self.method = method
self.epsilon = epsilon
#W = w.full()[0] #wait to build pending what is needed
#Wsp = w.sparse
ylag = ps.lag_spatial(w, self.y)
xlag = self.get_x_lag(w, regimes_att)
# call minimizer using concentrated log-likelihood to get lambda
methodML = method.upper()
if methodML in ['FULL', 'LU', 'ORD']:
if methodML == 'FULL':
W = w.full()[0] # need dense here
res = minimize_scalar(err_c_loglik, 0.0, bounds=(-1.0, 1.0),
args=(self.n, self.y, ylag, self.x,
xlag, W), method='bounded',
tol=epsilon)
elif methodML == 'LU':
I = sp.identity(w.n)
Wsp = w.sparse # need sparse here
res = minimize_scalar(err_c_loglik_sp, 0.0, bounds=(-1.0,1.0),
args=(self.n, self.y, ylag,
self.x, xlag, I, Wsp),
method='bounded', tol=epsilon)
elif methodML == 'ORD':
# check on symmetry structure
if w.asymmetry(intrinsic=False) == []:
ww = symmetrize(w)
WW = ww.todense()
evals = la.eigvalsh(WW)
else:
W = w.full()[0] # need dense here
evals = la.eigvals(W)
res = minimize_scalar(
err_c_loglik_ord, 0.0, bounds=(-1.0, 1.0),
args=(self.n, self.y, ylag, self.x,
xlag, evals), method='bounded',
tol=epsilon)
else:
raise Exception, "{0} is an unsupported method".format(method)
self.lam = res.x
# compute full log-likelihood, including constants
ln2pi = np.log(2.0 * np.pi)
llik = -res.fun - self.n / 2.0 * ln2pi - self.n / 2.0
self.logll = llik
# b, residuals and predicted values
ys = self.y - self.lam * ylag
xs = self.x - self.lam * xlag
xsxs = np.dot(xs.T, xs)
xsxsi = np.linalg.inv(xsxs)
xsys = np.dot(xs.T, ys)
b = np.dot(xsxsi, xsys)
self.betas = np.vstack((b, self.lam))
self.u = y - np.dot(self.x, b)
self.predy = self.y - self.u
# residual variance
self.e_filtered = self.u - self.lam * ps.lag_spatial(w, self.u)
self.sig2 = np.dot(self.e_filtered.T, self.e_filtered) / self.n
# variance-covariance matrix betas
varb = self.sig2 * xsxsi
# variance-covariance matrix lambda, sigma
a = -self.lam * W
np.fill_diagonal(a, 1.0)
ai = la.inv(a)
wai = np.dot(W, ai)
tr1 = np.trace(wai)
wai2 = np.dot(wai, wai)
tr2 = np.trace(wai2)
waiTwai = np.dot(wai.T, wai)
tr3 = np.trace(waiTwai)
v1 = np.vstack((tr2 + tr3,
tr1 / self.sig2))
v2 = np.vstack((tr1 / self.sig2,
self.n / (2.0 * self.sig2 ** 2)))
v = np.hstack((v1, v2))
self.vm1 = np.linalg.inv(v)
# create variance matrix for beta, lambda
vv = np.hstack((varb, np.zeros((self.k, 1))))
vv1 = np.hstack(
(np.zeros((1, self.k)), self.vm1[0, 0] * np.ones((1, 1))))
self.vm = np.vstack((vv, vv1))
def __init__(self, y, x, w, method='full', epsilon=0.0000001):
# set up main regression variables and spatial filters
self.y = y
self.x = x
self.n, self.k = self.x.shape
self.method = method
self.epsilon = epsilon
#W = w.full()[0]
#Wsp = w.sparse
ylag = ps.lag_spatial(w, y)
# b0, b1, e0 and e1
xtx = spdot(self.x.T, self.x)
xtxi = la.inv(xtx)
xty = spdot(self.x.T, self.y)
xtyl = spdot(self.x.T, ylag)
b0 = np.dot(xtxi, xty)
b1 = np.dot(xtxi, xtyl)
e0 = self.y - spdot(x, b0)
e1 = ylag - spdot(x, b1)
methodML = method.upper()
# call minimizer using concentrated log-likelihood to get rho
if methodML in ['FULL', 'LU', 'ORD']:
if methodML == 'FULL':
W = w.full()[0] # moved here
res = minimize_scalar(lag_c_loglik, 0.0, bounds=(-1.0, 1.0),
args=(
self.n, e0, e1, W), method='bounded',
tol=epsilon)
elif methodML == 'LU':
I = sp.identity(w.n)
Wsp = w.sparse # moved here
res = minimize_scalar(lag_c_loglik_sp, 0.0, bounds=(-1.0,1.0),
args=(self.n, e0, e1, I, Wsp),
method='bounded', tol=epsilon)
elif methodML == 'ORD':
# check on symmetry structure
if w.asymmetry(intrinsic=False) == []:
ww = symmetrize(w)
WW = ww.todense()
evals = la.eigvalsh(WW)
else:
W = w.full()[0] # moved here
evals = la.eigvals(W)
res = minimize_scalar(lag_c_loglik_ord, 0.0, bounds=(-1.0, 1.0),
args=(
self.n, e0, e1, evals), method='bounded',
tol=epsilon)
else:
# program will crash, need to catch
print("{0} is an unsupported method".format(methodML))
self = None
return
self.rho = res.x[0][0]
# compute full log-likelihood, including constants
ln2pi = np.log(2.0 * np.pi)
llik = -res.fun - self.n / 2.0 * ln2pi - self.n / 2.0
self.logll = llik[0][0]
# b, residuals and predicted values
b = b0 - self.rho * b1
self.betas = np.vstack((b, self.rho)) # rho added as last coefficient
self.u = e0 - self.rho * e1
self.predy = self.y - self.u
xb = spdot(x, b)
self.predy_e = inverse_prod(
w.sparse, xb, self.rho, inv_method="power_exp", threshold=epsilon)
self.e_pred = self.y - self.predy_e
# residual variance
self.sig2 = self.sig2n # no allowance for division by n-k
# information matrix
a = -self.rho * W
np.fill_diagonal(a, 1.0)
ai = la.inv(a)
wai = np.dot(W, ai)
tr1 = np.trace(wai)
wai2 = np.dot(wai, wai)
tr2 = np.trace(wai2)
waiTwai = np.dot(wai.T, wai)
tr3 = np.trace(waiTwai)
wpredy = ps.lag_spatial(w, self.predy_e)
wpyTwpy = np.dot(wpredy.T, wpredy)
xTwpy = spdot(x.T, wpredy)
# order of variables is beta, rho, sigma2
v1 = np.vstack(
(xtx / self.sig2, xTwpy.T / self.sig2, np.zeros((1, self.k))))
v2 = np.vstack(
(xTwpy / self.sig2, tr2 + tr3 + wpyTwpy / self.sig2, tr1 / self.sig2))
v3 = np.vstack(
(np.zeros((self.k, 1)), tr1 / self.sig2, self.n / (2.0 * self.sig2 ** 2)))
v = np.hstack((v1, v2, v3))
self.vm1 = la.inv(v) # vm1 includes variance for sigma2
self.vm = self.vm1[:-1, :-1] # vm is for coefficients only
def __init__(self,
y,
x,
w,
method='full',
epsilon=0.0000001,
regimes_att=None):
# set up main regression variables and spatial filters
self.y = y
if regimes_att:
self.x = x.toarray()
else:
self.x = x
self.n, self.k = self.x.shape
self.method = method
self.epsilon = epsilon
#W = w.full()[0] #wait to build pending what is needed
#Wsp = w.sparse
ylag = ps.lag_spatial(w, self.y)
xlag = self.get_x_lag(w, regimes_att)
# call minimizer using concentrated log-likelihood to get lambda
methodML = method.upper()
if methodML in ['FULL', 'LU', 'ORD']:
if methodML == 'FULL':
W = w.full()[0] # need dense here
res = minimize_scalar(err_c_loglik,
0.0,
bounds=(-1.0, 1.0),
args=(self.n, self.y, ylag, self.x, xlag,
W),
method='bounded',
tol=epsilon)
elif methodML == 'LU':
I = sp.identity(w.n)
Wsp = w.sparse # need sparse here
res = minimize_scalar(err_c_loglik_sp,
0.0,
bounds=(-1.0, 1.0),
args=(self.n, self.y, ylag, self.x, xlag,
I, Wsp),
method='bounded',
tol=epsilon)
elif methodML == 'ORD':
# check on symmetry structure
if w.asymmetry(intrinsic=False) == []:
ww = symmetrize(w)
WW = ww.todense()
evals = la.eigvalsh(WW)
else:
W = w.full()[0] # need dense here
evals = la.eigvals(W)
res = minimize_scalar(err_c_loglik_ord,
0.0,
bounds=(-1.0, 1.0),
args=(self.n, self.y, ylag, self.x, xlag,
evals),
method='bounded',
tol=epsilon)
else:
raise Exception, "{0} is an unsupported method".format(method)
self.lam = res.x
# compute full log-likelihood, including constants
ln2pi = np.log(2.0 * np.pi)
llik = -res.fun - self.n / 2.0 * ln2pi - self.n / 2.0
self.logll = llik
# b, residuals and predicted values
ys = self.y - self.lam * ylag
xs = self.x - self.lam * xlag
xsxs = np.dot(xs.T, xs)
xsxsi = np.linalg.inv(xsxs)
xsys = np.dot(xs.T, ys)
b = np.dot(xsxsi, xsys)
self.betas = np.vstack((b, self.lam))
self.u = y - np.dot(self.x, b)
self.predy = self.y - self.u
# residual variance
self.e_filtered = self.u - self.lam * ps.lag_spatial(w, self.u)
self.sig2 = np.dot(self.e_filtered.T, self.e_filtered) / self.n
# variance-covariance matrix betas
varb = self.sig2 * xsxsi
# variance-covariance matrix lambda, sigma
a = -self.lam * W
np.fill_diagonal(a, 1.0)
ai = la.inv(a)
wai = np.dot(W, ai)
tr1 = np.trace(wai)
wai2 = np.dot(wai, wai)
tr2 = np.trace(wai2)
waiTwai = np.dot(wai.T, wai)
tr3 = np.trace(waiTwai)
v1 = np.vstack((tr2 + tr3, tr1 / self.sig2))
v2 = np.vstack((tr1 / self.sig2, self.n / (2.0 * self.sig2**2)))
v = np.hstack((v1, v2))
self.vm1 = np.linalg.inv(v)
# create variance matrix for beta, lambda
vv = np.hstack((varb, np.zeros((self.k, 1))))
vv1 = np.hstack((np.zeros((1, self.k)), self.vm1[0, 0] * np.ones(
(1, 1))))
self.vm = np.vstack((vv, vv1))