Esempio n. 1
0
    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))
Esempio n. 2
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    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
Esempio n. 3
0
    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))