diff --git a/pywafo/src/wafo/stats/core.py b/pywafo/src/wafo/stats/core.py index 5d94b53..e78b9ef 100644 --- a/pywafo/src/wafo/stats/core.py +++ b/pywafo/src/wafo/stats/core.py @@ -7,6 +7,7 @@ import numpy as np from numpy import inf from numpy import atleast_1d, nan, ndarray, sqrt, vstack, ones, where, zeros from numpy import arange, floor, linspace, asarray #, reshape, repeat, product +from time import gmtime, strftime __all__ = ['edf', 'edfcnd','reslife', 'dispersion_idx','decluster','findpot', @@ -14,6 +15,12 @@ __all__ = ['edf', 'edfcnd','reslife', 'dispersion_idx','decluster','findpot', arr = asarray +def now(): + ''' + Return current date and time as a string + ''' + return strftime("%a, %d %b %Y %H:%M:%S", gmtime()) + def valarray(shape, value=nan, typecode=None): """Return an array of all value. """ @@ -646,6 +653,668 @@ def extremal_idx(ti): ei = min(1, 2*np.mean(t-1)**2/np.mean((t-1)*(t-2))) return ei +class RegLogit(object): + ''' + REGLOGIT Fit ordinal logistic regression model. + + CALL model = reglogit (options) + + model = fitted model object with methods + .compare() : Compare small LOGIT object versus large one + .predict() : Predict from a fitted LOGIT object + .summary() : Display summary of fitted LOGIT object. + + y = vector of K ordered categories + x = column vectors of covariates + options = struct defining performance of REGLOGIT + .maxiter : maximum number of iterations. + .accuracy : accuracy in convergence. + .betastart : Start value for BETA (default 0) + .thetastart : Start value for THETA (default depends on Y) + .alpha : Confidence coefficent (default 0.05) + .verbose : 1 display summary info about fitted model + 2 display convergence info in each iteration + otherwise no action + .deletecolinear : If true delete colinear covarites (default) + + + Methods + .predict : Predict from a fitted LOGIT object + .summary : Display summary of fitted LOGIT object. + .compare : Compare small LOGIT versus large one + + + + + Suppose Y takes values in K ordered categories, and let + gamma_i (x) be the cumulative probability that Y + falls in one of the first i categories given the covariate + X. The ordinal logistic regression model is + + logit (mu_i (x)) = theta_i + beta' * x, i = 1...k-1 + + The number of ordinal categories, K, is taken to be the number + of distinct values of round (Y). If K equals 2, + Y is binary and the model is ordinary logistic regression. The + matrix X is assumed to have full column rank. + + Given Y only, theta = REGLOGIT(Y) fits the model with baseline logit odds + only. + + Example + y=[1 1 2 1 3 2 3 2 3 3]' + x = (1:10)' + b = reglogit(y,x) + b.display() % members and methods + b.get() % return members + b.summary() + [mu,plo,pup] = b.predict(); + plot(x,mu,'g',x,plo,'r:',x,pup,'r:') + + y2 = [zeros(5,1);ones(5,1)]; + x1 = [29,30,31,31,32,29,30,31,32,33]; + x2 = [62,83,74,88,68,41,44,21,50,33]; + X = [x1;x2].'; + b2 = reglogit(y2,X); + b2.summary(); + b21 = reglogit(y2,X(:,1)); + b21.compare(b2) + + See also regglm, reglm, regnonlm + ''' + + #% Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007 + #% Kurt Hornik + #% + #% Reglogit is free software; you can redistribute it and/or modify it + #% under the terms of the GNU General Public License as published by + #% the Free Software Foundation; either version 3 of the License, or (at + #% your option) any later version. + #% + #% Reglogit is distributed in the hope that it will be useful, but + #% WITHOUT ANY WARRANTY; without even the implied warranty of + #% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + #% General Public License for more details. + #% + #% You should have received a copy of the GNU General Public License + #% along with Reglogit; see the file COPYING. If not, see + #% . + + + + #% Original for MATLAB written by Gordon K Smyth , + #% U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3, + #% 1992. + # + #% Author: Gordon K Smyth , + #% Adapted-By: KH + #% Revised by: pab + #% -renamed from logistic_regression to reglogit + #% -added predict, summary and compare + #% Description: Ordinal logistic regression + # + #% Uses the auxiliary functions logistic_regression_derivatives and + #% logistic_regression_likelihood. + + def __init__(self, maxiter=500,accuracy=1e-6, alpha=0.05, deletecolinear=True, verbose=False): + + self.maxiter =maxiter + self.accuracy = accuracy + self.alpha = alpha + self.deletcolinear = deletecolinear + self.verbose = False + self.family = None + self.link = None + self.numvar = None + self.numobs = None + self.numk = None + self.df = None + self.df_null = None + self.params = None + self.params_ci = None + self.params_cov = None + self.params_std = None + self.params_corr = None + self.params_tstat = None + self.params_pvalue = None + self.mu = None + self.eta = None + self.X = None + self.Y = None + self.theta = None + self.beta = None + self.residual = None + self.residual1d = None + self.deviance = None + self.deviance_null = None + self.d2L = None + self.dL = None + self.dispersionfit = None + self.dispersion = 1 + self.R2 = None + self.R2adj = None + self.numiter = None + self.converged = None + self.note = '' + self.date = now() + + + def _logit(self, p): + return np.log(p)-np.log1p(-p) + def _logitinv(self, x): + return 1.0/(np.exp(-x)+1) + + def check_xy(self, y, X): + y = np.round(np.atleast_2d(y)) + my, ny = y.shape + if X is None: + X = np.zeros((my, 0)) + elif self.deletecolinear: + X = np.atleast_2d(X) + # Make sure X is full rank + s = np.linalg.svd(X)[1] + tol = max(size(X)) * np.finfo(s.max()).eps + ix = np.flatnonzero(s>tol) + iy = np.flatnonzero(s<=tol) + if len(ix): + X = X[:, ix] + txt = [' %d,' % i for i in iy] + txt[-1] = ' %d' % iy[-1] + warnings.warn('Covariate matrix is singular. Removing column(s):%s',txt) + [mx, nx] = X.shape + if (mx != my): + raise ValueError('x and y must have the same number of observations'); + return y, X + + + def fit(self, y, X=None, theta0=None, beta0=None): + ''' + Member variables + .df : degrees of freedom for error. + .params : estimated model parameters + .params_ci : 100(1-alpha)% confidence interval for model parameters + .params_tstat : t statistics for model's estimated parameters. + .params_pvalue: p value for model's estimated parameters. + .params_std : standard errors for estimated parameters + .params_corr : correlation matrix for estimated parameters. + .mu : fitted values for the model. + .eta : linear predictor for the model. + .residual : residual for the model (Y-E(Y|X)). + .dispersnfit : The estimated error variance + .deviance : deviance for the model equal minus twice the log-likelihood. + .d2L : Hessian matrix (double derivative of log-likelihood) + .dL : First derivative of loglikelihood w.r.t. THETA and BETA. + + ''' + self.family = 'multinomial'; + self.link = 'logit'; + y, X = self.check_xy(y, X) + + + # initial calculations + tol = self.accuracy + incr = 10 + decr = 2 + ymin = y.min() + ymax = y.max() + yrange = ymax - ymin + z = (y * ones((1, yrange))) == ((y * 0 + 1) * np.arange(ymin, ymax)) + z1 = (y * ones((1, yrange))) == ((y * 0 + 1) * np.arange(ymin + 1, ymax+1)) + z = z[:, np.flatnonzero(z.any(axis=0))]; + z1 = z1[:, np.flatnonzero(z1.any(axis=0))] + [mz, nz] = z.shape + [mx, nx] = X.shape + [my, ny] = y.shape + + g = z.sum(axis=0).cumsum() / my + theta00 = np.log(g / (1 - g)) + beta00 = np.zeros((nx, 1)) + # starting values + if theta0 is None: + theta0 = theta00 + + if beta0 is None: + beta0 = beta00 + + tb = np.vstack((theta0, beta0)) + + # likelihood and derivatives at starting values + [dev,p,g, g1] = logistic_regression_likelihood (y, X, tb, z, z1); + [dl, d2l] = logistic_regression_derivatives (X, z, z1, g, g1, p); + epsilon = std (d2l) / 1000; + if np.any(beta) or np.any(theta!=theta0): + tb0 = np.vstack((theta00,beta00)) + nulldev = logistic_regression_likelihood (y, X, tb0, z, z1); + else: + nulldev = dev + + + # maximize likelihood using Levenberg modified Newton's method + iter = 0; + stop = False + while not stop: + iter += 1 + tbold = tb; + devold = dev; + tb = tbold - np.linalg.lstsq(d2l, dl) + [dev,p,g, g1] = logistic_regression_likelihood (y, X, tb, z, z1); + if ((dev - devold) / (dl.T * (tb - tbold)) < 0): + epsilon = epsilon / decr + else: + while ((dev - devold) / (dl.T * (tb - tbold)) > 0): + epsilon = epsilon * incr; + if (epsilon > 1e+15): + raise ValueError('epsilon too large'); + + tb = tbold - np.linalg.lstsq(d2l - epsilon * np.eye(d2l.shape), dl); + [dev,p,g, g1] = logistic_regression_likelihood (y, X, tb, z, z1); + print('epsilon %g' % epsilon) + #end %while + #end else + [dl, d2l] = logistic_regression_derivatives (X, z, z1, g, g1, p); + if (self.verbose>1): + + print('Iter: %d, Deviance: %8.6f',iter,dev) + + print('First derivative'); + print(dl.T); + print('Eigenvalues of second derivative'); + print(np.linalg.eig(d2l)[0].T); + #end + #end + stop = abs (dl.T * np.linalg.lstq(d2l, dl) / length (dl)) <= tol or iter>self.maxiter + #end %while + + #% tidy up output + + theta = tb[:nz, 0] + beta = tb[nz:(nz + nx), 1] + pcov = np.linalg.pinv(-d2l) + se = sqrt(np.diag (pcov)) + + + + + if (nx > 0): + eta = ((X * beta) * ones (1, nz)) + ((y * 0 + 1) * theta.T); + else: + eta = (y * 0 + 1) * theta.T; + #end + gammai = np.diff(np.hstack(((y * 0), self.logitinv(eta), (y * 0 + 1))),1,2) + k0 = min(y) + mu = (k0-1)+np.dot(gammai,np.arange(1,nz+2).T); #% E(Y|X) + r = np.corrcoef(np.hstack((y,mu))) + R2 = r[0,1]**2; #coefficient of determination + R2adj = max(1 - (1-R2)* (my-1)/(my-nx-nz-1),0); # adjusted coefficient of determination + + res = y-mu; + + if nz==1: + self.family = 'binomial'; + else: + self.family = 'multinomial'; + + self.link = 'logit'; + + self.numvar = nx+nz; + self.numobs = my; + self.numk = nz+1; + self.df = max(my-nx-nz,0); + self.df_null = my-nz; #nulldf; nulldf = n - nz; + self.params = tb[:(nz + nx),0].T; + self.params_ci = 1; + self.params_std = se.T; + self.params_cov = pcov + self.params_tstat = (self.params/self.params_std); + if False: # % options.estdispersn %dispersion_parameter=='mean_deviance' + self.params_pvalue=2.*cdft(-abs(self.params_tstat),self.df); + bcrit = -se.T*invt(self.alpha/2,self.df); + else: + self.params_pvalue=2.*cdfnorm(-abs(self.params_tstat)); + bcrit = -se.T*invnorm(self.alpha/2); + #end + self.params_ci = np.vstack((self.params+bcrit,self.params-bcrit)) + + self.mu = gammai; + self.eta = self.logit(gammai); + self.X = X; + + self.theta = theta; + self.beta = beta; + self.gamma = gammai; + self.residual = res.T; + self.residualD = sign(self.residual)*sqrt(-2*log(p)).T; + self.deviance = dev; + self.deviance_null = nulldev; + self.d2L = d2l; + self.dL = dl.T; + self.dispersnfit=1; + self.dispersn = 1; + self.R2 = R2; + self.R2adj = R2adj; + self.numiter = iter; + self.converged = iterobject2.numvar: + devL = self.deviance; + nL = self.numvar; + dfL = self.df; + Al = self.X; + disprsn = self.dispersionfit; + devs = object2.deviance; + ns = object2.numvar; + dfs = object2.df; + As = object2.X; + else: + devL = object2.deviance; + nL = object2.numvar; + dfL = object2.df; + Al = object2.X; + disprsn = object2.dispersionfit; + devs = self.deviance; + ns = self.numvar; + dfs = self.df; + As = self.X; + #end + + if (((As-np.dot(Al*np.linalg.lstsq(Al,As)))>500*np.finfo(float).eps).any() or + object2.family!=self.family or object2.link!=self.link): + warnings.warn('Small model not included in large model, result is rubbish!') + + + except: + raise ValueError('Apparently not a valid regression object') + + + + pmq = np.abs(nL-ns); + print(' ') + print(' Analysis of Deviance') + if False: # %options.estdispersn + localstat = abs(devL-devs)/disprsn/pmq; + localpvalue = 1-cdff(localstat, pmq, dfL) + print('Model DF Residual deviance F-stat Pr(>F)') + else: + localstat = abs(devL-devs)/disprsn; + localpvalue = 1-cdfchi2(localstat,pmq) + print('Model DF Residual deviance Chi2-stat Pr(>Chi2)') + #end + + + print('Small %d %12.4f %12.4f %12.4f' % (dfs,devs,localstat,localpvalue)) + print('Full %d %12.4f' % (dfL,devL)) + print(' ') + + return localpvalue + + def anode(self): + print(' ') + print(' Analysis of Deviance') + if False: # %options.estdispersn + localstat = abs(self.deviance_null-self.deviance)/self.dispersnfit/(self.numvar-1); + localpvalue = 1-cdff(localstat,self.numvar-1,self.df); + print('Model DF Residual deviance F-stat Pr(>F)') + else: + localstat = abs(self.deviance_null-self.deviance)/self.dispersnfit; + localpvalue = 1-cdfchi2(localstat,self.numvar-1); + print('Model DF Residual deviance Chi2-stat Pr(>Chi2)') + #end + + + print('Null %d %12.4f %12.4f %12.4f' % (self.df_null,self.deviance_null,localstat,localpvalue)) + print('Full %d %12.4f' % (self.df,self.deviance)) + print(' ') + + print(' R2 = %2.4f, R2adj = %2.4f' % (self.R2,self.R2adj)) + print(' ') + return localpvalue + def summary(self): + txtlink = self.link; + + print('Call:') + print('reglogit(formula = %s(Pr(grp(y)<=i)) ~ theta_i+beta*x, family = %s)' %(txtlink,self.family)) + print(' ') + print('Deviance Residuals:') + m,q1,me, q3,M = np.percentile(self.residualD,q=[0, 25, 50, 75, 100]) + print(' Min 1Q Median 3Q Max ') + print('%2.4f %2.4f %2.4f %2.4f %2.4f' % (m, q1, me, q3, M)) + print(' ') + print(' Coefficients:') + if False: # %options.estdispersn + print(' Estimate Std. Error t value Pr(>|t|)') + else: + print(' Estimate Std. Error z value Pr(>|z|)') + #end + e, s, z, p = self.params, self.params_std, self.params_tstat, self.params_pvalue + for i in range(self.numk): + print('theta_%d %2.4f %2.4f %2.4f %2.4f' % (i,e[i],s[i], z[i], p[i])) + + for i in range(self.numk, self.numvar): + print(' beta_%d %2.4f %2.4f %2.4f %2.4f\n' % (i-self.numk,e[i],s[i], z[i], p[i])) + + print(' ') + print('(Dispersion parameter for %s family taken to be %2.2f)' % (self.family,self.dispersionfit)) + print(' ') + if True: #%options.constant + printf(' Null deviance: %2.4f on %d degrees of freedom' % (self.deviance_null,self.df_null)) + #end + print('Residual deviance: %2.4f on %d degrees of freedom' % (self.deviance,self.df)) + + self.anode() + + #end % summary + + def predict(self, Xnew=None,alpha=0.05, fulloutput=False): +'''LOGIT/PREDICT Predict from a fitted LOGIT object + + CALL [y,ylo,yup] = predict(Xnew,options) + + y = predicted value + ylo,yup = 100(1-alpha)% confidence interval for y + + Xnew = new covariate + options = options struct defining the calculation + .alpha : confidence coefficient (default 0.05) + .size : size if binomial family (default 1). + +''' + +[mx, nx] = self.X.shape +if Xnew is None: + Xnew = self.X; +else: + Xnew = np.atleast_2d(Xnew) + notnans = np.flatnonzero(1-(1-np.isfinite(Xnew)).any(axis=1)) + Xnew = Xnew[notnans,:] + +[n,p] = Xnew.shape + + +if p != nx + raise ValueError('Number of covariates must match the number of regression coefficients') + + +nz = self.numk-1; +one = ones((n,1)) + if (nx > 0): + eta = np.dot(Xnew * self.beta) + self.theta.T; + else: + eta = one * self.theta.T + #end + y = np.diff(np.hstack((zeros((n,1)), self.logitinv(eta), one),1,2); +if fulloutput: + pcov = self.params_cov; + if (nx > 0) + np = size(pcov,1); + + [U S V]= np.linalg.svd(pcov,0); + R=(U*sqrt(S)*V.T); #%squareroot of pcov + ixb = nz+1:np; + + % Var(eta_i) = var(theta_i+Xnew*b) + vareta = zeros(n,nz); + for ix1 = 1:nz + vareta(:,ix1) = max(sum(([one Xnew]*R([ix1,ixb],[ix1,ixb])).^2,2),eps); + end + else + vareta = diag(pcov); + end + crit = -invnorm(alpha/2); + + + ecrit = crit * sqrt(vareta); + mulo = logitinv(eta-ecrit); + muup = logitinv(eta+ecrit); + ylo1 = diff ([zeros(n,1), mulo , one],1,2); + yup1 = diff ([zeros(n,1), muup , one],1,2); + + ylo = min(ylo1,yup1); + yup = max(ylo1,yup1); + + for ix1 = 2:self.numk-1 + yup(:,ix1) = max( [yup(:,ix1),muup(:,ix1)-mulo(:,ix1-1)],[],2); + end + return y,ylo,yup +end + + + + + +def logistic_regression_derivatives (x, z, z1, g, g1, p) +% [dl, d2l] = logistic_regression_derivatives (@var{x}, @var{z}, @var{z1}, @var{g}, @var{g1}, @var{p}) +% Called by logistic_regression. Calculates derivates of the +% log-likelihood for ordinal logistic regression model. + + +% Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007 +% Kurt Hornik +% +% +% Reglogit is free software; you can redistribute it and/or modify it +% under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 3 of the License, or (at +% your option) any later version. +% +% Reglogit is distributed in the hope that it will be useful, but +% WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Reglogit; see the file COPYING. If not, see +% . + +% Author: Gordon K. Smyth +% Adapted-By: KH +% Description: Derivates of log-likelihood in logistic regression + + + % first derivative + v = g .* (1 - g) ./ p; + v1 = g1 .* (1 - g1) ./ p; + dlogp = [(dmult (v, z) - dmult (v1, z1)), (dmult (v - v1, x))]; + dl = sum (dlogp)'; + + % second derivative + w = v .* (1 - 2 * g); w1 = v1 .* (1 - 2 * g1); + d2l = [z, x]' * dmult (w, [z, x]) - [z1, x]' * dmult (w1, [z1, x]) ... + - dlogp' * dlogp; + +return [dl, d2l] +end %function + +def logistic_regression_likelihood (y, x, beta, z, z1) +% [g, g1, p, dev] = logistic_regression_likelihood (y ,x,beta,z,z1) +% Calculates likelihood for the ordinal logistic regression model. +% Called by logistic_regression. + + + +% Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007 +% Kurt Hornik +% +% +% Reglogit is free software; you can redistribute it and/or modify it +% under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 3 of the License, or (at +% your option) any later version. +% +% Reglogit is distributed in the hope that it will be useful, but +% WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Reglogit; see the file COPYING. If not, see +% . + +% Author: Gordon K. Smyth +% Adapted-By: KH +% Description: Likelihood in logistic regression + e = exp ([z, x] * beta); + e1 = exp ([z1, x] * beta); + g = e ./ (1 + e); + g1 = e1 ./ (1 + e1); + g = max (y == max (y), g); + g1 = min (y > min(y), g1); + + p = g - g1; + dev = -2 * sum (log (p)); +return dev,p,g, g1 +end %function + +function M = dmult(A,B) +% PURPOSE: computes the product of diag(A) and B +% ----------------------------------------------------- +% USAGE: m = dmult(a,b) +% where: a = a matrix +% b = a matrix +% ----------------------------------------------------- +% RETURNS: m = diag(A) times B +% ----------------------------------------------------- +% NOTE: a Gauss compatability function +% ----------------------------------------------------- + +% written by: +% Gordon K Smyth, U of Queensland, Australia, gks@maths.uq.oz.au +% Nov 19, 1990. Last revision Aug 29, 1995. + +% documentation modifications made by: +% James P. LeSage, Dept of Economics +% University of Toledo +% 2801 W. Bancroft St, +% Toledo, OH 43606 +% jpl@jpl.econ.utoledo.edu + + +[mb,nb] = size(B); +M=A(:,ones(1,nb)).*B; +end + + + + def _test_dispersion_idx(): import wafo.data diff --git a/pywafo/src/wafo/stats/distributions.py b/pywafo/src/wafo/stats/distributions.py index 7112a5f..4d2c400 100644 --- a/pywafo/src/wafo/stats/distributions.py +++ b/pywafo/src/wafo/stats/distributions.py @@ -34,7 +34,6 @@ from numpy import flatnonzero as nonzero from wafo.stats.estimation import FitDistribution -from scipy.stats.distributions import floatinfo try: from scipy.stats.distributions import vonmises_cython @@ -3727,7 +3726,7 @@ class frechet_r_gen(rv_continuous): """ def link(self, x, logSF, phat, ix): - u = phat[1] + #u = phat[1] if ix == 0: phati = log(-logSF) / log((x - phat[1]) / phat[2]) elif ix == 1: @@ -5314,8 +5313,8 @@ class ncf_gen(rv_continuous): Px *= (n2+n1*x)**(-(n1+n2)/2) Px *= special.assoc_laguerre(-nc*n1*x/(2.0*(n2+n1*x)),n2/2,n1/2-1) Px /= special.beta(n1/2,n2/2) - #this function does not have a return - # drop it for now, the generic function seems to work ok + #this function does not have a return + # drop it for now, the generic function seems to work ok def _cdf(self, x, dfn, dfd, nc): return special.ncfdtr(dfn,dfd,nc,x) def _ppf(self, q, dfn, dfd, nc):