sar_gcbma.m

计量工具箱

function [rmin,rmax,time2] = sar_eigs(eflag,W,rmin,rmax,n);
% PURPOSE: compute the eigenvalues for the weight matrix
% ---------------------------------------------------
%  USAGE: [rmin,rmax,time2] = far_eigs(eflag,W,rmin,rmax,W)
% where eflag is an input flag, W is the weight matrix
%       rmin,rmax may be used as default outputs
% and the outputs are either user-inputs or default values
% ---------------------------------------------------


if eflag == 1 % compute eigenvalues
t0 = clock;
opt.tol = 1e-3; opt.disp = 0;
lambda = eigs(sparse(W),speye(n),1,'SR',opt);  
rmin = 1/real(lambda);   
rmax = 1;
time2 = etime(clock,t0);
else
time2 = 0;
end;


function [detval,time1] = sar_lndet(ldetflag,W,rmin,rmax,detval,order,iter);
% PURPOSE: compute the log determinant |I_n - rho*W|
% using the user-selected (or default) method
% ---------------------------------------------------
%  USAGE: detval = far_lndet(lflag,W,rmin,rmax)
% where eflag,rmin,rmax,W contains input flags 
% and the outputs are either user-inputs or default values
% ---------------------------------------------------


% do lndet approximation calculations if needed
if ldetflag == 0 % no approximation
t0 = clock;    
out = lndetfull(W,rmin,rmax);
time1 = etime(clock,t0);
tt=rmin:.001:rmax; % interpolate a finer grid
outi = interp1(out.rho,out.lndet,tt','spline');
detval = [tt' outi];
    
elseif ldetflag == 1 % use Pace and Barry, 1999 MC approximation

t0 = clock;    
out = lndetmc(order,iter,W,rmin,rmax);
time1 = etime(clock,t0);
results.limit = [out.rho out.lo95 out.lndet out.up95];
tt=rmin:.001:rmax; % interpolate a finer grid
outi = interp1(out.rho,out.lndet,tt','spline');
detval = [tt' outi];

elseif ldetflag == 2 % use Pace and Barry, 1998 spline interpolation

t0 = clock;
out = lndetint(W,rmin,rmax);
time1 = etime(clock,t0);
tt=rmin:.001:rmax; % interpolate a finer grid
outi = interp1(out.rho,out.lndet,tt','spline');
detval = [tt' outi];

elseif ldetflag == -1 % the user fed down a detval matrix
    time1 = 0;
        % check to see if this is right
        if detval == 0
            error('sar_g: wrong lndet input argument');
        end;
        [n1,n2] = size(detval);
        if n2 ~= 2
            error('sar_g: wrong sized lndet input argument');
        elseif n1 == 1
            error('sar_g: wrong sized lndet input argument');
        end;          
end;

function [j,visits] = find_new(i,vsave,vinew,visits)
% PURPOSE: determines if the variables in vinew represent a new model
%          (called by bma_g)
%-------------------------------------------------------
% USAGE: [j,visits] = find_new(i,vsave,vinew,visits)
% where:        i   = size of vsave to search = draw #
%             vsave = (i x nvar) matrix of indicators for models
%             vinew = (1 x nvar) vector with current model indicators
%            visits = (i x nvar) matrix for recording # of visits to a model
%-------------------------------------------------------
% RETURNS:      j = index to an old model found
%          visits = matrix recording visits to old models
%-------------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics 7/2003
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]

[junk nvar] = size(vsave);
vitmp = zeros(1,nvar);
for k=1:nvar
    for j=1:length(vinew)
      if vinew(1,j) == k
        vitmp(1,k) = 1;
      end;
    end;
end;

nobs = i;
new = 0;
j = 1;
while (new == 0 & j <= nobs)
if vsave(j,:) == vitmp(1,:)
visits(j,1) = visits(j,1) + 1;
new = 1;
end;
j = j+1;
end;

j = j-1;

function lmout = bmapost(y,xall,vin,W,detval,a1,a2,nu1,d1,g)
% PURPOSE: evaluates log marginal posterior of SAR bma model
%          (SAR Bayesian model averaging)
%-----------------------------------------------------------
% USAGE: lpost = bmapost(y,xall,vin,W,g)
% where:   y = dependent variable vector (nobs x 1)
%       xall = explanatory variables matrix (nobs x k)
%        vin = a 1xk vector of columns to use from x, e.g. [1 3 5]
%          W = spatial weight matrix
%          g = g prior hyperparameter
%      lndet = a vector with rho, lndet values
%-----------------------------------------------------------
% RETURNS: lpost = log marginal posterior, a vector the length of aval
%                  containing the log marginal over a grid of alpha values
%-----------------------------------------------------------
% REFERENCES: Raftery and Madigan (1997) 'Bayesian model averaging
% for linear regression models', 92, pp. 179-191
% ----------------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics 7/2003
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]


[nobs,nv1] = size(xall);
nvar = length(vin);
v1 = nvar;
for i=1:nvar
    if vin(1,i) >= nv1
        v1 = i; % # of variables in x1
    end;
end;    

xt = [ones(nobs,1) xall(:,vin)];
[nobs,k] = size(xt);
iota = ones(nobs,1);
Wy = sparse(W)*y;

% now compute vectorized log-marginal likelihood
% to use in trapezoid numerical integration over rho
          xpx = xt'*xt;
          b0t = (xpx)\(xt'*y);
          bdt = (xpx)\(xt'*Wy);
          e0 = y - xt*b0t;
          ed = Wy - xt*bdt;
          epe0 = e0'*e0;
          eped = ed'*ed;
          epe0d = ed'*e0;
          
          Qvec = zeros(length(detval(:,1)),1);
          for i=1:length(detval(:,1));
              ybar = mean(y) - detval(i,1)*mean(Wy);
              yhat = y - detval(i,1)*Wy - ybar*iota;
              Qvec(i,1) = (g/(1+g))*(yhat'*yhat);
          end;

% evaluate vectorized log-marginal likelihood
lmout = sar_marginal(detval,epe0,eped,epe0d,nobs,k,a1,a2,nu1,d1,g,Qvec);


function odds = model_odds(rho_vec,lmarg1,lmarg2)
% PURPOSE: computes Bayes factor for 2 models using vectorized log-marginals as input
% ---------------------------------------------------
%  USAGE: probs = model_odds(rho_vec,logmarginal1,logmargina2)
%  where: logmarginal1,logmarginal2 = vectors containing
%                                     the log-marginal posterior over a grid of rho values
%                          rho_vec = the vector of rho values used for log-marginals
% ---------------------------------------------------
% NOTES:
% log_marginals are returned by sar_marginal() function
% rho_vec is returned by lndet() function
% ---------------------------------------------------
%  RETURNS: a Bayes factor, a scalar
% ---------------------------------------------------

% written by:
% James P. LeSage, 7/2003
% Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]

 
nrho = length(rho_vec);

lmarginal = [lmarg1 lmarg2];

% now scale using all of the vectors of log-marginals
% we must scale before exponentiating 
adj = max(max(lmarginal));
madj = lmarginal - adj;

xx = exp(madj);

% trapezoid rule integration
yy = matmul(rho_vec,ones(nrho,2));
isum = zeros(1,2);
for j=1:2
    yj = yy(:,j);
    xj = xx(:,j);    
isum(1,j) = sum(diff(yj).*(xj(1:end-1)+xj(2:end))/2);
end;

% compute posterior probabilities
psum = sum(isum);
probs = isum/psum;
odds = (probs(1)+realmin)/(probs(2)+realmin);



function  out = sar_marginal(detval,epe0,eped,epe0d,nobs,nvar,a1,a2,nu1,d1,g,Qvec)
% PURPOSE: returns a vector of the log-marginal over a grid of rho-values
%          for the case of Zellner g-prior on beta
% -------------------------------------------------------------------------
% USAGE: out = sar_marginal(detval,e0,ed,epe0,eped,epe0d,nobs,nvar,a1,a2,g,Qvec)
% where:       detval = an ngrid x 2 matrix with rho-values and lndet values
%                  e0 = y - x*b0;
%                 ed = Wy - x*bd;
%               epe0 = e0'*e0;
%               eped = ed'*ed;
%              epe0d = ed'*e0;
%               nobs = # of observations
%               nvar = # of explanatory variables
%                 a1 = parameter for beta prior on rho
%                 a2 = parameter for beta prior on rho
%                nu1 = prior parameter for sigma^2
%                 d1 = prior parameter for sigma^2
%                 g = g-prior value
%              Qvec = vectorized (g/(1+g)*(yhat'*yhat)
%                     over all rho-values
% -------------------------------------------------------------------------
% RETURNS: out = a structure variable
%        out = log marginal, a vector the length of detval
% -------------------------------------------------------------------------

% written by:
% James P. LeSage, 7/2003
% Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]

n = length(detval);
nm1o2 = (nobs+nu1-1)/2;
no2 = (nobs+nu1)/2;
% C is a constant of integration that can vary with nvars, so for model
% comparisions involving different nvars we need to include this
bprior = beta_prior(detval(:,1),a1,a2);
%C = log(bprior) + gammaln(nmk) - nmk*log(2*pi);
iota = ones(n,1);
z = epe0*iota - 2*detval(:,1)*epe0d + detval(:,1).*detval(:,1)*eped;
% add quadratic terms based on prior for beta
logdetx = (nvar/2)*log(g/(1+g));
gterm = 1/(1+g);
den = log(bprior) + logdetx*iota + detval(:,2) - nm1o2*log(nu1*d1 + gterm*z + Qvec);
kterm = gammaln(nm1o2) -no2*log(pi);
out = kterm + den;


function out = beta_prior(rvec,a1,a2)
% PURPOSE: construct beta-prior for rho over -1,1 interval
%-----------------------------------------------------------
% USAGE: out = beta_prior(a1,a2,rvec);
% where:    rvec = grid over rmin,rmax interval, an n x 1 vector
%           a1 = (optional) prior parameter (default = 1.1)
%           a2 = (optional) prior parameter (default = 1.1)
% RETURNS: out = nx1 vector of prior weights for rho
%          in the interval rmin,rmax
%-----------------------------------------------------------
% NOTES: increasing a1,a2 to 1.5,1.5 or 2.0,2.0 increases
%        prior weight placed on zero for rho, and decreases
%        weights on non-zero values for rho
% to see what the prior looks like:
% rvec = -1:0.01:1;
% a1 = 1.1; a2 = 1.1;
% bprior = beta_prior(rvec',a1,a2);
% plot(rvec,bprior);
%-----------------------------------------------------------

% written by:
% James P. LeSage, 4/2003
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]

if nargin == 1
a1 = 1.01;
a2 = 1.01;
elseif nargin == 2
    a2 = 1.01;
elseif nargin > 3
    error('beta_prior: wrong # of inputs');
end;

B = beta(a1,a2);
num = (1+rvec).^(a1-1);
num = num.*(1-rvec).^(a2-1);
den = 2^(a1+a2-1);
out = (1/B)*num/den;
out(1) = eps;
out(end) = eps;

function [vinew,vonew] = sample(vin,vout)
% PURPOSE: function used by sar BMA models to sample variables for changing model size
% ----------------------------------------------------------
% USAGE: [vinew vonew] = sample(vin,vout)
% where:   vin  = a 1 x nvar1 vector of variable #'s for
%                 variables included in the model
%          vout = a 1 x nvar2 vector of variable #'s for
%                 variables excluded from the model
% ----------------------------------------------------------
% RETURNS: vinew = a 1 x nvar1+1 or 1 x nvar1-1 vector of
%                  variable #'s in the new model
%          vonew = a 1 x nvar2+1 or 1 x nvar2-1 vector of
%                  variable #'s excluded from the new model
% ----------------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]
% last modified June, 2004

% find size of variables in/out of the model
nv1 = length(vout); 
nv2 = length(vin);
nvar = nv1+nv2;

% decide on increase, move, decrease model size
coin = unif_rnd(1,0,1);
if coin < 0.33
    if nv1 == 0
        increase = 1;
    else
    increase = 0;
    end
elseif coin > 0.66
    if nv2 == 0
        increase = 0;
    else
    increase = 1;
    end
else
    increase = 2;
end;


switch increase
case {0} % decrease the # variables in the model
choose = round(unif_rnd(1,1,length(vout)));
vinew = [vin vout(choose)];
vonew = zeros(1,length(vout)-1);
cnt = 1;
for i=1:length(vout);
 if i~= choose
 vonew(cnt) = vout(i);
 cnt = cnt+1;
 end;
end; % end of for loop
case {1} % increase the # variables in the model
choose = round(unif_rnd(1,1,length(vin)));
vinew = zeros(1,length(vin)-1);
cnt = 1;
for i=1:length(vin);
 if i~= choose
 vinew(cnt) = vin(i);
 cnt = cnt+1;
 end;
end; % end of for loop
vonew = zeros(1,length(vout)+1);
cnt = 1;
for i=1:length(vout);
    vonew(cnt) = vout(cnt);
    cnt = cnt+1;
end;
vonew(cnt) = vin(choose);
case {2} % change a variable that is in with one that is out
    choose1 = round(unif_rnd(1,1,length(vout)));
    choose2 = round(unif_rnd(1,1,length(vin)));
vinew = vin;
vonew = vout;
for i=1:length(vout);
 if i == choose1
     for j=1:length(vin);
        if j == choose2
        vinew(j) = vout(i);
        vonew(i) = vin(j);
        end;
    end; % end of for j loop
 end; % end of if i == choose1
end; % end of for i loop


otherwise
disp('error in sample function');    
end; % end of switch