sar_panel.m

利用Matlab做面板数据分析（平行数据分析）的一个实例

elseif model==3
    intercept=mean(y)-mean(Wy)*results.rho-mean(x)*results.beta; % intercept calculated separately
    results.con=intercept;
    results.sfe=meanny-meannwy*results.rho-meannx*results.beta-kron(et,intercept);
    results.tfe=meanty-meantwy*results.rho-meantx*results.beta-kron(en,intercept);
    xhat=x*results.beta+kron(en,results.sfe)+kron(et,results.tfe)+kron(ent,intercept);
    tnvar=nvar+N+T;
else
    xhat=x*results.beta;
    tnvar=nvar+1; % +1 due to spatially lagged dependent variable
end    

yhat=zeros(nobs,1);
for t=1:T
    t1=1+(t-1)*N;t2=t*N;
    yhat([t1:t2],1)=(speye(N) - p*sparse(W))\xhat([t1:t2],1);
end

results.yhat = yhat;
results.resid = y - p*Wy - xhat; 

yme=y-mean(y);
rsqr2=yme'*yme;
rsqr1 = results.resid'*results.resid;
results.rsqr=1.0-rsqr1/rsqr2; %rsquared
rsqr3 = rsqr1/(nobs-tnvar);
rsqr2 = rsqr2/(nobs-1.0);
results.rbar = 1 - (rsqr3/rsqr2); % rbar-squared
results.tnvar=tnvar;

parm = [results.beta
        results.rho
        results.sige];

results.lik = f2_sarpanel(parm,ywith,xwith,W,detval,T); %Elhorst

if N <= 500
t0 = clock;
% asymptotic t-stats based on information matrix (page 80-81 Anselin, 1980),
% adjusted by Elhorst for spatial panels 
B = speye(N) - p*sparse(W); 
BI = inv(B); WB = W*BI;
pterm = trace(WB*WB + WB*WB');
xpx = zeros(nvar+2,nvar+2);               
% bhat,bhat
xpx(1:nvar,1:nvar) = (1/sige)*(xwith'*xwith);     
% bhat,rho
ysum=zeros(nvar,1);
for t=1:T
    t1=1+(t-1)*N;t2=t*N;
    ysum=ysum+(1/sige)*xwith([t1:t2],:)'*W*BI*xwith([t1:t2],:)*bhat;
end
xpx(1:nvar,nvar+1) = ysum;
xpx(nvar+1,1:nvar) = xpx(1:nvar,nvar+1)'; 
% rho,rho
ysom=0;
for t=1:T
    t1=1+(t-1)*N;t2=t*N;
    ysom=ysom+(1/sige)*bhat'*xwith([t1:t2],:)'*BI'*W'*W*BI*xwith([t1:t2],:)*bhat + pterm;
end
xpx(nvar+1,nvar+1) = ysom;
% sige, sige
xpx(nvar+2,nvar+2) = nobs/(2*sige*sige);     
% rho,sige
xpx(nvar+1,nvar+2) = (T/sige)*trace(WB);  
xpx(nvar+2,nvar+1) = xpx(nvar+1,nvar+2);
xpxi = xpx\eye(size(xpx));
tmp = diag(xpxi(1:nvar+1,1:nvar+1));
bvec = [results.beta
        results.rho];
tmp = bvec./(sqrt(tmp));
results.tstat = tmp;
time3 = etime(clock,t0);

else  % asymptotic t-stats using numerical hessian
t0 = clock;
% just computes the diagonal
dhessn = hessian('f2_sarpanel',parm,ywith,xwith,W,detval,T); %Elhorst
hessi = invpd(dhessn);
tvar = abs(diag(hessi));
tmp = [results.beta
       results.rho];
results.tstat = tmp./sqrt(tvar(1:end-1,1));
time3 = etime(clock,t0);

end; % end of t-stat calculations

% return stuff
results.y = y;
results.nobs = nobs; 
results.nvar = nvar;
results.rmax = rmax;      
results.rmin = rmin;
results.lflag = ldetflag;
results.order = order;
results.miter = miter;
results.time = etime(clock,timet);
results.time1 = time1;
results.time2 = time2;
results.time3 = time3;
results.time4 = time4;
results.lndet = detval;

function [rmin,rmax,convg,maxit,detval,ldetflag,eflag,order,iter,options] = sar_parse(info)
% PURPOSE: parses input arguments for sar model
% ---------------------------------------------------
%  USAGE: [rmin,rmax,convg,maxit,detval,ldetflag,eflag,order,iter,options] = sar_parse(info)
% where info contains the structure variable with inputs 
% and the outputs are either user-inputs or default values
% ---------------------------------------------------

% set defaults
options = zeros(1,18); % optimization options for fminbnd
options(1) = 0; 
options(2) = 1.e-6; 
options(14) = 500;

eflag = 0;     % default to not computing eigenvalues
ldetflag = 1;  % default to 1999 Pace and Barry MC determinant approx
order = 50;    % there are parameters used by the MC det approx
iter = 30;     % defaults based on Pace and Barry recommendation
rmin = -1;     % use -1,1 rho interval as default
rmax = 1;
detval = 0;    % just a flag
convg = 0.0001;
maxit = 500;

fields = fieldnames(info);
nf = length(fields);
if nf > 0
    
 for i=1:nf
    if strcmp(fields{i},'rmin')
        rmin = info.rmin;  eflag = 0;
    elseif strcmp(fields{i},'rmax')
        rmax = info.rmax; eflag = 0;
    elseif strcmp(fields{i},'convg')
        options(2) = info.convg;
    elseif strcmp(fields{i},'maxit')
        options(14) = info.maxit;  
    elseif strcmp(fields{i},'lndet')
    detval = info.lndet;
    ldetflag = -1;
    eflag = 0;
    rmin = detval(1,1);
    nr = length(detval);
    rmax = detval(nr,1);
    elseif strcmp(fields{i},'lflag')
        tst = info.lflag;
        if tst == 0,
        ldetflag = 0; % compute full lndet, no approximation
        elseif tst == 1,
        ldetflag = 1; % use Pace-Barry approximation
        elseif tst == 2,
        ldetflag = 2; % use spline interpolation approximation
        else
        error('sar: unrecognizable lflag value on input');
        end;
    elseif strcmp(fields{i},'order')
        order = info.order;  
    elseif strcmp(fields{i},'eig')
        eflag = info.eig;  
    elseif strcmp(fields{i},'iter')
        iter = info.iter; 
    end;
 end;
 
else, % the user has input a blank info structure
      % so we use the defaults
end; 

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 % do eigenvalue calculations
t0 = clock;
opt.tol = 1e-3; opt.disp = 0;
lambda = eigs(sparse(W),speye(n),1,'SR',opt);  
rmin = real(1/lambda);   
rmax = 1.0;
time2 = etime(clock,t0);
else % use rmin,rmax arguments from input or defaults -1,1
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: wrgon lndet input argument');
        end;
        [n1,n2] = size(detval);
        if n2 ~= 2
            error('sar: wrong sized lndet input argument');
        elseif n1 == 1
            error('sar: wrong sized lndet input argument');
        end;          
end;