【实例简介】地理加权回归(GWR)matlab代码，亲测可用，该代码利用matlab实现了地理加权回归的代码，内附实际算例。
【实例截图】
【核心代码】
function result = gwr(y,x,east,north,info);
% PURPOSE: compute geographically weighted regression
%----------------------------------------------------
% USAGE: results = gwr(y,x,east,north,info)
% where: y = dependent variable vector
% x = explanatory variable matrix
% east = x-coordinates in space
% north = y-coordinates in space
% info = a structure variable with fields:
% info.bwidth = scalar bandwidth to use or zero
% for cross-validation estimation (default)
% info.bmin = minimum bandwidth to use in CV search
% info.bmax = maximum bandwidth to use in CV search
% defaults: bmin = 0.1, bmax = 20
% info.dtype = 'gaussian' for Gaussian weighting (default)
% = 'exponential' for exponential weighting
% = 'tricube' for tri-cube weighting
% info.q = q-nearest neighbors to use for tri-cube weights
% (default: CV estimated)
% info.qmin = minimum # of neighbors to use in CV search
% info.qmax = maximum # of neighbors to use in CV search
% defaults: qmin = nvar 2, qmax = 4*nvar
% ---------------------------------------------------
% NOTE: res = gwr(y,x,east,north) does CV estimation of bandwidth
% ---------------------------------------------------
% RETURNS: a results structure
% results.meth = 'gwr'
% results.beta = bhat matrix (nobs x nvar)
% results.tstat = t-stats matrix (nobs x nvar)
% results.yhat = yhat
% results.resid = residuals
% results.sige = e'e/(n-dof) (nobs x 1)
% results.nobs = nobs
% results.nvar = nvars
% results.bwidth = bandwidth if gaussian or exponential
% results.q = q nearest neighbors if tri-cube
% results.dtype = input string for Gaussian, exponential weights
% results.iter = # of simplex iterations for cv
% results.north = north (y-coordinates)
% results.east = east (x-coordinates)
% results.y = y data vector
%---------------------------------------------------
% See also: prt,plt, prt_gwr, plt_gwr to print and plot results
%---------------------------------------------------
% References: Brunsdon, Fotheringham, Charlton (1996)
% Geographical Analysis, pp. 281-298
%---------------------------------------------------
% NOTES: uses auxiliary function scoref for cross-validation
%---------------------------------------------------
% written by: James P. LeSage 2/98
% University of Toledo
% Department of Economics
% Toledo, OH 43606
% jpl@jpl.econ.utoledo.edu
if nargin == 5 % user options
if ~isstruct(info)
error('gwr: must supply the option argument as a structure variable');
else
fields = fieldnames(info);
nf = length(fields);
% set defaults
[n k] = size(x);
bwidth = 0; dtype = 0; q = 0; qmin = k 2; qmax = 5*k;
bmin = 0.1; bmax = 20.0;
for i=1:nf
if strcmp(fields{i},'bwidth')
bwidth = info.bwidth;
elseif strcmp(fields{i},'dtype')
dstring = info.dtype;
if strcmp(dstring,'gaussian')
dtype = 0;
elseif strcmp(dstring,'exponential')
dtype = 1;
elseif strcmp(dstring,'tricube')
dtype = 2;
end;
elseif strcmp(fields{i},'q')
q = info.q;
elseif strcmp(fields{i},'qmax');
qmax = info.qmax;
elseif strcmp(fields{i},'qmin');
qmin = info.qmin;
elseif strcmp(fields{i},'bmin');
bmin = info.bmin;
elseif strcmp(fields{i},'bmax');
bmax = info.bmax;
end;
end; % end of for i
end; % end of if else
elseif nargin == 4
bwidth = 0; dtype = 0; dstring = 'gaussian';
bmin = 0.1; bmax = 20.0;
else
error('Wrong # of arguments to gwr');
end;
% error checking on inputs
[nobs nvar] = size(x);
[nobs2 junk] = size(y);
[nobs3 junk] = size(north);
[nobs4 junk] = size(east);
result.north = north;
result.east = east;
if nobs ~= nobs2
error('gwr: y and x must contain same # obs');
elseif nobs3 ~= nobs
error('gwr: north coordinates must equal # obs');
elseif nobs3 ~= nobs4
error('gwr: east coordinates must equal # in north');
end;
switch dtype
case{0,1} % bandwidth cross-validation
if bwidth == 0 % cross-validation
options = optimset('fminbnd');
optimset('MaxIter',500);
if dtype == 0 % Gaussian weights
[bdwt,junk,exitflag,output] = fminbnd('scoref',bmin,bmax,options,y,x,east,north,dtype);
elseif dtype == 1 % exponential weights
[bdwt,junk,exitflag,output] = fminbnd('scoref',bmin,bmax,options,y,x,east,north,dtype);
end;
if output.iterations == 500,
fprintf(1,'gwr: cv convergence not obtained in %4d iterations',output.iterations);
else
result.iter = output.iterations;
end;
else
bdwt = bwidth*bwidth; % user supplied bandwidth
end;
case{2} % q-nearest neigbhor cross-validation
if q == 0 % cross-validation
q = scoreq(qmin,qmax,y,x,east,north);
else
% use user-supplied q-value
end;
otherwise
end;
% do GWR using bdwt as bandwidth
[n k] = size(x);
bsave = zeros(n,k);
ssave = zeros(n,k);
sigv = zeros(n,1);
yhat = zeros(n,1);
resid = zeros(n,1);
wt = zeros(n,1);
d = zeros(n,1);
for iter=1:n;
dx = east - east(iter,1);
dy = north - north(iter,1);
d = (dx.*dx dy.*dy);
sd = std(sqrt(d));
% sort distance to find q nearest neighbors
ds = sort(d);
if dtype == 2, dmax = ds(q,1); end;
if dtype == 0, % Gausian weights
wt = stdn_pdf(sqrt(d)/(sd*bdwt));
elseif dtype == 1, % exponential weights
wt = exp(-d/bdwt);
elseif dtype == 2, % tricube weights
wt = zeros(n,1);
nzip = find(d <= dmax);
wt(nzip,1) = (1-(d(nzip,1)/dmax).^3).^3;
end; % end of if,else
wt = sqrt(wt);
% computational trick to speed things up
% use non-zero wt to pull out y,x observations
nzip = find(wt >= 0.01);
ys = y(nzip,1).*wt(nzip,1);
xs = matmul(x(nzip,:),wt(nzip,1));
xpxi = invpd(xs'*xs);
b = xpxi*xs'*ys;
% compute predicted values
yhatv = xs*b;
yhat(iter,1) = x(iter,:)*b;
resid(iter,1) = y(iter,1) - yhat(iter,1);
% compute residuals
e = ys - yhatv;
% find # of non-zero observations
nadj = length(nzip);
sige = (e'*e)/nadj;
% compute t-statistics
sdb = sqrt(sige*diag(xpxi));
% store coefficient estimates and std errors in matrices
% one set of beta,std for each observation
bsave(iter,:) = b';
ssave(iter,:) = sdb';
sigv(iter,1) = sige;
end;
% fill-in results structure
result.meth = 'gwr';
result.nobs = nobs;
result.nvar = nvar;
if (dtype == 0 | dtype == 1)
result.bwidth = sqrt(bdwt);
else
result.q = q;
end;
result.beta = bsave;
result.tstat = bsave./ssave;
result.sige = sigv;
result.dtype = dstring;
result.y = y;
result.yhat = yhat;
% compute residuals and conventional r-squared
result.resid = resid;
sigu = result.resid'*result.resid;
ym = y - mean(y);
rsqr1 = sigu;
rsqr2 = ym'*ym;
result.rsqr = 1.0 - rsqr1/rsqr2; % r-squared
rsqr1 = rsqr1/(nobs-nvar);
rsqr2 = rsqr2/(nobs-1.0);
result.rbar = 1 - (rsqr1/rsqr2); % rbar-squared
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