1
Matlab:地理加权回归模型命令简介
“gwr.m”函数命令的调用方式如下所示:
#%% 地理加权回归模型MATLAB程序代码如下
>> help gwr
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
---------------------------------------------------
选项含义为:
2
高斯距离权重函数地理加权回归模型
选择高斯距离权重函数进行地理加权回归模型代码如下:
%--------------------------------------------------------------------------
%计量经济学服务中心《空间计量经济学及Matlab应用》
%--------------------------------------------------------------------------
%高斯距离权重函数地理加权回归模型
% load the Anselin data set
% 导入数据
load anselin.dat;
y = anselin(:,1);
nobs = length(y);
x = [ones(nobs,1) anselin(:,2:3)];
[nobs nvar] = size(x);
north = anselin(:,4);
east = anselin(:,5);
vnames = strvcat('crime','constant','income','hvalue');
%--------------------------------------------------------------------------
%计量经济学服务中心《空间计量经济学及Matlab应用》
%--------------------------------------------------------------------------
% Gaussian distance weighting
%高斯距离权重函数地理加权回归模型
info.dtype = 'gaussian';
tic; result1 = gwr(y,x,east,north,info); toc;
prt(result1,vnames);
结果为:
14-49空间单元的参数估计结果不再展现,完整结果可以查看后面代码。
3
三种不同空间权重矩阵参数比较
命令为:
%--------------------------------------------------------------------------
%计量经济学服务中心《空间计量经济学及Matlab应用》
%--------------------------------------------------------------------------
% plot results for comparison (see also plt)
tt=1:nobs;
subplot(3,1,1),
plot(tt,result1.beta(:,1),tt,result2.beta(:,1),'--',tt,result3.beta(:,1),'-.');
legend('Gaussian','Exponential','tricube');
ylabel('Constant term');
subplot(3,1,2),
plot(tt,result1.beta(:,2),tt,result2.beta(:,2),'--',tt,result3.beta(:,2),'-.');
legend('Gaussian','Exponential','tricube');
ylabel('Household income');
subplot(3,1,3),
plot(tt,result1.beta(:,3),tt,result2.beta(:,3),'--',tt,result3.beta(:,3),'-.');
legend('Gaussian','Exponential','tricube');
ylabel('House value');
%--------------------------------------------------------------------------
%计量经济学服务中心《空间计量经济学及Matlab应用》
%--------------------------------------------------------------------------
结果为:
4
指数距离权重函数地理加权回归模型
2-49空间单元参数估计结果不再展现
5
立方距离权重函数地理加权回归模型
2-49空间单元参数估计结果不再展现
高斯距离权重函数地理加权回归模型1-49地理加权回归参数估计结果为:
%--------------------------------------------------------------------------
%计量经济学服务中心《空间计量经济学及Matlab应用》
%--------------------------------------------------------------------------
Vname =
Variable
Geometrically weighted regression estimates
Dependent Variable = crime
R-squared = 0.9418
Rbar-squared = 0.9393
Bandwidth = 0.6518
# iterations = 17
Decay type = gaussian
Nobs, Nvars = 49, 3
***************************************
Obs = 1, x-coordinate= 42.3800, y-coordinate= 35.6200, sige= 3.4125
Variable Coefficient t-statistic t-probability
constant 51.197363 9.212794 0.000000
income -0.461038 -1.678857 0.099547
hvalue -0.434237 -3.693955 0.000556
Obs = 2, x-coordinate= 40.5200, y-coordinate= 36.5000, sige= 6.7847
Variable Coefficient t-statistic t-probability
constant 63.564308 9.955778 0.000000
income -0.369902 -0.991321 0.326399
hvalue -0.683553 -4.656428 0.000025
Obs = 3, x-coordinate= 38.7100, y-coordinate= 36.7100, sige= 8.6457
Variable Coefficient t-statistic t-probability
constant 72.673672 9.395151 0.000000
income -0.161106 -0.269269 0.788853
hvalue -0.826921 -5.367996 0.000002
Obs = 4, x-coordinate= 38.4100, y-coordinate= 33.3600, sige= 5.2400
Variable Coefficient t-statistic t-probability
constant 81.381328 7.772343 0.000000
income 0.149437 0.194405 0.846662
hvalue -1.073198 -9.228621 0.000000
Obs = 5, x-coordinate= 44.0700, y-coordinate= 38.8000, sige= 0.6985
Variable Coefficient t-statistic t-probability
constant 46.737222 13.309854 0.000000
income -0.689933 -2.949392 0.004869
hvalue -0.223718 -4.843363 0.000013
Obs = 6, x-coordinate= 41.1800, y-coordinate= 39.8200, sige= 2.7853
Variable Coefficient t-statistic t-probability
constant 57.351504 10.979281 0.000000
income -0.971958 -2.506024 0.015580
hvalue -0.310679 -3.233765 0.002189
Obs = 7, x-coordinate= 38.0000, y-coordinate= 40.0100, sige= 2.2903
Variable Coefficient t-statistic t-probability
constant 79.683414 14.237667 0.000000
income -1.990153 -3.856516 0.000336
hvalue -0.402011 -2.423975 0.019088
Obs = 8, x-coordinate= 39.2800, y-coordinate= 43.7500, sige= 0.6613
Variable Coefficient t-statistic t-probability
constant 79.374676 10.227137 0.000000
income -3.294825 -6.536725 0.000000
hvalue 0.059876 0.936349 0.353686
Obs = 9, x-coordinate= 34.9100, y-coordinate= 39.6100, sige= 2.8503
Variable Coefficient t-statistic t-probability
constant 72.218154 10.454632 0.000000
income -1.988247 -2.094491 0.041410
hvalue -0.063618 -0.350051 0.727801
Obs = 10, x-coordinate= 36.4200, y-coordinate= 47.6100, sige= 0.3660
Variable Coefficient t-statistic t-probability
constant 54.058540 23.753628 0.000000
income -1.719995 -13.667469 0.000000
hvalue 0.033105 1.405730 0.166114
Obs = 11, x-coordinate= 34.4600, y-coordinate= 48.5800, sige= 0.6241
Variable Coefficient t-statistic t-probability
constant 55.363293 25.304369 0.000000
income -1.767205 -17.192082 0.000000
hvalue 0.019889 0.631315 0.530769
Obs = 12, x-coordinate= 32.6500, y-coordinate= 49.6100, sige= 1.1183
Variable Coefficient t-statistic t-probability
constant 54.800116 18.118969 0.000000
income -1.673002 -11.485387 0.000000
hvalue 0.000544 0.009703 0.992298
Obs = 13, x-coordinate= 29.9100, y-coordinate= 50.1100, sige= 1.8016
Variable Coefficient t-statistic t-probability
constant 49.090996 11.226397 0.000000
income -1.206984 -4.006017 0.000209
hvalue -0.061675 -0.484850 0.629943
Obs = 14, x-coordinate= 27.8000, y-coordinate= 51.2400, sige= 1.1740
Variable Coefficient t-statistic t-probability
constant 42.025898 8.693270 0.000000
income -1.049190 -2.353344 0.022662
hvalue 0.034076 0.168603 0.866803
Obs = 15, x-coordinate= 25.2400, y-coordinate= 50.8900, sige= 0.5074
Variable Coefficient t-statistic t-probability
constant 42.023487 9.931361 0.000000
income -2.035189 -4.285382 0.000085
hvalue 0.541132 2.264220 0.028021
Obs = 16, x-coordinate= 27.9300, y-coordinate= 48.4400, sige= 1.8858
Variable Coefficient t-statistic t-probability
constant 50.858338 11.840157 0.000000
income -0.970544 -2.036648 0.047108
hvalue -0.163386 -0.772214 0.443696
Obs = 17, x-coordinate= 31.9100, y-coordinate= 46.7300, sige= 1.9074
Variable Coefficient t-statistic t-probability
constant 63.935965 23.149085 0.000000
income -1.851883 -8.000266 0.000000
hvalue -0.065988 -0.739344 0.463225
Obs = 18, x-coordinate= 35.9200, y-coordinate= 43.4400, sige= 1.0826
Variable Coefficient t-statistic t-probability
constant 61.515865 14.934047 0.000000
income -1.892916 -5.019187 0.000007
hvalue 0.013062 0.157654 0.875377
Obs = 19, x-coordinate= 33.4600, y-coordinate= 43.3700, sige= 2.7225
Variable Coefficient t-statistic t-probability
constant 65.413374 17.271159 0.000000
income -2.860764 -4.125718 0.000143
hvalue 0.275876 1.222495 0.227368
Obs = 20, x-coordinate= 33.1400, y-coordinate= 41.1300, sige= 5.0673
Variable Coefficient t-statistic t-probability
constant 66.620907 8.186391 0.000000
income -1.619154 -1.246106 0.218651
hvalue -0.110761 -0.311593 0.756672
Obs = 21, x-coordinate= 31.6100, y-coordinate= 43.9500, sige= 2.6677
Variable Coefficient t-statistic t-probability
constant 68.176378 23.711500 0.000000
income -3.351877 -5.596394 0.000001
hvalue 0.449873 2.009607 0.049996
Obs = 22, x-coordinate= 30.4000, y-coordinate= 44.1000, sige= 2.6080
Variable Coefficient t-statistic t-probability
constant 68.744965 23.673393 0.000000
income -3.282837 -5.969185 0.000000
hvalue 0.438989 2.053138 0.045418
Obs = 23, x-coordinate= 29.1800, y-coordinate= 43.7000, sige= 2.8861
Variable Coefficient t-statistic t-probability
constant 69.068145 17.943117 0.000000
income -3.326136 -5.847206 0.000000
hvalue 0.468812 1.914810 0.061364
Obs = 24, x-coordinate= 28.7800, y-coordinate= 41.0400, sige= 8.1087
Variable Coefficient t-statistic t-probability
constant 77.271200 7.416531 0.000000
income -3.000189 -3.431018 0.001230
hvalue 0.167212 0.398976 0.691645
Obs = 25, x-coordinate= 27.3100, y-coordinate= 43.2300, sige= 4.0434
Variable Coefficient t-statistic t-probability
constant 67.368725 9.525528 0.000000
income -3.069044 -3.468780 0.001099
hvalue 0.363366 0.754567 0.454120
Obs = 26, x-coordinate= 24.9600, y-coordinate= 42.6700, sige= 2.5678
Variable Coefficient t-statistic t-probability
constant 61.306231 5.851086 0.000000
income 0.006368 0.004423 0.996489
hvalue -1.071954 -1.162870 0.250514
Obs = 27, x-coordinate= 25.9000, y-coordinate= 41.2100, sige= 6.2344
Variable Coefficient t-statistic t-probability
constant 59.819535 4.913992 0.000010
income -1.697764 -1.212751 0.231040
hvalue -0.138505 -0.170688 0.865172
Obs = 28, x-coordinate= 25.8500, y-coordinate= 39.3200, sige= 5.2496
Variable Coefficient t-statistic t-probability
constant 45.265068 2.954417 0.004803
income -2.135825 -1.284057 0.205161
hvalue 0.591982 0.883602 0.381226
Obs = 29, x-coordinate= 27.4900, y-coordinate= 41.0900, sige= 8.3927
Variable Coefficient t-statistic t-probability
constant 72.899979 6.290465 0.000000
income -3.258441 -2.970188 0.004599
hvalue 0.307426 0.555503 0.581078
Obs = 30, x-coordinate= 28.8200, y-coordinate= 38.3200, sige= 6.0199
Variable Coefficient t-statistic t-probability
constant 80.285094 7.449344 0.000000
income -0.676605 -0.717337 0.476572
hvalue -0.618717 -2.097025 0.041175
Obs = 31, x-coordinate= 30.9000, y-coordinate= 41.3100, sige= 5.9421
Variable Coefficient t-statistic t-probability
constant 68.118651 7.883805 0.000000
income -1.803631 -2.133632 0.037905
hvalue 0.059481 0.178766 0.858859
Obs = 32, x-coordinate= 32.8800, y-coordinate= 39.3600, sige= 4.5678
Variable Coefficient t-statistic t-probability
constant 58.637810 7.764366 0.000000
income 0.495270 0.487439 0.628121
hvalue -0.388646 -1.896549 0.063791
Obs = 33, x-coordinate= 30.6400, y-coordinate= 39.7200, sige= 5.1218
Variable Coefficient t-statistic t-probability
constant 70.568456 9.798923 0.000000
income -0.218856 -0.335471 0.738702
hvalue -0.448133 -1.933095 0.059014
Obs = 34, x-coordinate= 30.3500, y-coordinate= 38.2900, sige= 3.1096
Variable Coefficient t-statistic t-probability
constant 80.030552 12.784499 0.000000
income 0.036213 0.068159 0.945936
hvalue -0.786849 -5.179351 0.000004
Obs = 35, x-coordinate= 32.0900, y-coordinate= 36.6000, sige= 3.5543
Variable Coefficient t-statistic t-probability
constant 63.967857 8.009308 0.000000
income 0.337987 0.382854 0.703484
hvalue -0.492099 -3.556112 0.000846
Obs = 36, x-coordinate= 34.0800, y-coordinate= 37.6000, sige= 2.7764
Variable Coefficient t-statistic t-probability
constant 67.746908 11.590897 0.000000
income -0.755463 -0.934476 0.354641
hvalue -0.243619 -2.063643 0.044369
Obs = 37, x-coordinate= 36.1200, y-coordinate= 37.1300, sige= 5.2909
Variable Coefficient t-statistic t-probability
constant 65.979447 8.493093 0.000000
income -0.082415 -0.089905 0.928729
hvalue -0.420816 -3.386697 0.001402
Obs = 38, x-coordinate= 36.3000, y-coordinate= 37.8500, sige= 4.1933
Variable Coefficient t-statistic t-probability
constant 70.241135 9.853816 0.000000
income -0.851484 -1.007494 0.318647
hvalue -0.331039 -2.669386 0.010278
Obs = 39, x-coordinate= 36.4000, y-coordinate= 35.9500, sige= 7.5290
Variable Coefficient t-statistic t-probability
constant 60.058183 6.254403 0.000000
income 1.346573 1.335110 0.188010
hvalue -0.676333 -5.334379 0.000002
Obs = 40, x-coordinate= 35.6000, y-coordinate= 35.7200, sige= 6.1315
Variable Coefficient t-statistic t-probability
constant 59.441973 6.623725 0.000000
income 1.197840 1.197762 0.236772
hvalue -0.582346 -4.668150 0.000024
Obs = 41, x-coordinate= 34.6600, y-coordinate= 35.7600, sige= 4.4315
Variable Coefficient t-statistic t-probability
constant 64.924831 8.369141 0.000000
income 0.077997 0.082850 0.934308
hvalue -0.395195 -3.149189 0.002788
Obs = 42, x-coordinate= 33.9200, y-coordinate= 36.1500, sige= 2.7971
Variable Coefficient t-statistic t-probability
constant 68.995022 11.150905 0.000000
income -0.721014 -0.903935 0.370452
hvalue -0.276558 -2.460420 0.017450
Obs = 43, x-coordinate= 30.4200, y-coordinate= 34.0800, sige= 1.6449
Variable Coefficient t-statistic t-probability
constant 42.987174 3.069301 0.003493
income -0.130118 -0.085542 0.932179
hvalue -0.015665 -0.079318 0.937103
Obs = 44, x-coordinate= 28.2600, y-coordinate= 30.3200, sige= 1.5262
Variable Coefficient t-statistic t-probability
constant 38.427625 7.366893 0.000000
income -0.618892 -1.442734 0.155458
hvalue -0.192297 -0.847771 0.400688
Obs = 45, x-coordinate= 29.8500, y-coordinate= 27.9400, sige= 1.2787
Variable Coefficient t-statistic t-probability
constant 31.201319 5.045446 0.000007
income -0.603071 -1.601338 0.115730
hvalue -0.061387 -0.506869 0.614520
Obs = 46, x-coordinate= 28.2100, y-coordinate= 27.2700, sige= 1.5429
Variable Coefficient t-statistic t-probability
constant 27.113505 4.535402 0.000037
income -0.413367 -1.327768 0.190407
hvalue -0.043317 -0.586370 0.560318
Obs = 47, x-coordinate= 26.6900, y-coordinate= 24.2500, sige= 0.5555
Variable Coefficient t-statistic t-probability
constant 24.205091 3.701915 0.000542
income -0.278691 -0.853556 0.397505
hvalue -0.032273 -0.812649 0.420350
Obs = 48, x-coordinate= 25.7100, y-coordinate= 25.4700, sige= 0.6629
Variable Coefficient t-statistic t-probability
constant 24.211353 4.173486 0.000122
income -0.271872 -0.991422 0.326350
hvalue -0.034801 -0.854272 0.397112
Obs = 49, x-coordinate= 26.5800, y-coordinate= 29.0200, sige= 1.4185
Variable Coefficient t-statistic t-probability
constant 30.052990 5.675101 0.000001
income -0.431664 -1.644271 0.106522
hvalue -0.081504 -0.934733 0.354510
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