[R-sig-Geo] residuals of gwr and ols

[Roger Bivand]

On Tue, 12 Feb 2013, Milan Sharma wrote:

> Dear all,

> I fitted gwr and ols and I was expecting that residuals for gwr will 
> be smaller than that of ols. But, my result  (copied below) is kind of 
> mixed. Some ols residuals are smaller than gwr, some are not.

In general, unless you are basing your understanding of GWR on Paez et al.
2011, your work should be desk rejected by any reputable journal. They 
specifically state that their tests on GWR with n < 160 show that it 
should never be used on data sets of this size or smaller.

My guess would be that there is no non-stationarity in your covariates. 
You could try the gwrr package to check whether your output is being 
driven by induced collinearity (when the bandwidth is small, the kernel 
downweights all but very close observations, which, given positive spatial 
autocorrelation, will have very similar values on the response and 
covariates).

Roger

> Is it because of small samples? or anything else?
> Milan
>      -0.136016648  1.101457156 -1.578367473  0.105823902  2.564813044
>  [6]  2.180718179  0.045675369 -4.507514803 -1.292321914 -2.485451077
> [11] -0.368047977  1.691501792  2.684117999 -0.556613862 -0.289227113
> [16] -0.155533739 -0.021840369 -0.021840369  2.173046587 -3.416457929
> [21]  0.151411146  0.724629941 -2.876030643  1.023334130  0.918531627
> [26] -1.376270203 -2.474632837  3.183919800 -0.177862432  0.022877635
> [31] -2.141706576 -0.869152125  0.319373467 -1.648694491 -2.915420257
> [36]  0.116417634 -2.337159270  1.938201163  2.738647354  2.644367167
> [41]  2.550086985 -1.423905997  1.982824142  1.790273664 -0.748049508
> [46] -3.107517323 -3.971182584  0.681914115  3.726619604  4.143072934
> [51] -2.249552558 -2.790999526 -0.005880056  1.960107982  0.604239516
> [56]  0.926852572  1.894691740  1.249465628 -0.917200873 -2.698823361
> [61] -1.599490524  1.874868510  2.846065630 -0.201141839  1.391264890
> [66] -2.591306751
>> res.adpt$SDF$gwr.e
>  [1]  0.003574804  0.401173060 -0.098673920 -0.398602560  0.388960727
>  [6]  1.176528697  1.249810375 -3.083140986  0.875553761 -2.149192311
> [11] -0.104606457 -0.027614179  0.571800125 -2.374157297  0.742099604
> [16]  0.287192964 -0.250966065 -0.402284402  0.189696242 -1.393609850
> [21]  0.051342940  0.566711177 -1.692136783  1.043811603 -0.771654807
> [26] -0.055346083  0.122587447  1.031404349  0.173498890 -0.033888702
> [31] -0.301781064 -0.189544419 -0.148000181 -1.282745180 -1.208561844
> [36]  0.499945507 -0.199431072  0.152781739  0.351565548  3.161790009
> [41] -0.105187439  0.166309039  0.581371048 -0.140668745 -0.982077223
> [46] -0.657665352 -1.891088552 -0.496321984  1.332209404  1.874694434
> [51]  0.079247599 -1.043226527  0.523089114  0.420164685  0.021321941
> [56]  1.907471032  1.183379281  2.591380013 -0.333712724 -0.996557548
> [61] -0.214775620 -0.266639348  0.208623714  0.367054376 -0.013960720
> [66]  0.196095634
>
>
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-- 
Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no