[R-sig-Geo] Doubt about LMZ.F3GWR.test command in spgwr

[Roger Bivand]

As you should be aware, use of GWR in any circumstances is very insecure, 
and no statistical tests should be trusted. As Paez et al. (2011) 
demonstrate, GWR finds patterned local coefficients in completely random 
data. GWR proponents claim that the local coefficient standard errors are 
then large, but since users happily map and interpret local coefficient 
patterns, the method should be retired until it can definitely be shown to 
perform as advertised.

On Thu, 11 Apr 2013, Diana Gutiérrez wrote:

> Hi.
>
> I'm using GWR method in my research through the spgwr package (by the way,
> thanks to the programmers), and I've already obtained some results; but I
> would like to know why sometimes when I run the LMZ.F3GWR.test command, it
> shows me the following error message:
>
> "Error in  solve.default(t(x) %*% diag(wj) %*% x)
> system is computationally singular: reciprocal condition number =
> 1.81708e-18"
>
> As far as I know, this might be related to the B matrix used in the paper
> by Leung et al (2000), but I don't understand what's happening since I
> obtained the results of the test for certain regressions. I'm using a
> sample of 803 cases and thirteen variables (including the dependent one).
> In the "wrong" regression I use the default gaussian function for the
> weights (fixed kernel) and the AIC for the bandwidth, while I'd got fine
> results for combinations of bi-square function and CV score, and for
> gaussian function and CV score. Does it has to do with choosing the AIC
> (actually, I've tried a bi-square function with AIC, but I couldn't even
> obtain the bandwidth from it)? Does it depends on the value of the
> bandwidth (maybe too small)? or may it be solved in anyway?

As you say, the performance varies depending on the chosen kernel and 
bandwidth - these define the wj vector of weights, so if all very small, 
may erase any variability in the covariances of the x variables. This is 
to be expected, and illustrates how fallible the method can be. The 
functions in this package as far as we know implement the methods 
accurately, so the problem is in the methods not protecting the user from 
arbitrary choices.

Hope this clarifies,

Roger

>
> Thank you beforehand for any comment.
>
> Best regards,
>
> Diana.
>
>

-- 
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