[Gretl-users] matrix sorting: you save the day !

[Riccardo (Jack) Lucchetti]

On Fri, 25 Apr 2008, Franck Nadaud wrote:

> Hello all, Allin & Jack !
>
> You really saved my day ! Let me sum up the situation.
>
> I tested both scripts, they run perfectly !

Just for the record, let me post a version of the script that puts 
together Allin's version and mine.

<script>
function sq_distance(scalar from, series xcoord, series ycoord)
     scalar x = xcoord[from]
     scalar y = ycoord[from]
     matrix ret = (xcoord - x)^2 + (ycoord - y)^2
     return matrix ret
end function

open centroides_amazonas.txt
scalar m = 4
scalar n = $nobs
matrix nnlist = zeros(n, m)
matrix idx = seq(1,n)'

loop for i=1..n -q
     a = sq_distance(i, X_COORD, Y_COORD)
     xind = msortby(idx ~ a, 2)
     nnlist[i,] = (xind[2:m+1,1])'
end loop

print nnlist
</script>


> In fact the msortby command is not documented yet, this is why i had trouble
> to translate the find_nn command of James Lesage.

Isn't it? Which version of gretl are you using? With the current 
version, it is in the reference manual and in the on-line help for functions.

> Now I can compute the right neighborhood matrices from a whole sample and
> subsamples of interest. This is really neat because once they are created we
> can compute spatial autocorrelation coefficients directly using matrix
> commands or via regression with bootstrap of p-values :the moran scatterplots
> of Luc Anselin, which have the interest of providing real confidence
> intervals.
>
> My tests show small differences in results from GEODA and the GRETL scripts I
> use now. This is all good news and I will rest on your input to propose a few
> scripts and/or functions to compute tests for spatial autocorrelation I will
> submit to the community. I hope to write a short note and propose my scripts
> soon so that users can grasp the basics of those tests.

This would be great. Spatial models have become a very hot topic in the 
past few years, and the more we can do in gretl in this direction the better.

> Returning to the matter of neighbors, and programming, there are far smarter
> algorithms than the brute force hack I work on, but think it better to propose
> the simple scripts first before turning on the real smart ones which consist
> in exploring the neighborhood graph with special functions and pointers. More
> of this when the work will be more advanced.
>
> First i will propose the Moran spatial autocorrelation test as a function
> using two types of neighborhood structures: contiguity (common border) and
> nearest neighbors with choice in the number of neighbors on two kind of grids
> too: either square (checkboard) or hexagonal.
>
> Well, thanx very much Allin and Jack !
>
> more about that soon !

Looking forward to it!


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti