st: set minimum neighbors using spmat and idistance

[rraciborski@stata.com (Rafal Raciborski, StataCorp)]

Lyndsay Boggess <lboggess@gmail.com> has a question about the user-written
-spmat- command:

> I'm having trouble creating inverse distance weights on a population of
> 2054 census tracts. I use the following code in order to create the weights
> for only those tracts within 2 miles (a theoretically derived distance
> pertaining to travelling to crime):

> spmat idistance laweights longitude latitude, id(tract)
> dfunction(dhaversine, miles) vtruncate(1/2)

> This leaves me with 38 islands, which I think is the problem because when I
> try to create spatial lag variables, my variables end up with all values of
> zero. Is there a way to force spmat to make sure that each tract has a
> minimum of 1 neighbor even if it requires to extend the distance
> beyond two miles?

Lyndsay can create the desired spatial-weighting matrix by combining two
spatial-weighting matrices in the way I illustrate below.  For my example,
I will use the ancillary pollute.dta dataset that comes with the sppack suite.

First, I create a spatial-weighting matrix similar to Lyndsay's:

  . use pollute, clear
  . spmat idistance mat1 longitude latitude, id(id) df(dhav, mi) vtr(.01)

We can see that the spatial-weighting matrix contains 26 islands:

  . spmat su mat1, links detail

<snip>
Tabulation of links
-------------------------
 # of links |        Obs
------------+------------
          0 |         26
          1 |         20
          2 |         20
<snip>

Next, I use an undocumented -knn()- option of -spmat idistance- to create
a k-nearest neighbor (KNN) spatial-weighting matrix:

  . spmat idistance mat2 longitude latitude, id(id) df(dhav, mi) knn(1)

That command creates a spatial-weighting matrix in which the nearest neighbor
of each spatial unit is weighted by its inverse distance and all others
receive zero weights.

Now I extract the two spatial-matrices from the spmat objects into Mata

  . spmat get mat1 W1
  . spmat get mat2 W2

and loop through the rows of matrix W1 replacing rows that have all 0's with
the corresponding rows from matrix W2 that contain the nearest-neighbor:

  . mata:
  :         N = rows(W1)
  :         for (i=1; i<=N; i++) {
  >                 if (sum(W1[i,.]:==0) == N) W1[i,.] = W2[i,.]
  >         }
  : end

Next, I put matrix W1 back into the spmat object mat1.  We can see the new
matrix does not have any islands:

  . spmat put mat1 W1, replace
  . spmat su mat1, links detail

<snip>
Tabulation of links
-------------------------
 # of links |        Obs
------------+------------
          1 |         46
          2 |         20
<snip>

Finally, I drop the unneeded objects from Mata memory:

  . spmat drop mat2
  . mata mata drop W1 W2 i N

-- Rafal
rraciborski@stata.com

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