spmat idistance

[Dario Maimone Ansaldo Patti]

Dear All,

I am working to create an inverse distance weights Matrix for some spatial analysis. First I use:

spmat idistance dW longitude latitude, id(_ID) dfunction(rhaversine) norm(row)

Then, I want to create a distance cutoff, using 1000 km limits. Therefore, I write:

spmat idistance dW1000 longitude latitude, id(_ID) dfunction(rhaversine) norm(row) vtruncated(1/1000)

What is not clear to me is why I get a warning saying "spatial-weighting matrix contains 37 islands"

Of course I do not have 37 islands in my dataset. Moreover, I noticed that if I reduce the cutoff, say 1/500 the number of "supposed" islands increases to 63. Differently, it reduces if I set 1/2000.

As far as I understood, if I use vtruncated option, I set the weights of neighbors of each spatial unit to zero if they lie 1000 or more
km from a given unit. Therefore, why I get the warning above, which does not appear when I do not set vtruncated?

Thanks,

Dario

[Scott Merryman]

As far as I understood, if I use vtruncated option, I set the weights of neighbors of each spatial unit to zero if they lie 1000 or more
km from a given unit.

Yes and those areas that are islands have zero weights and therefore have zero links to other areas.

. clear*

. use pollute
(Dataset used in the help files for spmat, spreg, spivreg)

. sort longi

. keep in 1/10
(531 observations deleted)

. replace id = _n
(10 real changes made)

First estimate weight matrix without truncation:

. spmat idistance dobj longitude latitude, id(id) dfunction(dhaversine) replace

. spmat getmatrix dobj mymat

Display the calculated distance:

. mata:  1:/mymat
[symmetric]
                  1             2             3             4             5             6             7             8             9            10
     +---------------------------------------------------------------------------------------------------------------------------------------------+
   1 |            .                                                                                                                                |
   2 |  858.7211768             .                                                                                                                  |
   3 |  217.3526469   642.4249421             .                                                                                                    |
   4 |  452.5332616   407.5172598   235.4009689             .                                                                                      |
   5 |  293.1122069   568.7706027   76.25031625   161.2593068             .                                                                        |
   6 |  154.9431458    1008.76316   366.4825122   601.3442823   440.2488704             .                                                          |
   7 |  113.4742444   962.1936669   320.2569883    554.694974     393.49429   47.53902351             .                                            |
   8 |  1037.230999   183.4193258   820.1033986   584.7234386    745.255426   1185.366789   1138.398586             .                              |
   9 |  73.19565657   869.9652546   231.2181966   462.6921079   301.6045875   144.2963109   96.88165697   1044.712794             .                |
  10 |  162.8890043   717.9220322   91.29359608   311.3952831   151.6592864   295.7010176   248.2181349   891.9305749   152.9132906             .  |
     +---------------------------------------------------------------------------------------------------------------------------------------------+

. spmat sum dobj, link detail

Summary of spatial-weighting object dobj
-----------------------------------------
        Matrix |             Description
---------------+-------------------------
    Dimensions |                 10 x 10
     Stored as |                 10 x 10
 Links         |
         total |                      90
           min |                       9
          mean |                       9
           max |                       9
-----------------------------------------

Tabulation of links
-------------------------
 # of links |        Obs
------------+------------
          9 |         10
------------+------------
        Sum |         10
-------------------------

Now set truncation at 100 km:

. spmat idistance dobj longitude latitude, id(id) dfunction(dhaversine) replace vtrunc(1/100)
warning: spatial-weighting matrix contains 3 islands

. spmat getmatrix dobj mymat

Display distance - all distances greater than 100 have been set to 0 (and therefore 1/0 is missing) . Note that ares 2, 4, and 8 have zero links to the other areas and are now islands:

. mata:  1:/mymat
[symmetric]
                  1             2             3             4             5             6             7             8             9            10
     +---------------------------------------------------------------------------------------------------------------------------------------------+
   1 |            .                                                                                                                                |
   2 |            .             .                                                                                                                  |
   3 |            .             .             .                                                                                                    |
   4 |            .             .             .             .                                                                                      |
   5 |            .             .   76.25031625             .             .                                                                        |
   6 |            .             .             .             .             .             .                                                          |
   7 |            .             .             .             .             .   47.53902351             .                                            |
   8 |            .             .             .             .             .             .             .             .                              |
   9 |  73.19565657             .             .             .             .             .   96.88165697             .             .                |
  10 |            .             .   91.29359608             .             .             .             .             .             .             .  |
     +---------------------------------------------------------------------------------------------------------------------------------------------+

. spmat sum dobj, link detail

Summary of spatial-weighting object dobj
-----------------------------------------
        Matrix |             Description
---------------+-------------------------
    Dimensions |                 10 x 10
     Stored as |                 10 x 10
 Links         |
         total |                      10
           min |                       0
          mean |                       1
           max |                       2
-----------------------------------------

Tabulation of links
-------------------------
 # of links |        Obs
------------+------------
          0 |          3
          1 |          4
          2 |          3
------------+------------
        Sum |         10
-------------------------

Ids of observations with 0 links:
 2 4 8

Ids of observations with 2 links:
 3 7 9

[Dario Maimone Ansaldo Patti]

Thank you very much Scott. Now it is clear