{smcl}
{* 21feb2005/8mar2006}{...}
{hline}
help for {hi:spautoc}
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{title:Spatial autocorrelation (Moran and Geary measures)}
{p 8 17 2}
{cmd:spautoc}
{it:xvar}
{it:neivar}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}]
[, {cmdab:w:eight(}{it:strvar})
{cmdab:lmea:n(}{it:newvar}{cmd:)}
{cmdab:lmed:ian(}{it:newvar}{cmd:)}]
{title:Description}
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{cmd:spautoc} calculates Moran and Geary measures of spatial autocorrelation
for a spatial variable {it:xvar} and neighbourhood information given by
{it:neivar}.
{title:Remarks}
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For n values of a spatial variable x defined for various locations,
which might be points or areas, calculate the deviations
_
z = x - x
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and for pairs of locations i and j, define a weights matrix
W = ( w )
ij
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describing which locations are neighbours in some precise sense.
For example, a weight might be assigned as 1 if i and j are contiguous areas
and 0 otherwise; or it might be a function of the distance between
i and j and/or the length of boundary shared by i and j.
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The Moran measure of autocorrelation is
n n n n n 2
n ( SUM SUM z w z ) / ( 2 (SUM SUM w ) SUM z )
i=1 j=1 i ij j i=1 j=1 ij i=1 i
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and the Geary measure of autocorrelation is
n n 2 n n n 2
(n - 1) ( SUM SUM w (z - z ) ) / ( 4 (SUM SUM w ) SUM z )
i=1 j=1 ij i j i=1 j=1 ij i=1 i
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and these measures may used to test the null hypothesis of no spatial
autocorrelation, using both a sampling distribution assuming that x
is normally distributed and a sampling distribution assuming randomisation,
that is, we treat the data as one of n! assignments of the n values to
the n locations.
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{cmd:spautoc} avoids the use of Stata's matrix language, to avoid any limit
on the number of locations which that would imply, and to avoid the need
to handle a matrix that would typically be very sparse. The price
paid is a data structure for the neighbourhood information that is
idiosyncratic by Stata standards.
{p 4 4 2}Here is a toy example:
area neighbours value
{hline 4} {hline 10} {hline 5}
1 2, 3 and 4 3
2 1 and 4 2
3 1 and 4 2
4 1, 2 and 3 1
{p 4 4 2}This would be matched by the data
{cmd:_n} (obs no) {cmd:x} (numeric variable) {cmd:nei} (string variable)
{hline 11} {hline 20} {hline 21}
1 3 "2 3 4"
2 2 "1 4"
3 2 "1 4"
4 1 "1 2 3"
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That is, {cmd:nei} contains the observation numbers of the neighbours of
the location in the current observation, separated by spaces. Therefore,
the data must be in precisely this sort order when {cmd:spautoc} is called.
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Note various assumptions made here:
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1. The neighbourhood information can be fitted into at most a {cmd:str244}
variable.
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2. If i neighbours j, then j also neighbours i and both facts are
specified.
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By default this data structure implies that those locations listed
have weights in W that are 1, while all other pairs of locations are not
neighbours and have weights in W that are 0.
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If the weights in W are not binary (1 or 0), use the {cmd:weights()} option.
The variable specified must be another string variable.
{cmd:_n} (obs no) {cmd:nei} (string variable) {cmd:weight} (string variable)
{hline 11} {hline 21} {hline 24}
1 "2 3 4" ".1234 .5678 .9012"
etc.
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The weights matrix need not be symmetric.
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Again, the assumption here is that these weights can be fitted into
at most a {cmd:str244} variable.
{title:Options}
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{cmd:weight()} specifies a string variable containing numeric weights,
as explained above.
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{cmd:lmean()} and {cmd:lmedian()} specify that new variables
should be generated containing local means and local medians, that
is, means and medians of the neighbours of each location (not
including that location). Any weights specified will be used in
the calculation.
{title:Examples}
{p 4 8 2}{cmd:. spautoc cows nei}
{title:References}
{p 4 8 2}
Cliff, A.D. and Ord, J.K. 1973. {it:Spatial autocorrelation.} London: Pion.
{p 4 8 2}
Cliff, A.D. and Ord, J.K. 1981. {it:Spatial processes: models and applications.}
London: Pion.
{title:Author}
{p 4 4 2}Nicholas J. Cox, Durham University, U.K.{break}
n.j.cox@durham.ac.uk
{title:Also see}
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On-line: help for {help dupneigh}, {help neigh}, {help numids}