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实用文案
How can I
calculate Moran's I in Stata?
Note:
The
commands
shown
in
this
page
are
user-
written
Stata
commands
that
must be downloaded.
To install the package of
spatial analysis tools, type findit
spatgsa in the command window.
Moran's
I
is
a
measure
of
spatial
autocorrelation--how
related
the
values
of
a
variable
are
based
on
the
locations
where
they
were
measured.
Using
a
set
of
user-written Stata commands, we can
calculate Moran's I in Stata.
We will be using
the
spatwmat command to generate a matrix of weights
based on the locations in
our
data
and
the
spatgsa
command
to
calculate
Moran's
I
or
other
spatial
autocorrelation measures.
Let's look at
an example. Our dataset, ozone, contains ozone
measurements from
thirty-two
locations
in
the
Los
Angeles
area
aggregated
over
one
month.
The
dataset
includes
the
station
number
(station),
the
latitude
and
longitude
of
the
station
(lat
and
lon),
and
the
average
of
the
highest
eight
hour
daily
averages
(av8top).
This
data,
and
other
spatial
datasets,
can
be
downloaded
from
the
University
of
Illinois's
Spatial
Analysis
Lab.
We
can
look
at
a
summary
of
our
location variables to
see the range of locations under consideration.
use /stat/stata/faq/, clear
summarize lat lon
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实用文案
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+----------
----------------------------------------------
lat |
32
34.0146
.2228168
33.6275
34.69012
lon |
32
-117.7078
.5683853
-118.5347
-116.2339
Based
on the minimum and maximum values of these
variables, we can calculate
the
greatest
Euclidean
distance
we
might
measure
between
two
points
in
our
dataset.
display sqrt((34.69012 - 33.6275)^2 +
(-116.2339 - -118.5347)^2)
2.5343326
Knowing this
maximum distance between two points in our data,
we can generate a
matrix
based
on
the
distances
between
points.
In
the
spatwmat
command,
we
name
the weights matrix to be generated, indicate which
of our variables are the x-
and
y-coordinate
variables,
and
provide
a
range
of
distance
values
that
are
of
interest in the band
option.
All of the
distances are of interest in this example, so
we create a band with an upper bound
greater than our largest possible distance. If
we did not care about distances greater
than 2, we could indicate this in the band
option.
spatwmat, name(ozoneweights)
xcoord(lon) ycoord(lat) band(0 3)
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The following matrix has been created:
1. Inverse distance weights
matrix ozoneweights
Dimension:
32x32
Distance band: 0 < d <= 3
Friction
parameter: 1
Minimum distance: 0.1
1st quartile distance: 0.4
Median distance: 0.6
3rd quartile distance: 1.0
Maximum distance: 2.4
Largest minimum distance: 0.50
Smallest maximum distance: 1.23
As described in
the output, the command above generated a matrix
with 32 rows
and 32 columns because our
data includes 32 locations. Each off-diagonal
entry [i, j]
in the matrix is equal to
1/(distance between point i and point j).
Thus, the matrix
entries for pairs of points that are
close together are higher than for pairs of points
that are far apart.
If you
wish to
look at
the matrix, you
can
display
it
with the
matrix list
command. With our matrix of weights, we can now
calculate Moran's I.
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实用文案
spatgsa
av8top, weights(ozoneweights) moran
Measures of global spatial
autocorrelation
Weights matrix
-------------
-------------------------------------------------
Name: ozoneweights
Type:
Distance-based (inverse distance)
Distance band: 0.0 < d <= 3.0
Row-standardized: No
-------
--------------------------------------------------
-----
Moran's I
--------------------------------------------------
------------
Variables |
I
E(I)
sd(I)
z
p-value*
--------------------+------------------------
-----------------
av8top |
0.248
-0.032
0.036
7.679
0.000
----------
--------------------------------------------------
--
*1-tail test
Based on these results, we can reject
the null hypothesis that there is zero spatial
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实用文案
autocorrelation present in the variable
av8top at alpha = .05.
Variations
Binary
Matrix:
If
there
exists
some
threshold
distance
d
such
that
pairs
with
distances less than d are neighbors and
pairs with distances greater than d are not,
you can create a binary neighbors
matrix with the spatwmat command (indicating
bin and setting band to have an upper
bound of d) and use this weights matrix for
calculating Moran's I.
We could do this for d = .75:
spatwmat,
name(ozoneweights) xcoord(lon) ycoord(lat) band(0
.75) bin
The following
matrix has been created:
1.
Distance-based binary weights matrix ozoneweights
Dimension: 32x32
Distance band:
0 < d <= .75
Friction parameter: 1
Minimum
distance: 0.1
1st quartile
distance: 0.4
Median
distance: 0.6
3rd quartile
distance: 1.0
Maximum
distance: 2.4
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实用文案
Largest minimum distance:
0.50
Smallest maximum distance:
1.23
spatgsa av8top,
weights(ozoneweights) moran
Measures of global spatial
autocorrelation
Weights matrix
-------------
-------------------------------------------------
Name: ozoneweights
Type:
Distance-based (binary)
Distance band:
0.0 < d <= 0.75
Row-standardized: No
-----------------------------------------
---------------------
Moran's I
------------------
--------------------------------------------
Variables |
I
E(I)
sd(I)
z
p-value*
-------------------
-+-----------------------------------------
av8top |
0.188
-0.032
0.033
6.762
0.000
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实用文案
------------
--------------------------------------------------
*1-tail test
In
this example, the binary formulation of distance
yields a similar result.
We
can
reject the null hypothesis that
there is zero spatial autocorrelation present in
the
variable av8top at alpha = .05.
Using an
existing matrix: If you have calculated a weights
matrix according to some
other
metric
than
those
available
in
spatwmat
and
wish
to
use
it
in
calculating
Moran's
I,
spatwmat
allows
you
to
read
in
a
Stata
dataset
of
the
required
dimensions
and
format
it
as
a
distance
matrix
that
can
be
used
by
spatgsa.
If
is a dataset with 32 columns and 32
rows, it could be converted to a
weighted matrix aweights to be used in
spatgsa analyzing av8top:
spatwmat using
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