Agriculture Reference
In-Depth Information
>
prod98
<
- as.geodata(soja98, coords.col¼1:2, data.col¼"PH")
>
locat
<
- expand.grid(seq(min(soja98$X),max(soja98$X),l
¼
100),
+ seq(min(soja98$Y),max(soja98$Y),l
¼
100))
>
kc
<
- krige.conv(prod98, loc
¼
locat, krige
¼
krige.control(type.krige
¼
+ "ok",cov.pars
¼
c(1,20)))
>
image(kc,col
¼
gray((5:50)/50),axes
¼
T)
>
contour(kc,axes
¼
T,add
¼
T)
>
points(prod98,cex.min
¼
0.1,cex.max
¼
1.5,pch
¼
19,add
¼
T)
More details of the geoR package can be found in the reference manual at
http://
1.4.3.2 Lattice Data Analysis
Let (
y
(z
1
),
y
(z
2
),
,
y
(z
n
)) denote lattice data at
n
sites. As is the case for
geostatistical data, it is useful to regard lattice data as derived from a single
realization of a random process. However, in contrast to geostatistical data, a lattice
process is often observed at every site of the domain under investigation.
In lattice analysis, the sites are generally represented by regions. The observation
for each region is operationally considered to have taken place at its centroid. To
appropriately model lattice data, a neighborhood must be defined for each site. For
example, if the sites are contiguous regions (e.g., counties or other administrative
units), then a site
...
s neighbors are commonly defined as those with which it shares a
'
border.
The most popular approaches used in the statistical analysis of lattice data are the
conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models.
A starting point for the definition of a CAR model is to consider the spatial
Markov property defined as
Pr
y
z
ðÞy
z
j
,
j
¼ Pr
y
z
ðÞy
z
j
, z
j
2 NðÞ
,
j
;
6
¼
i
6
¼
i
ð
1
:
44
Þ
where
N
(
i
) is the set of all neighbors of site z
i
. The condition in Eq. (
1.44
) shows
that the probability of a phenomenon occurring in z
i
depends only on occurrences of
the same phenomenon in this neighborhood. If the spatial process satisfies the
assumption in Eq. (
1.44
), the process
y
(z) is called Markov random field (MRF).
Consider a continuous variable. A spatial model that satisfies the first-order
Markov property in Eq. (
1.44
) is the auto-normal or conditional autoregressive
model (CAR, Besag
1974
). It assumes that the conditional density functions of each
random variable with respect to the others is Gaussian and can be expressed as
Search WWH ::
Custom Search