dgp.spq {spqdep} | R Documentation |
Generation of qualitative process with spatial structure
Description
The purpose of the function dgp.spq
is to generate a random dataset
with the dimensions and spatial structure decided by the user. This function may be
useful in pure simulation experiments or with the aim of showing specific properties
and characteristics of a spatial qualitative dataset.
Usage
dgp.spq(listw = listw, p = p, rho = rho, control = list())
Arguments
listw |
A |
p |
a vector with the percentage of elements of each categories. The lengths must be the number of categories. The sum of the elements of vector must be 1. |
rho |
the level of spatial dependence (values between -1 y 1) |
control |
List of additional control arguments. See control argument section. |
Details
In order to obtain categorical random variables with controlled degrees
of spatial dependence, we have designed a two- stage data generating process:
Firstly, we simulate autocorrelated data using the following model:
Y = (I - \rho W)^{-1} \epsilon
where \epsilon = N(0,1)
I is the N \times N
identity matrix, \rho
is a parameter
of spatial dependence, and W is a connectivity matrix that
determines the set of spatial relationships among points.
In the second step of the data generation process, the continuous spatially
autocorrelated variable Y is used to define a discrete spatial process
as follows. Let b_{ij}
be defined by:
p(Y \leq b_{ij})= {i \over j} \ \ \ with \ \ \ i<j
Let A =\{a_1,a_2,...,a_k\}
and define the discrete spatial process as:
X_s=a_1 \ \ \ if \ \ \ Y_s \leq b_{1k}
X_s=a_i \ \ \ if \ \ \ b_{i-1k} < Y_s \leq b_{ik}
X_s=a_k \ \ \ if \ \ \ Y_s > b_{k-1k}
Value
a factor of length N (listw
is a matrix of order (NxN)) with
levels the first capital letters: "A", "B", ....
The description of the DGP is available in Páez et al. 2010 (pag 291) and in details section.
Control arguments
- seedinit
seed to generate the data sets
Author(s)
Fernando López | fernando.lopez@upct.es |
Román Mínguez | roman.minguez@uclm.es |
Antonio Páez | paezha@gmail.com |
Manuel Ruiz | manuel.ruiz@upct.es |
References
Ruiz M, López FA, A Páez. (2010). Testing for spatial association of qualitative data using symbolic dynamics. Journal of Geographical Systems. 12 (3) 281-309
See Also
Q.test
, Q.map.test
, sp.runs.test
, scan.test
Examples
#
N <- 100
cx <- runif(N)
cy <- runif(N)
coor <- cbind(cx,cy)
p <- c(1/6,3/6,2/6)
rho = 0.5
listw <- spdep::nb2listw(spdep::knn2nb(spdep::knearneigh(cbind(cx,cy), k = 4)))
xf <- dgp.spq(list = listw, p = p, rho = rho)
data(provinces_spain)
listw <- spdep::poly2nb(provinces_spain, queen = FALSE)
p <- c(1/6,3/6,2/6)
rho = 0.9
xf <- dgp.spq(p = p, listw = listw, rho = rho)
provinces_spain$xf <- xf
plot(provinces_spain["xf"])