SpatialPOP: package for generation of spatial data along with spatial coordinates and spatially varying model parameters
Introduction
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In this R package, a spatial dataset can be generated
under the assumption that observations are collected from a two
dimensional uniform grid consists of (m2) lattice points
having unit distance between any two neighbouring points along the
horizontal and vertical directions.
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Generation of simulated dataset based on spatially varying regression model
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generation of spatial coordinates of locations
The size of the population is N= m2. The spatial coordinates of the locations of observations can be computed by the following expressions
( Latitudei, Longitudei )= ( mod(i-1,m), [(i-1)/m] ), i= 1,…, m2
where, mod(i-1,m) is the remainder of (i-1) divided by m and [(i-1)/m] is the integer part of the number (i-1)/m
generation of auxiliary variable from uniform distribution
X =runif(N,0,1)
error term drawn independently from normal distribution i.e. N(0,1)
e =rnorm(N, mean=0, sd=1)
generation of spatially varying regression coefficients
B0=(Latitudei+Longitudei)/6
B1=(Latitudei/3)
spatially varying regression model for generating the response variable
Yi = B0( Latitudei,Longitudei ) + B1( Latitudei,Longitudei )*Xi + ei ; i= 1,…, N
# Examples: generate an uniform two dimensional grid of lattice points
library(SpatialPOP)
coord_grid=spatial_grid(c(1:5),c(1:5))
coord_grid=as.data.frame(coord_grid)
names(coord_grid)=cbind("x","y")
coord_grid## x y
## 1 1 1
## 2 2 1
## 3 3 1
## 4 4 1
## 5 5 1
## 6 1 2
## 7 2 2
## 8 3 2
## 9 4 2
## 10 5 2
## 11 1 3
## 12 2 3
## 13 3 3
## 14 4 3
## 15 5 3
## 16 1 4
## 17 2 4
## 18 3 4
## 19 4 4
## 20 5 4
## 21 1 5
## 22 2 5
## 23 3 5
## 24 4 5
## 25 5 5
# Examples: simulated data along with spatial coordinates and spatially varying model parameters
library(SpatialPOP)
coord_grid=spatial_grid(c(1:5),c(1:5))
coord_grid=as.data.frame(coord_grid)
names(coord_grid)=cbind("x","y")
coord_grid## x y
## 1 1 1
## 2 2 1
## 3 3 1
## 4 4 1
## 5 5 1
## 6 1 2
## 7 2 2
## 8 3 2
## 9 4 2
## 10 5 2
## 11 1 3
## 12 2 3
## 13 3 3
## 14 4 3
## 15 5 3
## 16 1 4
## 17 2 4
## 18 3 4
## 19 4 4
## 20 5 4
## 21 1 5
## 22 2 5
## 23 3 5
## 24 4 5
## 25 5 5## [1] 25## [1] 5## Y X latitude longitude B0 B1
## 1 -0.09036574 0.91416432 0 0 0.0000000 0.0000000
## 2 2.00336187 0.24996962 1 0 0.1666667 0.3333333
## 3 -0.40821779 0.32837207 2 0 0.3333333 0.6666667
## 4 0.94348782 0.67031801 3 0 0.5000000 1.0000000
## 5 2.05243495 0.54335601 4 0 0.6666667 1.3333333
## 6 1.38693555 0.21026237 0 1 0.1666667 0.0000000
## 7 -0.27211172 0.05739187 1 1 0.3333333 0.3333333
## 8 2.31933055 0.50813546 2 1 0.5000000 0.6666667
## 9 0.36960799 0.29021876 3 1 0.6666667 1.0000000
## 10 1.08190039 0.47325103 4 1 0.8333333 1.3333333
## 11 0.62293420 0.80592874 0 2 0.3333333 0.0000000
## 12 0.28289018 0.67826374 1 2 0.5000000 0.3333333
## 13 2.24279593 0.89029969 2 2 0.6666667 0.6666667
## 14 2.44773816 0.81179440 3 2 0.8333333 1.0000000
## 15 3.82959508 0.09154762 4 2 1.0000000 1.3333333
## 16 -0.88985431 0.11119743 0 3 0.5000000 0.0000000
## 17 0.75665933 0.79464957 1 3 0.6666667 0.3333333
## 18 3.27277815 0.70842163 2 3 0.8333333 0.6666667
## 19 1.86216707 0.03714377 3 3 1.0000000 1.0000000
## 20 2.64382874 0.47663032 4 3 1.1666667 1.3333333
## 21 1.12548736 0.55948127 0 4 0.6666667 0.0000000
## 22 0.91673155 0.18721948 1 4 0.8333333 0.3333333
## 23 2.32869598 0.73549713 2 4 1.0000000 0.6666667
## 24 1.89653303 0.78204512 3 4 1.1666667 1.0000000
## 25 0.86462394 0.20929364 4 4 1.3333333 1.3333333