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 -1.05933556 0.75720344 0 0 0.0000000 0.0000000
## 2 -1.95262460 0.12203700 1 0 0.1666667 0.3333333
## 3 0.98110106 0.23175341 2 0 0.3333333 0.6666667
## 4 0.76762249 0.96280613 3 0 0.5000000 1.0000000
## 5 0.69533170 0.67198425 4 0 0.6666667 1.3333333
## 6 -0.26959830 0.20771006 0 1 0.1666667 0.0000000
## 7 0.52930406 0.11334830 1 1 0.3333333 0.3333333
## 8 1.74154798 0.24197594 2 1 0.5000000 0.6666667
## 9 0.43629029 0.77760356 3 1 0.6666667 1.0000000
## 10 1.20277535 0.96573816 4 1 0.8333333 1.3333333
## 11 1.43733272 0.22971666 0 2 0.3333333 0.0000000
## 12 -0.52495415 0.91109954 1 2 0.5000000 0.3333333
## 13 0.61210058 0.27271729 2 2 0.6666667 0.6666667
## 14 2.99949307 0.81141608 3 2 0.8333333 1.0000000
## 15 2.71262848 0.62634909 4 2 1.0000000 1.3333333
## 16 0.11029462 0.61563372 0 3 0.5000000 0.0000000
## 17 0.05976224 0.86840142 1 3 0.6666667 0.3333333
## 18 -1.65625467 0.06615634 2 3 0.8333333 0.6666667
## 19 1.80491819 0.64978061 3 3 1.0000000 1.0000000
## 20 3.23481104 0.85583566 4 3 1.1666667 1.3333333
## 21 2.48457528 0.61436772 0 4 0.6666667 0.0000000
## 22 1.41686026 0.45674801 1 4 0.8333333 0.3333333
## 23 -0.31369738 0.48102453 2 4 1.0000000 0.6666667
## 24 1.45131015 0.76594872 3 4 1.1666667 1.0000000
## 25 2.80121315 0.10185962 4 4 1.3333333 1.3333333