# 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
plot(coord_grid)

# 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
N<-nrow(coord_grid)
N
## [1] 25
m<-sqrt(nrow(coord_grid))
m
## [1] 5
spatial_data<-spatialPOP(25,5,c(1:5),c(1:5))
spatial_data
##              Y           X latitude longitude        B0        B1
## 1   1.26605154 0.006507932        0         0 0.0000000 0.0000000
## 2   1.91073017 0.831351819        1         0 0.1666667 0.3333333
## 3   1.77223415 0.775538277        2         0 0.3333333 0.6666667
## 4   0.98887579 0.030592480        3         0 0.5000000 1.0000000
## 5   1.93925956 0.299020177        4         0 0.6666667 1.3333333
## 6  -0.78809243 0.493949025        0         1 0.1666667 0.0000000
## 7   0.36148401 0.112926966        1         1 0.3333333 0.3333333
## 8   2.59411089 0.165608979        2         1 0.5000000 0.6666667
## 9   0.42654596 0.548260471        3         1 0.6666667 1.0000000
## 10  0.08807018 0.341807150        4         1 0.8333333 1.3333333
## 11  0.24545099 0.591042310        0         2 0.3333333 0.0000000
## 12  0.49500650 0.878522104        1         2 0.5000000 0.3333333
## 13  2.03860208 0.988028942        2         2 0.6666667 0.6666667
## 14 -0.02443551 0.128406113        3         2 0.8333333 1.0000000
## 15  0.89838614 0.274969956        4         2 1.0000000 1.3333333
## 16  0.90267101 0.718683174        0         3 0.5000000 0.0000000
## 17 -0.07287275 0.190991892        1         3 0.6666667 0.3333333
## 18  1.89283723 0.961637693        2         3 0.8333333 0.6666667
## 19  1.61050756 0.705824186        3         3 1.0000000 1.0000000
## 20  0.96746652 0.215200857        4         3 1.1666667 1.3333333
## 21  1.00901668 0.285288519        0         4 0.6666667 0.0000000
## 22 -1.41153583 0.371939152        1         4 0.8333333 0.3333333
## 23  0.96834603 0.480729702        2         4 1.0000000 0.6666667
## 24  2.78982231 0.310368277        3         4 1.1666667 1.0000000
## 25  0.37798502 0.623950482        4         4 1.3333333 1.3333333