R/gensd.R
In Sewanou/genspatattr: Generates skewed spatial attributes
Defines functions
gensd
multigensd
Documented in
gensd
multigensd
#' @name gsd
#' @title Spatial dependent attribute with unknown skewness
#' @description Generates a spatial dependent attributes of which skewness is provided as output.
#'
#'
#' @usage gsd (size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#'
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a list:
#' \item{spdata}{the generated attribute.}
#' \item{skew.coef}{effective skewness coefficient from generated data}
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#' @references Mohadeseh Alsadat Farzammehr, Mohammad Reza Zadkarami & Geoffrey J. McLachlan (2019): Skew-normal generalized spatial panel data model, Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2019.1622718
#'
#'
gsd <- function (size, grid, sk = 0, dep = 0.5, mu = 0, v = 1, method = "SAR",
dst= "skewnormal")
{
mk <- match.call()
miSiz <- missing(size)
if(miSiz){
stop("You must provide the size (number of subjects and number of observations per
subject")
}
if(!miSiz && !is.vector(size)){
stop("The size must be a vector")
}
if(!miSiz && is.vector(size) && length(size) != 2){
stop("The size must be a vector with two elements: numbers of subjects
and observations per subject, respectively.")
}
miGrid <- missing(grid)
if(miGrid){
stop("You must provide the grid (numbers of rows and columns")
}
if(!miGrid && !is.vector(grid)){
stop("The grid must be a vector")
}
if(!miGrid && is.vector(grid) && length(grid) != 2){
stop("The grid must be a vector with two elements: numbers of rows and columns,
respectively.")
}
if(size[1] != grid[1] * grid[2]){
stop("The number of observations must be equal to the product
of numbers of rows and columns of the grid matrix")
}
if(sk < 0 || sk > 1 && dst == "skewnormal"){
warning("The skewnormal distribution does not work on this skewness coefficient.
You may choose the lognormal distribution instead.")
return(gsd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = "lognormal"))
}
if(method == "SAR"){
varrho <- numeric(2)
}
if(method == "SARMA"){
varrho <- runif(n = 2, min = -1, max = 1)
}
k1 <- spdep::cell2nb(grid[1], grid[2])
k2 <- spdep::nb2listw(k1, style="W")
k3 <- spdep::invIrW(k2, rho = dep, method="solve", feasible=NULL)
B1 <- B2 <- solve(k3)
W <- (diag(dim(B1)[1]) - B1) / dep
D1 <- diag(dim(B1)[1]) + varrho[1] * W
D2 <- diag(dim(B2)[1]) + varrho[2] * W
A1 <- solve(D1) %*% B1
A2 <- solve(D2) %*% B2
if(dst == "skewnormal"){
ic <- ((2 * sk) / (4 - pi))^(1/3)
theta_k <- ic / (sqrt(1 + ic^2))
theta_t <- theta_k / sqrt(2 / pi)
alph <- theta_t / sqrt(1 - theta_t^2)
muz <- sqrt(2 / pi) * (alph / (sqrt(1 + alph^2)))
sc <- sqrt(v / (1 - muz^2))
loc <- mu - sc * muz
mui <- VGAM::rskewnorm(n = size[1], location = loc, scale = sc, shape = alph)
sc2 <- 4 * sqrt(v / (1 - muz^2))
loc2 <- mu - sc2 * muz
nuit <- VGAM::rskewnorm(n = size[1], location = loc2, scale = sc2, shape = alph)
}
if(dst == "lognormal"){
sig <- function(gamma1){
X <- polyroot(c(-gamma1^2 - 4, 0, 3, 1))
X <- Re(X[Im(X)^2 <= min(Im(X)^2)])
X <- log(X)
X
}
sigma2 <- sig(sk)
mui <- rlnorm(n = size[1], mean = mu, sd = sqrt(sigma2))
nuit <- rlnorm(n = size[1], mean = mu, sd = 4 * sqrt(sigma2))
}
u1 <- solve(A1) %*% mui
u2t <- solve(A2) %*% nuit
ut <- u1 + u2t
md <- function(N, t, u){
x01 <-5 + 10 * runif(n = 1, min = -0.5, max = 0.5)
x02 <-5 + 10 * runif(n = 1, min = -0.5, max = 0.5)
x1 <- x2 <- yt <- matrix(numeric(N * t), nrow = N)
x1[, 1] <- 0.1 + 0.5 * x01 + runif(n = 1, min = -0.5, max = 0.5)
x2[, 1] <- 0.1 + 0.5 * x02 + runif(n = 1, min = -0.5, max = 0.5)
yt[, 1] <- 0.5 * x1[, 1] + 7 * x2[, 1] + u
for(i in 2 : t){
x1[,i] <- 0.1 * i + 0.5 * x1[,i-1] + runif(n = 1, min = -0.5, max = 0.5)
x2[,i] <- 0.1 * i + 0.5 * x2[,i-1] + runif(n = 1, min = -0.5, max = 0.5)
yt[,i] <- 0.5 * x1[, 1] + 7 * x2[, 1] + u
}
return(c(yt))
}
y <- md(N = size[1], t = size[2], u = ut)
return(list(spdata = y, skew.coef = round(e1071::skewness(y), 1)))
}
#' @name gensd
#' @title Spatial dependent attribute with fixed skewness
#' @description Generates a spatial dependent attribute with a fixed skewness.
#'
#'
#' @usage gensd (size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#'
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a gsd object.
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#'
#'
gensd <- function(size, grid, sk = 1, dep = 0.5, mu = 0, v = 1,
method = "SAR", dst = "skewnormal")
{
sk.calc <- sk + 100
i <- 0
n.iter <- 0
while(sk.calc != sk){
spd <- gsd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v, method = method, dst = dst)
sk.calc <- spd$skew.coef
if(sk.calc == sk) break
if(n.iter == 10000) stop("Impossible to generate spatial attribute with the required skewness coefficient")
i <- i + 1
n.iter <- n.iter + 1
}
return(spd)
}
#' @name multigensd
#' @title Multiple Attributes skewed and dependent
#' @description Generates multiple spatial dependent attributes with fixed skewness.
#'
#'
#' @usage multigensd (n.attr, size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#' @param n.attr Number of attributes to be generated.
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a list.
#' \item{mat.attributes}{Multiple spatial dependent and skewed attributes generated.}
#' \item{spatial.dependence}{Racall of the spatial dependence existing within values of a given attribute generated}
#' \item{skewness.coef}{Coefficient of skewness of spatial attributes generated.}
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#'
#' @examples
#'
#' Consider a simulation study that requires 10 skewed (3.6) spatial attribbutes with a spatial autoregressive coefficient (spatial correlation) of 0.5.
#' Each attribute has 100 subjects and 7 observations (time points) per subject. We choose to design 10 x 10 square grids.
#'
#' # Loading package
#' library(genspatattr)
#'
#' # As the skewness required exceeds the interval [0,1], we use the lognormal distribution and SAR method to maintain null the spatial moving average coefficient.
#' k1 <- c(100, 7)
#' k2 <- c(10, 10)
#' dt <- multigensd(n.attr = 10, size = k1, grid = k2, sk = 3.6, dst = "lognormal")
#' > head(dt$mat.attributes)
#' [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#' [1,] 36.76639 29.65413 321.04957 54.14535 5.620346 38.27667 118.73450 44.93622 56.44374
#' [2,] 21.99757 27.46571 95.71541 37.93883 8.538977 82.19352 44.64520 39.25272 45.69996
#' [3,] 40.25177 32.81329 31.67804 34.86756 18.055213 384.21476 20.64373 42.84450 62.49243
#' [4,] 20.91775 50.49171 17.53125 35.79660 49.848041 171.73468 35.92800 44.00423 138.66885
#' [5,] 17.16706 37.16105 12.95207 50.99651 38.020209 159.57852 26.01867 75.07399 55.96092
#' [6,] 13.39583 35.46820 15.07685 36.63703 71.563533 43.86750 73.75986 173.56775 44.58139
#' [,10]
#' [1,] 24.85834
#' [2,] 25.51857
#' [3,] 21.10237
#' [4,] 23.60568
#' [5,] 30.25069
#' [6,] 28.92886
#'
#' > e1071::skewness(dt$mat.attributes[,1])
#' [1] 3.643574
#' > e1071::skewness(dt$mat.attributes[,10])
#' [1] 3.606651
#' > dt$spatial.dependence
#' [1] 0.5
#' > dt$skewness.coef
#' [1] 3.6
multigensd <- function(n.attr, size, grid, sk = 1, dep = 0.5, mu = 0, v = 1,
method = "SAR", dst = "skewnormal")
{
if(n.attr == 1) {
warning("You may simply use the function gensd to generate one attribute.")
return(gensd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = dst))
}
if(n.attr <= 0){
stop("This function requires a non null positive integer to perform generation
of attribute(s)")
}
at <- matrix(numeric(size[1] * size[2] * n.attr), ncol = n.attr)
for(i in 1 : n.attr){
k <- gensd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = dst)
at[, i] <- k$spdata
}
return(list(mat.attributes = at, spatial.dependence = dep, skewness.coef = sk))
}
Sewanou/genspatattr documentation built on Oct. 30, 2019, 11:52 p.m.
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Defines functions gensd multigensd
Documented in gensd multigensd
#' @name gsd
#' @title Spatial dependent attribute with unknown skewness
#' @description Generates a spatial dependent attributes of which skewness is provided as output.
#'
#'
#' @usage gsd (size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#'
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a list:
#' \item{spdata}{the generated attribute.}
#' \item{skew.coef}{effective skewness coefficient from generated data}
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#' @references Mohadeseh Alsadat Farzammehr, Mohammad Reza Zadkarami & Geoffrey J. McLachlan (2019): Skew-normal generalized spatial panel data model, Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2019.1622718
#'
#'
gsd <- function (size, grid, sk = 0, dep = 0.5, mu = 0, v = 1, method = "SAR",
dst= "skewnormal")
{
mk <- match.call()
miSiz <- missing(size)
if(miSiz){
stop("You must provide the size (number of subjects and number of observations per
subject")
}
if(!miSiz && !is.vector(size)){
stop("The size must be a vector")
}
if(!miSiz && is.vector(size) && length(size) != 2){
stop("The size must be a vector with two elements: numbers of subjects
and observations per subject, respectively.")
}
miGrid <- missing(grid)
if(miGrid){
stop("You must provide the grid (numbers of rows and columns")
}
if(!miGrid && !is.vector(grid)){
stop("The grid must be a vector")
}
if(!miGrid && is.vector(grid) && length(grid) != 2){
stop("The grid must be a vector with two elements: numbers of rows and columns,
respectively.")
}
if(size[1] != grid[1] * grid[2]){
stop("The number of observations must be equal to the product
of numbers of rows and columns of the grid matrix")
}
if(sk < 0 || sk > 1 && dst == "skewnormal"){
warning("The skewnormal distribution does not work on this skewness coefficient.
You may choose the lognormal distribution instead.")
return(gsd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = "lognormal"))
}
if(method == "SAR"){
varrho <- numeric(2)
}
if(method == "SARMA"){
varrho <- runif(n = 2, min = -1, max = 1)
}
k1 <- spdep::cell2nb(grid[1], grid[2])
k2 <- spdep::nb2listw(k1, style="W")
k3 <- spdep::invIrW(k2, rho = dep, method="solve", feasible=NULL)
B1 <- B2 <- solve(k3)
W <- (diag(dim(B1)[1]) - B1) / dep
D1 <- diag(dim(B1)[1]) + varrho[1] * W
D2 <- diag(dim(B2)[1]) + varrho[2] * W
A1 <- solve(D1) %*% B1
A2 <- solve(D2) %*% B2
if(dst == "skewnormal"){
ic <- ((2 * sk) / (4 - pi))^(1/3)
theta_k <- ic / (sqrt(1 + ic^2))
theta_t <- theta_k / sqrt(2 / pi)
alph <- theta_t / sqrt(1 - theta_t^2)
muz <- sqrt(2 / pi) * (alph / (sqrt(1 + alph^2)))
sc <- sqrt(v / (1 - muz^2))
loc <- mu - sc * muz
mui <- VGAM::rskewnorm(n = size[1], location = loc, scale = sc, shape = alph)
sc2 <- 4 * sqrt(v / (1 - muz^2))
loc2 <- mu - sc2 * muz
nuit <- VGAM::rskewnorm(n = size[1], location = loc2, scale = sc2, shape = alph)
}
if(dst == "lognormal"){
sig <- function(gamma1){
X <- polyroot(c(-gamma1^2 - 4, 0, 3, 1))
X <- Re(X[Im(X)^2 <= min(Im(X)^2)])
X <- log(X)
X
}
sigma2 <- sig(sk)
mui <- rlnorm(n = size[1], mean = mu, sd = sqrt(sigma2))
nuit <- rlnorm(n = size[1], mean = mu, sd = 4 * sqrt(sigma2))
}
u1 <- solve(A1) %*% mui
u2t <- solve(A2) %*% nuit
ut <- u1 + u2t
md <- function(N, t, u){
x01 <-5 + 10 * runif(n = 1, min = -0.5, max = 0.5)
x02 <-5 + 10 * runif(n = 1, min = -0.5, max = 0.5)
x1 <- x2 <- yt <- matrix(numeric(N * t), nrow = N)
x1[, 1] <- 0.1 + 0.5 * x01 + runif(n = 1, min = -0.5, max = 0.5)
x2[, 1] <- 0.1 + 0.5 * x02 + runif(n = 1, min = -0.5, max = 0.5)
yt[, 1] <- 0.5 * x1[, 1] + 7 * x2[, 1] + u
for(i in 2 : t){
x1[,i] <- 0.1 * i + 0.5 * x1[,i-1] + runif(n = 1, min = -0.5, max = 0.5)
x2[,i] <- 0.1 * i + 0.5 * x2[,i-1] + runif(n = 1, min = -0.5, max = 0.5)
yt[,i] <- 0.5 * x1[, 1] + 7 * x2[, 1] + u
}
return(c(yt))
}
y <- md(N = size[1], t = size[2], u = ut)
return(list(spdata = y, skew.coef = round(e1071::skewness(y), 1)))
}
#' @name gensd
#' @title Spatial dependent attribute with fixed skewness
#' @description Generates a spatial dependent attribute with a fixed skewness.
#'
#'
#' @usage gensd (size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#'
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a gsd object.
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#'
#'
gensd <- function(size, grid, sk = 1, dep = 0.5, mu = 0, v = 1,
method = "SAR", dst = "skewnormal")
{
sk.calc <- sk + 100
i <- 0
n.iter <- 0
while(sk.calc != sk){
spd <- gsd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v, method = method, dst = dst)
sk.calc <- spd$skew.coef
if(sk.calc == sk) break
if(n.iter == 10000) stop("Impossible to generate spatial attribute with the required skewness coefficient")
i <- i + 1
n.iter <- n.iter + 1
}
return(spd)
}
#' @name multigensd
#' @title Multiple Attributes skewed and dependent
#' @description Generates multiple spatial dependent attributes with fixed skewness.
#'
#'
#' @usage multigensd (n.attr, size, grid, sk = 1, dep = 0.5, mu = 0, v = 1, method = "SAR", dst = "skewnormal")
#'
#' @param n.attr Number of attributes to be generated.
#' @param size a vector of two elements specifying respectively numbers of indivuals and time points of the attribute to be generated.
#' @param grid number of rows and columns for grids.
#' @param sk a scalar that represents the skewness coefficient to be considered.
#' @param dep a scalar that represents the dependence correlation between values within a given attribute.
#' @param mu the mean value
#' @param v the variance value
#' @param dst a character string naming the distribution to be used for vectors generation. "skewnormal" the skew-normal distribution is limited to a range of [0,1[ for the coefficient of skewness. "lognormal" the lognormal distribution allows a large range of coefficients skewness values.
#' @param method a character string naming the the approach used to create spatial dependence between variables. The "SAR" method is the Kapoor, Kelejian, and Prucha (2007)-spatial autoregressive random effects (SAR-RE) model. The "SARMA" method represents the Lee and Yu (2012) spatial autoregressive moving average random effects (SARMA-RE) model.
#' @return Returns a list.
#' \item{mat.attributes}{Multiple spatial dependent and skewed attributes generated.}
#' \item{spatial.dependence}{Racall of the spatial dependence existing within values of a given attribute generated}
#' \item{skewness.coef}{Coefficient of skewness of spatial attributes generated.}
#'
#' @export
#'
#' @author Sewanou Honfo \url{<honfosewanou@gmail.com>} and Brezesky Kotanmi \url{<kotangaebrezesky@gmail.com>} and Eunice Gnanvi \url{<eunysgnanvi@gmail.com>} and Chenangnon Tovissode \url{<chenangnon@gmail.com>} and Romain glèlè Kakaï \url{<glele.romain@gmail.com>} / LABEF_08_2019
#'
#'
#' @examples
#'
#' Consider a simulation study that requires 10 skewed (3.6) spatial attribbutes with a spatial autoregressive coefficient (spatial correlation) of 0.5.
#' Each attribute has 100 subjects and 7 observations (time points) per subject. We choose to design 10 x 10 square grids.
#'
#' # Loading package
#' library(genspatattr)
#'
#' # As the skewness required exceeds the interval [0,1], we use the lognormal distribution and SAR method to maintain null the spatial moving average coefficient.
#' k1 <- c(100, 7)
#' k2 <- c(10, 10)
#' dt <- multigensd(n.attr = 10, size = k1, grid = k2, sk = 3.6, dst = "lognormal")
#' > head(dt$mat.attributes)
#' [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#' [1,] 36.76639 29.65413 321.04957 54.14535 5.620346 38.27667 118.73450 44.93622 56.44374
#' [2,] 21.99757 27.46571 95.71541 37.93883 8.538977 82.19352 44.64520 39.25272 45.69996
#' [3,] 40.25177 32.81329 31.67804 34.86756 18.055213 384.21476 20.64373 42.84450 62.49243
#' [4,] 20.91775 50.49171 17.53125 35.79660 49.848041 171.73468 35.92800 44.00423 138.66885
#' [5,] 17.16706 37.16105 12.95207 50.99651 38.020209 159.57852 26.01867 75.07399 55.96092
#' [6,] 13.39583 35.46820 15.07685 36.63703 71.563533 43.86750 73.75986 173.56775 44.58139
#' [,10]
#' [1,] 24.85834
#' [2,] 25.51857
#' [3,] 21.10237
#' [4,] 23.60568
#' [5,] 30.25069
#' [6,] 28.92886
#'
#' > e1071::skewness(dt$mat.attributes[,1])
#' [1] 3.643574
#' > e1071::skewness(dt$mat.attributes[,10])
#' [1] 3.606651
#' > dt$spatial.dependence
#' [1] 0.5
#' > dt$skewness.coef
#' [1] 3.6
multigensd <- function(n.attr, size, grid, sk = 1, dep = 0.5, mu = 0, v = 1,
method = "SAR", dst = "skewnormal")
{
if(n.attr == 1) {
warning("You may simply use the function gensd to generate one attribute.")
return(gensd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = dst))
}
if(n.attr <= 0){
stop("This function requires a non null positive integer to perform generation
of attribute(s)")
}
at <- matrix(numeric(size[1] * size[2] * n.attr), ncol = n.attr)
for(i in 1 : n.attr){
k <- gensd(size = size, grid = grid, sk = sk, dep = dep, mu = mu, v = v,
method = method, dst = dst)
at[, i] <- k$spdata
}
return(list(mat.attributes = at, spatial.dependence = dep, skewness.coef = sk))
}
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