func.obs.ord {clespr}

Latent Response Transformation for Spatial Ordinal Data

Description

func.obs.ord transforms a vector of latent responses into the corresponding observed ones under the spatial Probit model.

Usage

func.obs.ord(vec.ylat, vec.alpha)

Arguments

vec.ylat

a vector of latent responses for all N sites.

vec.alpha

a vector of prespecified cutoff points, ascending with length at least 3, including -Inf, 0, and Inf.

Value

func.obs.prop returns a vector of observed responses.

References

Feng, Xiaoping, Zhu, Jun, Lin, Pei-Sheng, and Steen-Adams, Michelle M. (2014) Composite likelihood Estimation for Models of Spatial Ordinal Data and Spatial Proportional Data with Zero/One values. Environmetrics 25(8): 571–583.

Examples

# True parameter
vec.cutoff <- 2; vec.beta <- c(1, 2, 1, 0, -1); sigmasq <- 0.8; rho <- 0.6; radius <- 5
vec.par <- c(vec.cutoff, vec.beta, sigmasq, rho)

# Coordinate matrix
n.cat <- 3; n.lati <- 30; n.long <- 30
n.site <- n.lati * n.long
mat.lattice <- cbind(rep(1:n.lati, n.long), rep(1:n.long, each=n.lati))
mat.dist <- as.matrix(dist(mat.lattice, upper=TRUE, diag=TRUE))
mat.cov <- sigmasq * rho^mat.dist

set.seed(1228)
# Generate regression (design) matrix with intercept
mat.X <- cbind(rep(1, n.site),scale(matrix(rnorm(n.site*(length(vec.beta)-1)),nrow=n.site)))
vec.Z <- t(chol(mat.cov)) %*% rnorm(n.site) + mat.X %*% vec.beta
vec.epsilon <- diag(sqrt(1-sigmasq), n.site) %*% rnorm(n.site)
vec.ylat <- as.numeric(vec.Z + vec.epsilon)

# Convert to the vector of observation
vec.yobs <- func.obs.ord(vec.ylat, vec.alpha=c(-Inf,0,vec.cutoff,Inf))