#context("test-jSDM_poisson_log")

#== Without traits ======
#================= Single species distribution model (SDM) ======================

# Data simulation
#= Number of sites
nsite <- 50
#= Number of species
nsp <- 1
#= Set seed for repeatability
seed <- 1234
#= Number of visits associated to each site
set.seed(seed)

# Ecological process (suitability)
set.seed(2*seed)
x1 <- rnorm(nsite,0,1)
set.seed(seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-2,2), byrow=TRUE, nrow=nsp)
log.theta <- X %*% t(beta.target)
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 

#= Site-occupancy model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin,# Chains
                        # Response variable
                        count_data=Y,
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        # Starting values
                        beta_start=0,
                        # Priors
                        mu_beta=0, V_beta=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)

test_that("jSDM_poisson_log works with one species", {
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,np))
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
})

#================ Joint species distribution model (JSDM) ========================

# Data simulation
#= Number of sites
nsite <- 50
#= Number of species
nsp <- 5
#= Set seed for repeatability
seed <- 1234

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(2*seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
log.theta <- X %*% t(beta.target)
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin,# Chains
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        # Starting values
                        beta_start=0,
                        # Priors
                        mu_beta=0, V_beta=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)
# Tests
test_that("jSDM_poisson_log works ", {
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,np))
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
})

#========== JSDM with fixed site effect ====================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-2,2), byrow=TRUE, nrow=nsp)
set.seed(seed)
alpha.target <- runif(nsite,-2,2)
alpha.target[1] <- 0
log.theta <- X %*% t(beta.target) + alpha.target
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 

# Fit the model 
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin, # Chains
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        site_effect="fixed", 
                        # Starting values
                        alpha_start=0,
                        beta_start=0,
                        # Priors
                        V_alpha=10,
                        mu_beta=0, V_beta=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)

# Tests
test_that("jSDM_poisson_log works with fixed site effect", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
})
#========== JSDM with random site effect ====================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log.theta <- X %*% t(beta.target) + alpha.target
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 


# Fit the model 
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin, # Chains
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        site_effect="random", 
                        # Starting values
                        alpha_start=0,
                        beta_start=0,
                        V_alpha=1,
                        # Priors
                        shape_Valpha=0.5, rate_Valpha=0.0005,
                        mu_beta=0, V_beta=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)

# Tests
test_that("jSDM_poisson_log works with random site effect", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
})

#=========== JSDM with latent variables ===================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(2*seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
#= Number of latent variables
n_latent <-  ncol(W)
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*2-3,-1,1)
lambda.target <- matrix(c(l.diag[1],l.zero,l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
log.theta <- X %*% t(beta.target) + W %*% t(lambda.target)
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 


# Fit the model
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin,# Chains
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        n_latent=n_latent,
                        # Starting values
                        beta_start=0, lambda_start = 0,
                        W_start=0,
                        # Priors
                        mu_beta=0, V_beta=1,
                        mu_lambda=0, V_lambda=1,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)
# Tests
test_that("jSDM_poisson_log works with latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)+n_latent))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
})

#============ JSDM with latent variables and fixed site effect =======================================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(2*seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
#= Number of latent variables
n_latent <- ncol(W)
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*2-3,-1,1)
lambda.target <- matrix(c(l.diag[1],l.zero,l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
set.seed(seed)
alpha.target <- runif(nsite,-1,1)
alpha.target[1] <- 0
log.theta <- X %*% t(beta.target) + W %*% t(lambda.target) + alpha.target
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 


# Fit the model 
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin, # Chains 
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        n_latent= n_latent,
                        site_effect ="fixed",
                        # Starting values
                        alpha_start=0,
                        beta_start=0,
                        lambda_start = 0,
                        W_start=0,
                        # Priors
                        V_alpha=10,
                        mu_beta=0, V_beta=10,
                        mu_lambda=0, V_lambda=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)
# Tests 
test_that("jSDM_poisson_log works with fixed site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)+n_latent))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
})

#============= JSDM with latent variables and random site effect ======================================

# Ecological process (suitability)
set.seed(2*seed)
x1 <- rnorm(nsite,0,1)
set.seed(seed)
x2 <- rnorm(nsite,0,1)
X <- cbind(rep(1,nsite),x1,x2)
np <- ncol(X)
set.seed(2*seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
#= Number of latent variables
n_latent <- ncol(W)
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*2-3,-1,1)
lambda.target <- matrix(c(l.diag[1],l.zero,l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log.theta <- X %*% t(beta.target) + W %*% t(lambda.target) + alpha.target
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 


# Fit the model 
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin, # Chains 
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~x1+x2, site_data=X,
                        n_latent= n_latent,
                        site_effect ="random",
                        # Starting values
                        alpha_start=0,
                        beta_start=0,
                        lambda_start = 0,
                        W_start=0,
                        V_alpha=1,
                        # Priors
                        shape_Valpha=0.5, rate_Valpha=0.0005,
                        mu_beta=0, V_beta=10,
                        mu_lambda=0, V_lambda=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)
# Tests 
test_that("jSDM_poisson_log works with random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)+n_latent))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
})

#== JSDM with intercept only, latent variables and random site effect ===================================

# Ecological process (suitability)
X <- matrix(1, nsite, 1)
colnames(X)<- "Int"
np <- ncol(X)
set.seed(2*seed)
W <- cbind(rnorm(nsite, 0, 1),rnorm(nsite, 0, 1))
#= Number of latent variables
n_latent <- ncol(W)
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*2-3,-1,1)
lambda.target <- matrix(c(l.diag[1], l.zero,l.other[1], l.diag[2], l.other[-1]), byrow=TRUE, nrow=nsp)
set.seed(seed)
beta.target <- matrix(runif(nsp*np,-1,1), byrow=TRUE, nrow=nsp)
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log.theta <- X %*% t(beta.target) + W %*% t(lambda.target) + alpha.target
theta <- exp(log.theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite) 


# Fit the model 
mod <- jSDM::jSDM_poisson_log(burnin, mcmc, thin, # Chains 
                        # Response variable
                        count_data=Y,  
                        # Explanatory variables
                        site_formula=~Int-1, site_data=X,
                        n_latent= n_latent,
                        site_effect ="random",
                        # Starting values
                        alpha_start=0,
                        beta_start=0,
                        lambda_start = 0,
                        W_start=0,
                        V_alpha=1,
                        # Priors
                        shape_Valpha=0.5, rate_Valpha=0.0005,
                        mu_beta=0, V_beta=10,
                        mu_lambda=0, V_lambda=10,
                        # Various
                        seed=1234, ropt=0.44, verbose=0)
# Tests 
test_that("jSDM_poisson_log works with random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(unique(lapply(mod$mcmc.sp,dim))[[1]],c(nsamp,ncol(X)+n_latent))
  expect_equal(sum(is.na(mod$mcmc.sp)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
})

#== With traits ===========
#======== Joint species distribution model (JSDM) ====================

# Data simulation
#= Number of sites
nsite <- 50
#= Set seed for repeatability
seed <- 1234
set.seed(seed)

#= Number of species
nsp <- 5

# Ecological process (suitability)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1, x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)), SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2) + x2:I(SLA^2)
form.Tr <- function(trait_formula, trait_data,X){
  data <- trait_data
  # add column of 1 with names of covariables in site_data
  data[,colnames(X)] <- 1
  mf.suit.tr <- model.frame(formula=trait_formula, data=data)
  # full design matrix corresponding to formula
  mod.mat <- model.matrix(attr(mf.suit.tr,"terms"), data=mf.suit.tr)
  # Remove duplicated columns to get design matrix for traits
  Tr <- as.matrix(mod.mat[,!duplicated(mod.mat,MARGIN=2)])
  colnames(Tr) <- colnames(mod.mat)[!duplicated(mod.mat,MARGIN=2)]
  # Rename columns according to considered trait
  for(p in 1:np){
    if(sum(colnames(Tr)==colnames(X)[p])==0){
      colnames(Tr) <- gsub(pattern=paste0(":",colnames(X)[p]), replacement="",
                           x=colnames(Tr), fixed=TRUE)
      colnames(Tr) <- gsub(pattern=paste0(colnames(X)[p],":"), replacement="",
                           x=colnames(Tr), fixed=TRUE)
    }
  }
  nt <- ncol(Tr)
  n_Tint <- sum(sapply(apply(Tr,2,unique), FUN=function(x){all(x==1)}))
  col_Tint <- which(sapply(apply(Tr,2,unique), FUN=function(x){all(x==1)}))
  gamma_zeros <- matrix(0,nt,np)
  rownames(gamma_zeros) <- colnames(Tr)
  colnames(gamma_zeros) <- colnames(X)
  for(t in 1:nt){
    for(p in 1:np){
      term <- c(grep(paste0(colnames(X)[p],":"), colnames(mod.mat), value=TRUE, fixed=TRUE),grep(paste0(":",colnames(X)[p]), colnames(mod.mat), value=TRUE, fixed=TRUE))
      if(length(term)==0) next
      # fixed=TRUE pattern is a string to be matched as is
      # not a regular expression because of special characters in formula (^, /, [, ...)
      gamma_zeros[t,p] <- length(c(grep(paste0(":",colnames(Tr)[t]), term, fixed=TRUE),grep(paste0(colnames(Tr)[t],":"), term, fixed=TRUE)))
    }
    gamma_zeros[t,1] <- length(which(colnames(mod.mat)==colnames(Tr)[t]))
  }
  gamma_zeros[col_Tint,] <- 1
  return(list(gamma_zeros=gamma_zeros,Tr=Tr))
}
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-1,1), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
log_theta <- as.matrix(X) %*% beta.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin=burnin, mcmc=mcmc, thin=thin,
                              count_data=Y,
                              site_formula = site_formula,
                              site_data = X,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              beta_start=0,
                              mu_beta=0, V_beta=10,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#============= JSDM with latent variables ===============

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)), SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2) + x2:I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-0.5, 0.5), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
#= Number of latent variables
n_latent <- ncol(W)
l.zero <- 0
set.seed(seed)
l.diag <- runif(n_latent,0,1)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-0.5,0.5)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin=burnin, mcmc=mcmc, thin=thin,
                              count_data=Y,
                              site_formula = site_formula,
                              site_data = X, site_effect="none",
                              n_latent=n_latent,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              beta_start=0,
                              lambda_start=0, W_start=0,
                              mu_beta=0, V_beta=10,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits, latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#============== JSDM with fixed site effect =================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)), SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2) + x2:I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-0.5,0.5), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
alpha.target <- runif(nsite,-1,1)
alpha.target[1] <- 0
log_theta <- as.matrix(X) %*% beta.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin=burnin, mcmc=mcmc, thin=thin,
                              count_data=Y,
                              n_latent=0,
                              site_formula = site_formula,
                              site_data = X, site_effect="fixed",
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              alpha_start=0, beta_start=0,
                              V_alpha=10,
                              mu_beta=0, V_beta=10,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits, fixed site effect", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#=============== JSDM with random site effect ================

# Ecological process (suitability)
set.seed(2*seed)
x1 <- rnorm(nsite,0,1)
set.seed(seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(2*seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)),
                         SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2) + x2:I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-1,1), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log_theta <- as.matrix(X) %*% beta.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin=burnin, mcmc=mcmc, thin=thin,
                              count_data=Y,
                              n_latent=0,
                              site_formula =site_formula,
                              site_data = X, site_effect="random",
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              alpha_start=0, beta_start=0,
                              V_alpha=1,
                              shape_Valpha=0.5, rate_Valpha=0.0005,
                              mu_beta=0, V_beta=10,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits, random site effect", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#======= JSDM with fixed site effect and latent variables ==============================

# Ecological process (suitability)
set.seed(2*seed)
x1 <- rnorm(nsite,0,1)
set.seed(seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)),
                         SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2)+ x2:I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-0.5,0.5), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,2)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-1,1)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
set.seed(seed)
alpha.target <- runif(nsite,-1,1)
alpha.target[1] <- 0
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(burnin=burnin, mcmc=mcmc, thin=thin,
                              count_data=Y,
                              site_formula=site_formula,
                              site_data=X, n_latent=2,
                              site_effect = "fixed",
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              alpha_start=0, beta_start=0,
                              lambda_start=0, W_start=0,
                              V_alpha=10,
                              mu_beta=0, V_beta=10,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits, fixed site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#============ JSDM with random site effect and latent variables ==================================

# Ecological process (suitability)
set.seed(2*seed)
x1 <- rnorm(nsite,0,1)
set.seed(seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
set.seed(seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)),
                         SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + x1:I(WSD^2)+ x2:I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-0.5,0.5), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-1,1)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(count_data=Y,
                              site_formula=site_formula,
                              site_data=X, n_latent=2,
                              site_effect = "random",
                              burnin=burnin, mcmc=mcmc, thin=thin,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              alpha_start=0, beta_start=0,
                              lambda_start=0, W_start=0,
                              V_alpha=1,
                              shape_Valpha=0.5, rate_Valpha=0.0005,
                              mu_beta=0, V_beta=10,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with traits, random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#== JSDM with intercept only in X, random site effect and latent variables ===============================

# Ecological process (suitability)
X <- data.frame(Int=rep(1,nsite))
np <- ncol(X)
set.seed(2*seed)
trait_data <- data.frame(WSD=scale(runif(nsp,0,1000)),
                         SLA=scale(runif(nsp,0,250)))
trait_formula <- ~ WSD + SLA + I(WSD^2) + I(SLA^2)
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(2*seed)
gamma.target <- matrix(runif(nt*np,-1,1), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-1,1)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(count_data=Y,
                              site_formula=~Int-1,
                              site_data=X, n_latent=2,
                              site_effect = "random",
                              burnin=burnin, mcmc=mcmc, thin=thin,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=10,
                              alpha_start=0, beta_start=0,
                              lambda_start=0, W_start=0,
                              V_alpha=1,
                              shape_Valpha=0.5, rate_Valpha=0.0005,
                              mu_beta=0, V_beta=10,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with  intercept only in X, random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(sapply(mod$mcmc.gamma,colMeans)!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#== JSDM with intercept only in Tr, random site effect and latent variables ===============================

# Ecological process (suitability)
set.seed(seed)
x1 <- rnorm(nsite,0,1)
set.seed(2*seed)
x2 <- rnorm(nsite,0,1)
site_data <- data.frame(x1=x1,x2=x2)
site_formula <- ~ x1 + x2
X <- model.matrix(site_formula, site_data)
np <- ncol(X)
trait_data <- data.frame(Int=rep(1,nsp))
trait_formula <- ~. -1
# trait_formula <- ~ Int + x1:Int + x2:Int + I(x1^2):Int + I(x2^2):Int -1
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(seed)
gamma.target <- matrix(runif(nt*np,-1,1), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,1)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-1,1)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(count_data=Y,
                              site_formula=site_formula,
                              site_data=X, n_latent=2,
                              site_effect = "random",
                              burnin=burnin, mcmc=mcmc, thin=thin,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=1,
                              alpha_start=0, beta_start=0,
                              lambda_start=0, W_start=0,
                              V_alpha=1,
                              shape_Valpha=0.5, rate_Valpha=0.0005,
                              mu_beta=0, V_beta=1,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with  intercept only in Tr, traits, random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(as.matrix(sapply(mod$mcmc.gamma,colMeans))!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})

#== JSDM with intercept only in Tr and X, random site effect and latent variables ===============================
# Ecological process (suitability)
X <- data.frame(Int=rep(1,nsite))
np <- ncol(X)
trait_data <- data.frame(Int=rep(1,nsp))
trait_formula <- ~. -1
# trait_formula <- ~ Int + x1:Int + x2:Int + I(x1^2):Int + I(x2^2):Int -1
result <- form.Tr(trait_formula,trait_data,X)
Tr <- result$Tr
nt <- ncol(Tr)
gamma_zeros <- result$gamma_zeros
set.seed(2*seed)
gamma.target <- matrix(runif(nt*np,-3,3), byrow=TRUE, nrow=nt)
mu_beta <- as.matrix(Tr) %*% (gamma.target*gamma_zeros)
V_beta <- diag(1,np)
beta.target <- matrix(NA,nrow=np,ncol=nsp)
for(j in 1:nsp){
  set.seed(seed)
  beta.target[,j] <- MASS::mvrnorm(n=1, mu=mu_beta[j,], Sigma=V_beta)
}
set.seed(seed)
W <- cbind(rnorm(nsite,0,1),rnorm(nsite,0,1))
l.zero <- 0
set.seed(seed)
l.diag <- runif(2,0,2)
set.seed(seed)
l.other <- runif(nsp*n_latent-3,-2,2)
lambda.target <- t(matrix(c(l.diag[1],l.zero,
                            l.other[1],l.diag[2],l.other[-1]), byrow=TRUE, nrow=nsp))
Valpha.target <- 0.5
set.seed(seed)
alpha.target <- rnorm(nsite,0,sqrt(Valpha.target))
log_theta <- as.matrix(X) %*% beta.target + W %*% lambda.target + alpha.target
theta <- exp(log_theta)
set.seed(seed)
Y <- apply(theta, 2, rpois, n=nsite)

# Fit the model
burnin <- 1000
mcmc <- 1000
thin <- 1
nsamp <- mcmc/thin
mod <- jSDM::jSDM_poisson_log(count_data=Y,
                              site_formula=~Int-1,
                              site_data=X, n_latent=2,
                              site_effect = "random",
                              burnin=burnin, mcmc=mcmc, thin=thin,
                              trait_formula = trait_formula,
                              trait_data = trait_data,
                              gamma_start=0,
                              mu_gamma=0, V_gamma=1,
                              alpha_start=0, beta_start=0,
                              lambda_start=0, W_start=0,
                              V_alpha=1,
                              shape_Valpha=0.5, rate_Valpha=0.0005,
                              mu_beta=0, V_beta=1,
                              mu_lambda=0, V_lambda=1,
                              seed=1234, verbose=0)
# Tests
test_that("jSDM_poisson_log works with intercept only in Tr and X, random site effect and latent variables", {
  expect_equal(length(mod$mcmc.sp),nsp)
  expect_equal(dim(mod$mcmc.sp[["sp_1"]]),c(nsamp,ncol(X)+n_latent))
  expect_equal(length(mod$mcmc.gamma),ncol(X))
  expect_equal(dim(mod$mcmc.gamma[[1]]),c(nsamp,ncol(Tr)))
  expect_equal(which(as.matrix(sapply(mod$mcmc.gamma,colMeans))!=0), which(gamma_zeros!=0))
  expect_equal(dim(mod$mcmc.latent$lv_1),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_1)),0)
  expect_equal(dim(mod$mcmc.latent$lv_2),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.latent$lv_2)),0)
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(dim(mod$mcmc.alpha),c(nsamp,nsite))
  expect_equal(sum(is.na(mod$mcmc.alpha)),0)
  expect_equal(sum(is.na(mod$log_theta_latent)),0)
  expect_equal(dim(mod$log_theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$theta_latent)),0)
  expect_equal(dim(mod$theta_latent),c(nsite,nsp))
  expect_equal(sum(is.na(mod$mcmc.V_alpha)),0)
  expect_equal(dim(mod$mcmc.V_alpha),c(nsamp,1))
  expect_equal(sum(is.na(mod$mcmc.Deviance)),0)
  expect_equal(dim(mod$mcmc.Deviance),c(nsamp,1))
})