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1-rattiness_nonspatial_model_fns.R
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1-rattiness_nonspatial_model_fns.R
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# Functions for Rattiness - epidemiology project
# 1. Log-likelihood function for rattiness ecology model (without human data) with no spatial correlation
llik.non.spatial.rattiness.fn <- function(par) {
# Set up parameters
alpha <- par[1:n.inst]
sigma <- exp(par[((n.inst+1):(2*n.inst))])
n.loc <- length(unique(ID))
out <- 0
for(j in 1:n.loc) { # we use j to denote location
R.halton <- U.halton
rat.j <- rat[ID==j,]
data_type.j <- rat.j$data_type
ind.traps.j <- which(data_type.j=="traps")
ind.plates.j <- which(data_type.j=="plates")
ind.burrows.j <- which(data_type.j=="burrows")
ind.faeces.j <- which(data_type.j=="faeces")
ind.trails.j <- which(data_type.j=="trails")
out.traps.j <- 1
out.plates.j <- 1
out.burrows.j <- 1
out.faeces.j <- 1
out.trails.j <- 1
if(length(ind.traps.j) > 0) {
eta.traps.j <- sapply(R.halton,function(R.j) alpha[1]+sigma[1]*R.j)
lambda.traps.j <- exp(eta.traps.j)
t.j <- rep(1,length(ind.traps.j))
if(any(rat.j$offset_req[ind.traps.j]==1)) t.j[rat.j$offset_req[ind.traps.j]==1] <- 0.5
llik.traps.j <- sapply(1:length(ind.traps.j),
function(h) dbinom(rat.j$outcome[ind.traps.j][h],1,
prob = 1-exp(-t.j[h]*lambda.traps.j),
log=TRUE))
if(length(ind.traps.j) > 1) {
out.traps.j <- apply(llik.traps.j,1,function(row) exp(sum(row)))
} else {
out.traps.j <- exp(llik.traps.j)
}
}
if(length(ind.plates.j) > 0) {
eta.plates.j <- sapply(R.halton,function(R.j) alpha[2]+sigma[2]*R.j)
q.plates.j <- 1/(1+exp(-eta.plates.j))
llik.plates.j <- sapply(1:length(ind.plates.j),
function(h) dbinom(rat.j$outcome[ind.plates.j][h],
rat.j$offset[ind.plates.j][h],
prob = q.plates.j,
log=TRUE))
if(length(ind.plates.j) > 1) {
out.plates.j <- apply(llik.plates.j,1,function(row) exp(sum(row)))
} else {
out.plates.j <- exp(llik.plates.j)
}
}
if(length(ind.burrows.j) > 0) {
eta.burrows.j <- sapply(R.halton,function(R.j) alpha[3]+sigma[3]*R.j)
lambda.burrows.j <- exp(eta.burrows.j)
llik.burrows.j <- sapply(1:length(ind.burrows.j),
function(h) -lambda.burrows.j + rat.j$outcome[ind.burrows.j][h]*log(lambda.burrows.j))
if(length(ind.burrows.j) > 1) {
out.burrows.j <- apply(llik.burrows.j,1,function(row) exp(sum(row)))
} else {
out.burrows.j <- exp(llik.burrows.j)
}
}
if(length(ind.faeces.j)>0) {
eta.faeces.j <- sapply(R.halton,function(R.j) alpha[4]+sigma[4]*R.j)
p.faeces.j <- 1/(1+exp(- eta.faeces.j))
llik.faeces.j <- sapply(1:length(ind.faeces.j), function(h) rat.j$outcome[ind.faeces.j][h]*log(p.faeces.j)+
(1-rat.j$outcome[ind.faeces.j][h])*log(1-p.faeces.j))
if(length(ind.faeces.j) > 1) {
out.faeces.j <- apply(llik.faeces.j,1,function(row) exp(sum(row)))
} else {
out.faeces.j <- exp(llik.faeces.j)
}
}
if(length(ind.trails.j)>0) {
eta.trails.j <- sapply(R.halton,function(R.j) alpha[5]+sigma[5]*R.j)
p.trails.j <- 1/(1+exp(- eta.trails.j))
llik.trails.j <- sapply(1:length(ind.trails.j), function(h) rat.j$outcome[ind.trails.j][h]*log(p.trails.j)+
(1-rat.j$outcome[ind.trails.j][h])*log(1-p.trails.j))
if(length(ind.trails.j) > 1) {
out.trails.j <- apply(llik.trails.j,1,function(row) exp(sum(row)))
} else {
out.trails.j <- exp(llik.trails.j)
}
}
out <- out+log(mean(exp(log(out.traps.j)+log(out.plates.j)+
log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j))))
}
return(out)
}
# 2. Compute predicted Uj values at each location (no covariates)
compute.pred.mean.Uj.no.cov.fn <- function(par,j) {
alpha <- par[1:n.inst]
sigma <- exp(par[((n.inst+1):(2*n.inst))])
n.loc <- length(unique(ID))
eta.R.j <- sum(D[j,]*beta)
R.halton <- eta.R.j+U.halton
rat.j <- rat[ID==j,]
data_type.j <- rat.j$data_type
ind.traps.j <- which(data_type.j=="traps")
ind.plates.j <- which(data_type.j=="plates")
ind.burrows.j <- which(data_type.j=="burrows")
ind.faeces.j <- which(data_type.j=="faeces")
ind.trails.j <- which(data_type.j=="trails")
out.traps.j <- 1
out.plates.j <- 1
out.burrows.j <- 1
out.faeces.j <- 1
out.trails.j <- 1
if(length(ind.traps.j) > 0) {
eta.traps.j <- sapply(R.halton,function(R.j) alpha[1]+sigma[1]*R.j)
lambda.traps.j <- exp(eta.traps.j)
t.j <- rep(1,length(ind.traps.j))
if(any(rat.j$offset_req[ind.traps.j]==1)) t.j[rat.j$offset_req[ind.traps.j]==1] <- 0.5
llik.traps.j <- sapply(1:length(ind.traps.j),
function(h) dbinom(rat.j$outcome[ind.traps.j][h],1,
prob = 1-exp(-t.j[h]*lambda.traps.j),
log=TRUE))
if(length(ind.traps.j) > 1) {
out.traps.j <- apply(llik.traps.j,1,function(row) exp(sum(row)))
} else {
out.traps.j <- exp(llik.traps.j)
}
}
if(length(ind.plates.j) > 0) {
eta.plates.j <- sapply(R.halton,function(R.j) alpha[2]+sigma[2]*R.j)
q.plates.j <- 1/(1+exp(-eta.plates.j))
llik.plates.j <- sapply(1:length(ind.plates.j),
function(h) dbinom(rat.j$outcome[ind.plates.j][h],
rat.j$offset[ind.plates.j][h],
prob = q.plates.j,
log=TRUE))
if(length(ind.plates.j) > 1) {
out.plates.j <- apply(llik.plates.j,1,function(row) exp(sum(row)))
} else {
out.plates.j <- exp(llik.plates.j)
}
}
if(length(ind.burrows.j) > 0) {
eta.burrows.j <- sapply(R.halton,function(R.j) alpha[3]+sigma[3]*R.j)
lambda.burrows.j <- exp(eta.burrows.j)
llik.burrows.j <- sapply(1:length(ind.burrows.j),
function(h) -lambda.burrows.j + rat.j$outcome[ind.burrows.j][h]*log(lambda.burrows.j))
if(length(ind.burrows.j) > 1) {
out.burrows.j <- apply(llik.burrows.j,1,function(row) exp(sum(row)))
} else {
out.burrows.j <- exp(llik.burrows.j)
}
}
if(length(ind.faeces.j)>0) {
eta.faeces.j <- sapply(R.halton,function(R.j) alpha[4]+sigma[4]*R.j)
p.faeces.j <- 1/(1+exp(- eta.faeces.j))
llik.faeces.j <- sapply(1:length(ind.faeces.j), function(h) rat.j$outcome[ind.faeces.j][h]*log(p.faeces.j)+
(1-rat.j$outcome[ind.faeces.j][h])*log(1-p.faeces.j))
if(length(ind.faeces.j) > 1) {
out.faeces.j <- apply(llik.faeces.j,1,function(row) exp(sum(row)))
} else {
out.faeces.j <- exp(llik.faeces.j)
}
}
if(length(ind.trails.j)>0) {
eta.trails.j <- sapply(R.halton,function(R.j) alpha[5]+sigma[5]*R.j)
p.trails.j <- 1/(1+exp(- eta.trails.j))
llik.trails.j <- sapply(1:length(ind.trails.j), function(h) rat.j$outcome[ind.trails.j][h]*log(p.trails.j)+
(1-rat.j$outcome[ind.trails.j][h])*log(1-p.trails.j))
if(length(ind.trails.j) > 1) {
out.trails.j <- apply(llik.trails.j,1,function(row) exp(sum(row)))
} else {
out.trails.j <- exp(llik.trails.j)
}
}
den <- mean(exp(log(out.traps.j)+log(out.plates.j)+
log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j)))
num <- mean(U.halton*exp(log(out.traps.j)+log(out.plates.j)+
log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j)))
num/den
}
# 3. Fit non-spatial rattiness-ecology model with covariates
llik.non.spatial.rattiness.with.covariates.fn <- function(par) {
# Set up parameters
alpha <- par[1:n.inst]
sigma <- exp(par[((n.inst+1):(2*n.inst))])
n.loc <- length(unique(ID))
beta <- par[(2*n.inst+1):(2*n.inst+p)]
eta.R <- as.numeric(D%*%beta)
out <- 0
for(j in 1:n.loc) { # we use j to denote location
R.halton <- eta.R[j] + U.halton
rat.j <- rat[ID==j,]
data_type.j <- rat.j$data_type
ind.traps.j <- which(data_type.j=="traps")
ind.plates.j <- which(data_type.j=="plates")
ind.burrows.j <- which(data_type.j=="burrows")
ind.faeces.j <- which(data_type.j=="faeces")
ind.trails.j <- which(data_type.j=="trails")
out.traps.j <- 1
out.plates.j <- 1
out.burrows.j <- 1
out.faeces.j <- 1
out.trails.j <- 1
if(length(ind.traps.j) > 0) {
eta.traps.j <- sapply(R.halton,function(R.j) alpha[1]+sigma[1]*R.j)
lambda.traps.j <- exp(eta.traps.j)
t.j <- rep(1,length(ind.traps.j))
if(any(rat.j$offset_req[ind.traps.j]==1)) t.j[rat.j$offset_req[ind.traps.j]==1] <- 0.5
llik.traps.j <- sapply(1:length(ind.traps.j),
function(h) dbinom(rat.j$outcome[ind.traps.j][h],1,
prob = 1-exp(-t.j[h]*lambda.traps.j),
log=TRUE))
if(length(ind.traps.j) > 1) {
out.traps.j <- apply(llik.traps.j,1,function(row) exp(sum(row)))
} else {
out.traps.j <- exp(llik.traps.j)
}
}
if(length(ind.plates.j) > 0) {
eta.plates.j <- sapply(R.halton,function(R.j) alpha[2]+sigma[2]*R.j)
q.plates.j <- 1/(1+exp(-eta.plates.j))
llik.plates.j <- sapply(1:length(ind.plates.j),
function(h) dbinom(rat.j$outcome[ind.plates.j][h],
rat.j$offset[ind.plates.j][h],
prob = q.plates.j,
log=TRUE))
if(length(ind.plates.j) > 1) {
out.plates.j <- apply(llik.plates.j,1,function(row) exp(sum(row)))
} else {
out.plates.j <- exp(llik.plates.j)
}
}
if(length(ind.burrows.j) > 0) {
eta.burrows.j <- sapply(R.halton,function(R.j) alpha[3]+sigma[3]*R.j)
lambda.burrows.j <- exp(eta.burrows.j)
llik.burrows.j <- sapply(1:length(ind.burrows.j),
function(h) -lambda.burrows.j + rat.j$outcome[ind.burrows.j][h]*log(lambda.burrows.j))
if(length(ind.burrows.j) > 1) {
out.burrows.j <- apply(llik.burrows.j,1,function(row) exp(sum(row)))
} else {
out.burrows.j <- exp(llik.burrows.j)
}
}
if(length(ind.faeces.j)>0) {
eta.faeces.j <- sapply(R.halton,function(R.j) alpha[4]+sigma[4]*R.j)
p.faeces.j <- 1/(1+exp(- eta.faeces.j))
llik.faeces.j <- sapply(1:length(ind.faeces.j), function(h) rat.j$outcome[ind.faeces.j][h]*log(p.faeces.j)+
(1-rat.j$outcome[ind.faeces.j][h])*log(1-p.faeces.j))
if(length(ind.faeces.j) > 1) {
out.faeces.j <- apply(llik.faeces.j,1,function(row) exp(sum(row)))
} else {
out.faeces.j <- exp(llik.faeces.j)
}
}
if(length(ind.trails.j)>0) {
eta.trails.j <- sapply(R.halton,function(R.j) alpha[5]+sigma[5]*R.j)
p.trails.j <- 1/(1+exp(- eta.trails.j))
llik.trails.j <- sapply(1:length(ind.trails.j), function(h) rat.j$outcome[ind.trails.j][h]*log(p.trails.j)+
(1-rat.j$outcome[ind.trails.j][h])*log(1-p.trails.j))
if(length(ind.trails.j) > 1) {
out.trails.j <- apply(llik.trails.j,1,function(row) exp(sum(row)))
} else {
out.trails.j <- exp(llik.trails.j)
}
}
out <- out+log(mean(exp(log(out.traps.j)+log(out.plates.j)+
log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j))))
}
return(out)
}
# 4. Compute predicted Uj values at each location (with covariates)
# compute.pred.mean.Uj.with.cov.fn <- function(par,j) {
# n.loc <- length(unique(ID))
#
# alpha <- par[1:n.inst]
# sigma <- exp(par[((n.inst+1):(2*n.inst))])
# beta <- par[(2*n.inst+1):(2*n.inst+p)]
#
# n.loc <- length(unique(ID))
#
# eta.R.j <- sum(D[j,]*beta)
#
# R.halton <- eta.R.j+U.halton
# R.halton <- U.halton
# rat.j <- rat[ID==j,]
# data_type.j <- rat.j$data_type
# ind.plates.j <- which(data_type.j=="plates")
# ind.traps.j <- which(data_type.j=="traps")
# ind.signs.j <- which(data_type.j=="signs")
#
# out.signs.j <- 1
# out.traps.j <- 1
# out.plates.j <- 1
#
# if(length(ind.signs.j)>0) {
# eta.signs.j <- sapply(R.halton,function(R.j) alpha[1]+sigma[1]*R.j)
# p.signs.j <- 1/(1+exp(- eta.signs.j))
#
# llik.signs.j <-
# rat.j$outcome[ind.signs.j]*log(p.signs.j)+
# (1-rat.j$outcome[ind.signs.j])*log(1-p.signs.j)
# out.signs.j <- exp(llik.signs.j)
# }
#
# if(length(ind.traps.j) > 0) {
# eta.traps.j <- sapply(R.halton,function(R.j) alpha[2]+sigma[2]*R.j)
# lambda.traps.j <- exp(eta.traps.j)
# t.j <- rep(1,length(ind.traps.j))
# if(any(rat.j$offset_req[ind.traps.j]==1)) t.j[rat.j$offset_req[ind.traps.j]==1] <- 0.5
# llik.traps.j <- sapply(1:length(ind.traps.j),
# function(h) dbinom(rat.j$outcome[ind.traps.j][h],1,
# prob = 1-exp(-t.j[h]*lambda.traps.j),
# log=TRUE))
# if(length(ind.traps.j) > 1) {
# out.traps.j <- apply(llik.traps.j,1,function(row) exp(sum(row)))
# } else {
# out.traps.j <- exp(llik.traps.j)
# }
# }
#
# if(length(ind.plates.j) > 0) {
# eta.plates.j <- sapply(R.halton,function(R.j) alpha[3]+sigma[3]*R.j)
# q.plates.j <- 1/(1+exp(-eta.plates.j))
# llik.plates.j <- sapply(1:length(ind.plates.j),
# function(h) dbinom(rat.j$outcome[ind.plates.j][h],
# rat.j$offset[ind.plates.j][h],
# prob = q.plates.j,
# log=TRUE))
# if(length(ind.plates.j) > 1) {
# out.plates.j <- apply(llik.plates.j,1,function(row) exp(sum(row)))
# } else {
# out.plates.j <- exp(llik.plates.j)
# }
# }
# den <- mean(exp(log(out.signs.j)+log(out.traps.j)+log(out.plates.j)))
# num <- mean(U.halton*exp(log(out.signs.j)+log(out.traps.j)+log(out.plates.j)))
# num/den
# }
# compute.pred.mean.Uj.with.cov.fn <- function(par,j) {
# n.loc <- length(unique(ID))
#
# alpha <- par[1:n.inst]
# sigma <- exp(par[((n.inst+1):(2*n.inst))])
# beta <- par[(2*n.inst+1):(2*n.inst+p)]
#
# n.loc <- length(unique(ID))
#
# eta.R.j <- sum(D[j,]*beta)
#
# R.halton <- eta.R.j+U.halton
# R.halton <- U.halton
# rat.j <- rat[ID==j,]
# data_type.j <- rat.j$data_type
# ind.traps.j <- which(data_type.j=="traps")
# ind.plates.j <- which(data_type.j=="plates")
# ind.burrows.j <- which(data_type.j=="burrows")
# ind.faeces.j <- which(data_type.j=="faeces")
# ind.trails.j <- which(data_type.j=="trails")
#
# out.traps.j <- 1
# out.plates.j <- 1
# out.burrows.j <- 1
# out.faeces.j <- 1
# out.trails.j <- 1
#
# if(length(ind.traps.j) > 0) {
# eta.traps.j <- sapply(R.halton,function(R.j) alpha[1]+sigma[1]*R.j)
# lambda.traps.j <- exp(eta.traps.j)
# t.j <- rep(1,length(ind.traps.j))
# if(any(rat.j$offset_req[ind.traps.j]==1)) t.j[rat.j$offset_req[ind.traps.j]==1] <- 0.5
#
# llik.traps.j <- sapply(1:length(ind.traps.j),
# function(h) dbinom(rat.j$outcome[ind.traps.j][h],1,
# prob = 1-exp(-t.j[h]*lambda.traps.j),
# log=TRUE))
# if(length(ind.traps.j) > 1) {
# out.traps.j <- apply(llik.traps.j,1,function(row) exp(sum(row)))
# } else {
# out.traps.j <- exp(llik.traps.j)
# }
# }
#
# if(length(ind.plates.j) > 0) {
# eta.plates.j <- sapply(R.halton,function(R.j) alpha[2]+sigma[2]*R.j)
# q.plates.j <- 1/(1+exp(-eta.plates.j))
# llik.plates.j <- sapply(1:length(ind.plates.j),
# function(h) dbinom(rat.j$outcome[ind.plates.j][h],
# rat.j$offset[ind.plates.j][h],
# prob = q.plates.j,
# log=TRUE))
# if(length(ind.plates.j) > 1) {
# out.plates.j <- apply(llik.plates.j,1,function(row) exp(sum(row)))
# } else {
# out.plates.j <- exp(llik.plates.j)
# }
# }
#
# if(length(ind.burrows.j) > 0) {
# eta.burrows.j <- sapply(R.halton,function(R.j) alpha[3]+sigma[3]*R.j)
# lambda.burrows.j <- exp(eta.burrows.j)
#
# llik.burrows.j <- sapply(1:length(ind.burrows.j),
# function(h) -lambda.burrows.j + rat.j$outcome[ind.burrows.j][h]*log(lambda.burrows.j))
#
# if(length(ind.burrows.j) > 1) {
# out.burrows.j <- apply(llik.burrows.j,1,function(row) exp(sum(row)))
# } else {
# out.burrows.j <- exp(llik.burrows.j)
# }
# }
#
# if(length(ind.faeces.j)>0) {
# eta.faeces.j <- sapply(R.halton,function(R.j) alpha[4]+sigma[4]*R.j)
# p.faeces.j <- 1/(1+exp(- eta.faeces.j))
#
# llik.faeces.j <- sapply(1:length(ind.faeces.j), function(h) rat.j$outcome[ind.faeces.j][h]*log(p.faeces.j)+
# (1-rat.j$outcome[ind.faeces.j][h])*log(1-p.faeces.j))
#
# if(length(ind.faeces.j) > 1) {
# out.faeces.j <- apply(llik.faeces.j,1,function(row) exp(sum(row)))
# } else {
# out.faeces.j <- exp(llik.faeces.j)
# }
# }
#
# if(length(ind.trails.j)>0) {
# eta.trails.j <- sapply(R.halton,function(R.j) alpha[5]+sigma[5]*R.j)
# p.trails.j <- 1/(1+exp(- eta.trails.j))
#
# llik.trails.j <- sapply(1:length(ind.trails.j), function(h) rat.j$outcome[ind.trails.j][h]*log(p.trails.j)+
# (1-rat.j$outcome[ind.trails.j][h])*log(1-p.trails.j))
#
# if(length(ind.trails.j) > 1) {
# out.trails.j <- apply(llik.trails.j,1,function(row) exp(sum(row)))
# } else {
# out.trails.j <- exp(llik.trails.j)
# }
# }
#
# den <- mean(exp(log(out.traps.j)+log(out.plates.j)+
# log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j)))
# num <- mean(U.halton*exp(log(out.traps.j)+log(out.plates.j)+
# log(out.burrows.j)+log(out.faeces.j)+log(out.trails.j)))
# num/den
# }