######################################################################## # Fit of the model # # Beware to install JAGS on your computer and in a second time # the R package rjags, before using the script. # # Author : Thibaut Lurier # Email : thibaut.lurier@vetagro-sup.fr ######################################################################## require(rjags) require(lattice) # Data data <- read.table("Data_Lurier_LCM_Cburnetii_VetRes_2021.txt",header = TRUE) ############################################ # Description of the model in JAGS language# ############################################ model.lclass <- "model { # Number of animal from each population (herd) in each of the 8 categories of tests results for (i in 1:Npop) { n[i,] ~ dmulti(p[i,],N[i]) p[i,1] <- Pinf[i] * ((1 - Se1) * (1 - Se2) * (1 - Se3) + covse_000) + (1 - Pinf[i]) * ((Sp1 * Sp2 * Sp3) + covsp_000) p[i,2] <- Pinf[i] * ((1 - Se1) * (1 - Se2) * Se3 + covse_001) + (1 - Pinf[i]) * (Sp1 * Sp2 * (1 - Sp3) + covsp_001) p[i,3] <- Pinf[i] * ((1 - Se1) * Se2 * (1 - Se3) + covse_010 ) + (1 - Pinf[i]) * (Sp1 * (1 - Sp2) * Sp3 + covsp_010) p[i,4] <- Pinf[i] * ((1 - Se1) * Se2 * Se3 + covse_011) + (1 - Pinf[i]) * (Sp1 * (1 - Sp2) * (1 - Sp3) + covsp_011) p[i,5] <- Pinf[i] * (Se1 * (1 - Se2) * (1 - Se3) + covse_100) + (1 - Pinf[i]) * ((1 - Sp1) * Sp2 * Sp3 + covsp_100) p[i,6] <- Pinf[i] * (Se1 * (1 - Se2) * Se3 + covse_101) + (1 - Pinf[i]) * ((1 - Sp1) * Sp2 * (1 - Sp3) + covsp_101) p[i,7] <- Pinf[i] * (Se1 * Se2 * (1 - Se3) + covse_110) + (1 - Pinf[i]) * ((1 - Sp1) * (1 - Sp2) * Sp3 + covsp_110) p[i,8] <- Pinf[i] * (Se1 * Se2 * Se3 + covse_111) + (1 - Pinf[i]) * ((1 - Sp1) * (1 - Sp2) * (1 - Sp3) + covsp_111) } # zero inflated beta-binomial distribution of the prevalence in each heard for(e in 1:Npop) { herdstatus[e] ~ dbern(Pherd[numdpt[e]]) P[e] ~ dbeta(mup * (1 - gamma) / gamma, (1 - mup) * (1 - gamma) / gamma)T(0.00001,0.99999) Pinf[e] <- P[e] * herdstatus[e] # P[e] is at least 1 out the herdsize y_P[e] ~ dinterval(P[e], 1/Nherd[e]) } # Calculation of the covariance terms covse_100 <- covse_011 + covse_111 - covse_000 covse_101 <- -(covse_001 + covse_011 + covse_111) covse_110 <- covse_000 + covse_001 - covse_111 covse_010 <- -(covse_000 + covse_001 + covse_011) covsp_100 <- covsp_011 + covsp_111 - covsp_000 covsp_101 <- -(covsp_001 + covsp_011 + covsp_111) covsp_110 <- covsp_000 + covsp_001 - covsp_111 covsp_010 <- -(covsp_000 + covsp_001 + covsp_011) ######## # Prior# ######## # Between herd prevalence of the jth departement for(j in 1:Ndpt) { Pherd[j] ~ dbeta(0.5,0.5) } mup ~ dbeta(0.5,0.5)T(0.00001,0.99999) gamma ~ dbeta(0.5,0.5)T(0.00001,0.99999) Se1 ~ dbeta(0.5,0.5) Se2 ~ dbeta(0.5,0.5) Se3 ~ dbeta(0.5,0.5) Sp1 ~ dbeta(0.5,0.5) Sp2 ~ dbeta(0.5,0.5) Sp3 ~ dbeta(0.5,0.5) covse_111 ~ dt(0, 1/0.039^2 , 1) covse_011 ~ dt(0, 1/0.039^2 , 1) covse_000 ~ dt(0, 1/0.039^2 , 1) covse_001 ~ dt(0, 1/0.039^2 , 1) covsp_111 ~ dt(0, 1/0.039^2 , 1) covsp_011 ~ dt(0, 1/0.039^2 , 1) covsp_000 ~ dt(0, 1/0.039^2 , 1) covsp_001 ~ dt(0, 1/0.039^2 , 1) ########################## # Inequality constraints # ########################## # Se > 1-Sp yse1 ~ dinterval(Se1 ,c(1-Sp1,1)) yse2 ~ dinterval(Se2 ,c(1-Sp2,1)) yse3 ~ dinterval(Se3 ,c(1-Sp3,1)) # inequality constraints for covariance terms yse_000 ~ dinterval(covse_000 ,c(-(1-Se1)*(1-Se2)*(1-Se3),min(1-Se1, min(1-Se2, 1-Se3))-(1-Se1)*(1-Se2)*(1-Se3))) yse_001 ~ dinterval(covse_001 ,c(-(1-Se1)*(1-Se2)*Se3,min(1-Se1, min(1-Se2, Se3))-(1-Se1)*(1-Se2)*Se3)) yse_010 ~ dinterval(covse_010 ,c(-(1-Se1)*Se2*(1-Se3),min(1-Se1, min(Se2, 1-Se3))-(1-Se1)*Se2*(1-Se3))) yse_011 ~ dinterval(covse_011 ,c(-(1-Se1)*Se2*Se3, min(1-Se1, min(Se2, Se3))-(1-Se1)*Se2*Se3)) yse_100 ~ dinterval(covse_100 ,c(-Se1*(1-Se2)*(1-Se3),min(Se1, min((1-Se2), (1-Se3))) -Se1*(1-Se2)*(1-Se3))) yse_101 ~ dinterval(covse_101 ,c(-Se1*(1-Se2)*Se3, min(Se1, min((1-Se2), Se3))-Se1*(1-Se2)*Se3)) yse_110 ~ dinterval(covse_110 ,c(-Se1*Se2*(1-Se3),min(Se1, min(Se2, 1-Se3))-Se1*Se2*(1-Se3))) yse_111 ~ dinterval(covse_111 ,c(-Se1*Se2*Se3,min(Se1, min(Se2, Se3)) -Se1*Se2*Se3)) ysp_000 ~ dinterval(covsp_000 ,c(-Sp1*Sp2*Sp3,min(Sp1, min(Sp2, Sp3))-Sp1*Sp2*Sp3)) ysp_001 ~ dinterval(covsp_001 ,c(-Sp1*Sp2*(1-Sp3), min(Sp1, min(Sp2, 1-Sp3))-Sp1*Sp2*(1-Sp3))) ysp_010 ~ dinterval(covsp_010 ,c(-Sp1*(1-Sp2)*Sp3,min(Sp1, min(1-Sp2, Sp3))-Sp1*(1-Sp2)*Sp3)) ysp_011 ~ dinterval(covsp_011 ,c(-Sp1*(1-Sp2)*(1-Sp3),min(Sp1, min(1-Sp2, 1-Sp3))-Sp1*(1-Sp2)*(1-Sp3))) ysp_100 ~ dinterval(covsp_100 ,c(-(1-Sp1)*Sp2*Sp3,min((1-Sp1),min(Sp2, Sp3))-(1-Sp1)*Sp2*Sp3)) ysp_110 ~ dinterval(covsp_110 ,c(-(1-Sp1)*(1-Sp2)*Sp3,min((1-Sp1), min((1-Sp2), Sp3))-(1-Sp1)*(1-Sp2)*(1-Sp3))) ysp_101 ~ dinterval(covsp_101 ,c(-(1-Sp1)*Sp2*(1-Sp3),min((1-Sp1), min(Sp2, 1-Sp3))-(1-Sp1)*Sp2*(1-Sp3))) ysp_111 ~ dinterval(covsp_111 ,c(-(1-Sp1)*(1-Sp2)*(1-Sp3),min(1-Sp1, min(1-Sp2, 1-Sp3))-(1-Sp1)*(1-Sp2)*(1-Sp3))) }" ####################################################### ##################### SHEEP ##################### ####################################################### data_O <- subset(data, data$species == "sheep") data_O$Nherd[is.na(data_O$Nherd)] <- median(data_O$Nherd,na.rm = T) #Creation of argument data for jags.model N <- rowSums(data_O[,4:11]) data4jags.lclass_O <- list(Npop = nrow(data_O), N = N, Nherd = data_O$Nherd, n = as.matrix(data_O[,4:11]), Ndpt=10, numdpt = data_O$dpt, yse_000 = 1, yse_001 = 1, yse_010 = 1, yse_011 = 1, yse_100 = 1, yse_101 = 1, yse_110 = 1, yse_111 = 1, ysp_000 = 1, ysp_001 = 1, ysp_010 = 1, ysp_011 = 1, ysp_100 = 1, ysp_101 = 1, ysp_110 = 1, ysp_111 = 1, yse1 = 1, yse2 = 1, yse3 = 1, y_P = rep(1,nrow(data_O))) ################## # Initialisation # ################## # initialization ensures that the parameters respect the constraints of the model inits <- list(list(),list(),list()) for (k in 1:3) { Sp1 <- rbeta(1,5,1) Sp2 <- rbeta(1,5,1) Sp3 <- rbeta(1,5,1) Se1 <- runif(1,1-Sp1,1) Se2 <- runif(1,1-Sp2,1) Se3 <- runif(1,1-Sp3,1) covse_111 <- 0 covse_011 <- 0 covse_001 <- 0 covse_000 <- 0 covsp_111 <- 0 covsp_011 <- 0 covsp_001 <- 0 covsp_000 <- 0 P <- runif(length(data_O$Nherd),1/data_O$Nherd,1) inits[[k]] <- list(Se1 = Se1, Se2 = Se2, Se3 = Se3,Sp1 = Sp1, Sp2 = Sp2, Sp3 = Sp3, covse_111 = covse_111, covse_011 = covse_011, covse_001 = covse_001, covse_000 = covse_000, covsp_111 = covsp_111, covsp_011 = covsp_011, covsp_001 = covsp_001, covsp_000 = covsp_000, P = P) } ################################## # Inference using MCMC algorithm # # This step can take a few hours # ################################## m.lclass_O<- jags.model(file = textConnection(model.lclass), data = data4jags.lclass_O, n.chains = 3, inits = inits) update(m.lclass_O, n.iter = 10000) # burnin mcmc.lclass_O<- coda.samples(m.lclass_O, c("mup","gamma","Pherd","Se1","Se2","Se3", "Sp1","Sp2","Sp3","covse_000","covse_001", "covse_011", "covse_111","covsp_000","covsp_001", "covsp_011", "covsp_111"), n.iter = 100000, thin = 20) ############################## # Estimation and diagnostics # ############################## # Check of the convergence xyplot((mcmc.lclass_O),layout=c(3,6)) gelman.diag(mcmc.lclass_O) # Parameter estimations summary( mcmc.lclass_O) densityplot(mcmc.lclass_O,layout=c(3,6)) ####################################################### ##################### GOAT ##################### ####################################################### data_C <- subset(data, data$species == "goat") data_C$Nherd[is.na(data_C$Nherd)] <- median(data_C$Nherd,na.rm = T) #Creation of argument data for jags.model N <- rowSums(data_C[,4:11]) data4jags.lclass_C <- list(Npop = nrow(data_C), N = N, Nherd = data_C$Nherd, n = as.matrix(data_C[,4:11]), Ndpt=10, numdpt = data_C$dpt, yse_000 = 1, yse_001 = 1, yse_010 = 1, yse_011 = 1, yse_100 = 1, yse_101 = 1, yse_110 = 1, yse_111 = 1, ysp_000 = 1, ysp_001 = 1, ysp_010 = 1, ysp_011 = 1, ysp_100 = 1, ysp_101 = 1, ysp_110 = 1, ysp_111 = 1, yse1 = 1, yse2 = 1, yse3 = 1, y_P = rep(1,nrow(data_C))) ################## # Initialisation # ################## # initialization ensures that the parameters respect the constraints of the model inits <- list(list(),list(),list()) for (k in 1:3) { Sp1 <- rbeta(1,5,1) Sp2 <- rbeta(1,5,1) Sp3 <- rbeta(1,5,1) Se1 <- runif(1,1-Sp1,1) Se2 <- runif(1,1-Sp2,1) Se3 <- runif(1,1-Sp3,1) covse_111 <- 0 covse_011 <- 0 covse_001 <- 0 covse_000 <- 0 covsp_111 <- 0 covsp_011 <- 0 covsp_001 <- 0 covsp_000 <- 0 P <- runif(length(data_C$Nherd),1/data_C$Nherd,1) inits[[k]] <- list(Se1 = Se1, Se2 = Se2, Se3 = Se3,Sp1 = Sp1, Sp2 = Sp2, Sp3 = Sp3, covse_111 = covse_111, covse_011 = covse_011, covse_001 = covse_001, covse_000 = covse_000, covsp_111 = covsp_111, covsp_011 = covsp_011, covsp_001 = covsp_001, covsp_000 = covsp_000, P = P) } ################################## # Inference using MCMC algorithm # # This step can take a few hours # ################################## m.lclass_C<- jags.model(file = textConnection(model.lclass), data = data4jags.lclass_C, n.chains = 3, inits = inits) update(m.lclass_C, n.iter = 10000) # burnin mcmc.lclass_C<- coda.samples(m.lclass_C, c("mup","gamma","Pherd","Se1","Se2","Se3", "Sp1","Sp2","Sp3","covse_000","covse_001", "covse_011", "covse_111","covsp_000","covsp_001", "covsp_011", "covsp_111"), n.iter = 100000, thin = 20) ############################## # Estimation and diagnostics # ############################## # Check of the convergence xyplot((mcmc.lclass_C),layout=c(3,6)) gelman.diag(mcmc.lclass_C) # Parameter estimations summary( mcmc.lclass_C) densityplot(mcmc.lclass_C,layout=c(3,6)) ####################################################### ######## CATTLE without 7th Department ############# ####################################################### data_B_s7 <- subset(data, data$species == "cattle" & data$dpt!=7) data_B_s7$Nherd <- as.integer(data_B_s7$Nherd) data_B_s7$Nherd[is.na(data_B_s7$Nherd)] <- median(data_B_s7$Nherd,na.rm = T) #Creation of argument data for jags.model N <- rowSums(data_B_s7[,4:11]) data4jags.lclass_B_s7 <- list(Npop = nrow(data_B_s7), N = N, Nherd = data_B_s7$Nherd , n = as.matrix(data_B_s7[,4:11]), Ndpt=10, numdpt = data_B_s7$dpt, yse_000 = 1, yse_001 = 1, yse_010 = 1, yse_011 = 1, yse_100 = 1, yse_101 = 1, yse_110 = 1, yse_111 = 1, ysp_000 = 1, ysp_001 = 1, ysp_010 = 1, ysp_011 = 1, ysp_100 = 1, ysp_101 = 1, ysp_110 = 1, ysp_111 = 1, yse1 = 1, yse2 = 1, yse3 = 1, y_P = rep(1,nrow(data_B_s7))) ################## # Initialisation # ################## # initialization ensures that the parameters respect the constraints of the model inits <- list(list(),list(),list()) for (k in 1:3) { Sp1 <- rbeta(1,5,1) Sp2 <- rbeta(1,5,1) Sp3 <- rbeta(1,5,1) Se1 <- runif(1,1-Sp1,1) Se2 <- runif(1,1-Sp2,1) Se3 <- runif(1,1-Sp3,1) covse_111 <- 0 covse_011 <- 0 covse_001 <- 0 covse_000 <- 0 covsp_111 <- 0 covsp_011 <- 0 covsp_001 <- 0 covsp_000 <- 0 P <- runif(length(data_B_s7$Nherd),1/data_B_s7$Nherd,1) inits[[k]] <- list(Se1 = Se1, Se2 = Se2, Se3 = Se3,Sp1 = Sp1, Sp2 = Sp2, Sp3 = Sp3, covse_111 = covse_111, covse_011 = covse_011, covse_001 = covse_001, covse_000 = covse_000, covsp_111 = covsp_111, covsp_011 = covsp_011, covsp_001 = covsp_001, covsp_000 = covsp_000, P = P) } ################################## # Inference using MCMC algorithm # # This step can take a few hours # ################################## m.lclass_B_s7<- jags.model(file = textConnection(model.lclass), data = data4jags.lclass_B_s7, n.chains = 3, inits = inits) update(m.lclass_B_s7, n.iter = 10000) # burnin mcmc.lclass_B_s7<- coda.samples(m.lclass_B_s7, c("mup","gamma","Pherd","Se1","Se2","Se3", "Sp1","Sp2","Sp3","covse_000","covse_001", "covse_011", "covse_111","covsp_000","covsp_001", "covsp_011", "covsp_111"), n.iter = 100000, thin = 20) ############################## # Estimation and diagnostics # ############################## # Check of the convergence xyplot((mcmc.lclass_B_s7),layout=c(3,6)) gelman.diag(mcmc.lclass_B_s7) # Parameter estimations summary( mcmc.lclass_B_s7) densityplot(mcmc.lclass_B_s7,layout=c(3,6)) ####################################################### ####### CATTLE only in the 7th Department ########## ####################################################### data_B_7 <- subset(data, data$species == "cattle" & data$dpt==7) data_B_7$Nherd[is.na(data_B_7$Nherd)] <- median(data_B_7$Nherd,na.rm = T) #Creation of argument data for jags.model N <- rowSums(data_B_7[,4:11]) data4jags.lclass_B_7 <- list(Npop = nrow(data_B_7), N = N, Nherd = data_B_7$Nherd, n = as.matrix(data_B_7[,4:11]), Ndpt=10, numdpt = data_B_7$dpt, yse_000 = 1, yse_001 = 1, yse_010 = 1, yse_011 = 1, yse_100 = 1, yse_101 = 1, yse_110 = 1, yse_111 = 1, ysp_000 = 1, ysp_001 = 1, ysp_010 = 1, ysp_011 = 1, ysp_100 = 1, ysp_101 = 1, ysp_110 = 1, ysp_111 = 1, yse1 = 1, yse2 = 1, yse3 = 1, y_P = rep(1,nrow(data_B_7))) ################## # Initialisation # ################## # initialization ensures that the parameters respect the constraints of the model inits <- list(list(),list(),list()) for (k in 1:3) { Sp1 <- rbeta(1,5,1) Sp2 <- rbeta(1,5,1) Sp3 <- rbeta(1,5,1) Se1 <- runif(1,1-Sp1,1) Se2 <- runif(1,1-Sp2,1) Se3 <- runif(1,1-Sp3,1) covse_111 <- 0 covse_011 <- 0 covse_001 <- 0 covse_000 <- 0 covsp_111 <- 0 covsp_011 <- 0 covsp_001 <- 0 covsp_000 <- 0 P <- runif(length(data_B_7$Nherd),1/data_B_7$Nherd,1) inits[[k]] <- list(Se1 = Se1, Se2 = Se2, Se3 = Se3,Sp1 = Sp1, Sp2 = Sp2, Sp3 = Sp3, covse_111 = covse_111, covse_011 = covse_011, covse_001 = covse_001, covse_000 = covse_000, covsp_111 = covsp_111, covsp_011 = covsp_011, covsp_001 = covsp_001, covsp_000 = covsp_000, P = P) } ################################## # Inference using MCMC algorithm # # This step can take a few hours # ################################## m.lclass_B_7<- jags.model(file = textConnection(model.lclass), data = data4jags.lclass_B_7, n.chains = 3, inits = inits) update(m.lclass_B_7, n.iter = 10000) # burnin mcmc.lclass_B_7<- coda.samples(m.lclass_B_7, c("mup","gamma","Pherd","Se1","Se2","Se3", "Sp1","Sp2","Sp3","covse_000","covse_001", "covse_011", "covse_111","covsp_000","covsp_001", "covsp_011", "covsp_111"), n.iter = 100000, thin = 20) ############################## # Estimation and diagnostics # ############################## # Check of the convergence xyplot((mcmc.lclass_B_7),layout=c(3,6)) gelman.diag(mcmc.lclass_B_7) # Parameter estimations summary( mcmc.lclass_B_7) densityplot(mcmc.lclass_B_7,layout=c(3,6))