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Popmodels_statespace2_incl diag.R
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Popmodels_statespace2_incl diag.R
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#AllMeans <- read.csv("AllMeans.csv")
Popdata <- data.frame(MDperKMsqFall_mean=AllMeans$MDperKMsqFall_mean, year=AllMeans$year, macrounit=AllMeans$macrounit, HuntDen_All_mean=AllMeans$HuntDen_All_mean)#remove NAs
Popdata <- Popdata[which(complete.cases(Popdata)==TRUE),]
library(rjags)
# 5.2 A simple model ----------------------------------------
# Specify the model in JAGS:
sink("model_ss.jags")
cat("
model{
#Priors
N.est[1] ~ dunif(0.00001, 10) # Prior for initial population density (max in dataset:6.6)
mean.rmax ~ dunif(0.00001, 4) # Prior for mean rmax (geommean in dataset 0.2, max 3.4)
K ~ dunif(0.00001, 100) # prior for carrying capacity
sigma.proc ~ dunif(0.00001, 50) # Prior for sd of state process
sigma2.proc <- pow(sigma.proc, 2) # Variance = sd^2
tau.proc <- pow(sigma.proc, -2) # Tau = sqrt(sd)
sigma.obs ~ dunif(0.00001, 50) # Prior for sd of observation process
sigma2.obs <- pow(sigma.obs, 2)
tau.obs <- pow(sigma.obs, -2)
pH ~ dunif(0,1)
# Likelihood
# State process
for (t in 1:(T-1)){
rmax[t] ~ dnorm(mean.rmax, tau.proc)T(0, 10) # Truncated normal distribution to prevent values < 0
rd[t] <- rmax[t]*(1-N.est[t]/K)
N.est[t+1] <- N.est[t]+N.est[t]*rd[t]-pH*HuntDen[t]
}
# Observation process
for (t in 1:T){
y[t] ~ dnorm(N.est[t], tau.obs)
}
}
", fill=TRUE)
sink()
dev.off()
png("StateSpace2_30000_60000.png", width=2200, height=1500)
par(mfrow=c(2,2),oma=c(5,5,5,5),mar=c(10, 10, 10, 10))
parinfo <- data.frame("0-1" = numeric(21), "0-2" = numeric(21), "0-3" = numeric(21), "0-4" = numeric(21), row.names=c("mean of mean.rmax","sd. mean.rmax","se.mean.rmax", "median mean.rmax","mean of K", "sd.K", "se.K", "median.K","mean of sigma2.obs", "mean of sigma2.proc", "mean of sd.N.est","mean of se.N.est","mean of pH","sd.pH", "se.pH","2.5% quantile pH", "25% quantile pH","median pH","75% quantile pH","97.5% quantile pH","MSS"))
macrounits <- levels(Popdata$macrounit)
ylimmax <- c(3.5,3.5,3.5,6.5)
result_final <- list()
GelmanDiag <- list()
N_list <- list()
for (i in 1:length(macrounits)){
cond = which(Popdata$macrounit==macrounits[i])
tsteps <- length(Popdata$MDperKMsqFall_mean[cond])
# Bundle the data:
model.data <- list(y = Popdata$MDperKMsqFall_mean[cond], T = tsteps, HuntDen = Popdata$HuntDen_All_mean)
# Initial values:
# inits <- function(){list(sigma.proc = runif(1, 0, 10), mean.rmax = runif(1, 0.01, 10), K = runif(1, 0.1, 10), sigma.obs = runif(1, 0, 10), N.est = c(runif(1, 0.1, 10), rep(NA, (tsteps-1))))}
inits <- function(){list(sigma.proc = 1, mean.rmax = 0.1, K = 2, sigma.obs = 1, N.est = c(1, rep(NA, (tsteps-1))), pH=0.1);
list(sigma.proc = 1, mean.rmax = 0.5, K = 4, sigma.obs = 1, N.est = c(1, rep(NA, (tsteps-1))), pH=0.1)
list(sigma.proc = 1, mean.rmax = 1, K = 5, sigma.obs = 1, N.est = c(1, rep(NA, (tsteps-1))), pH=0.1)}
# Compile the model and run MCMC for burn-in phase:
model_fit <- jags.model(file = "model_ss.jags", data = model.data, inits = inits, n.chains = 3, n.adapt = 30000)
# Specify parameters whose posterior values are to be saved:
parameters <- c("mean.rmax", "sigma2.obs", "sigma2.proc", "K", "N.est","pH")
# Continue running the MCMC to produce posterior distributions:
result_sss <- coda.samples(model = model_fit, variable.names = parameters, n.iter = 60000)
# Extract relevant data for Convergence Diagnostics
b <- list(length(result_sss))
for (g in 1:3){#all 3 chains
incl <- which (!grepl("N.est", varnames(result_sss[[g]])))#exclude N.est for Gelman Diag
b[[g]] <- result_sss[[g]][,incl]
varnames(b[[g]]) <- varnames(result_sss[[g]][,incl])
}
result_final <- append(result_final,b)
GelmanDiag <- append(GelmanDiag, gelman.diag(result_sss))
#extract data
summ <- summary(result_sss)
res_means <- as.data.frame(summ$statistics)
res_quant <- as.data.frame(summ$quantiles)
N.est_mean <- res_means[which(rownames(res_means) == "N.est[1]"):(which(rownames(res_means) == "N.est[1]")+tsteps-1),] # plus tstep-1 in order to keep flexible for different lengths of data sets due to NAs
mean.rmax_mean <- res_means[which(rownames(res_means) == "mean.rmax"),]
K_mean <- res_means[which(rownames(res_means) == "K"),]
sigmas_mean <- res_means[c(which(rownames(res_means) == "sigma2.obs"), which(rownames(res_means) == "sigma2.proc")),]
pH_mean <- res_means[which(rownames(res_means) == "pH"),]
N.est_quant <- res_quant[which(rownames(res_quant) == "N.est[1]"):(which(rownames(res_means) == "N.est[1]")+tsteps-1),]
mean.rmax_quant <- res_quant[which(rownames(res_quant) == "mean.rmax"),]
K_quant <- res_quant[which(rownames(res_quant) == "K"),]
pH_quant <- res_quant[which(rownames(res_quant) == "pH"),]
MSE <- sum((abs(N.est_mean[,1]-Popdata$MDperKMsqFall_mean[cond]))^2, na.rm=TRUE)/length(Popdata$MDperKMsqFall_mean[cond])
# Make a nice graph with data and model result:
plot(Popdata$MDperKMsqFall_mean[cond]~Popdata$year[cond], cex=0.5, cex.axis=2.5, cex.main = 3, ylab = "", xlab = "", las = 1, col = "black", type = "p", main=macrounits[i], ylim=c(0,ylimmax[i]))
polygon(x = c(Popdata$year[cond], rev(Popdata$year[cond])), y = c(N.est_quant[,5], rev(N.est_quant[,1])), col = "gray90", border = "gray90")
lines (Popdata$MDperKMsqFall_mean[cond]~Popdata$year[cond], col="black", lwd=1)
lines (N.est_mean[,1]~Popdata$year[cond], col="red", lwd=2)
#legend("topleft", legend = c("Observed", "Estimated", "95% Quantile Estimated"), lty = c(1, 1, 1), lwd = c(1,1,1), col = c("black", "red", "grey"), bty = "n", cex = 1)
# display sd of estimate
#polygon(x = c(Popdata$year[cond], rev(Popdata$year[cond])), y = c((N.est_mean[,1]+2*N.est_mean[,2]), rev(N.est_mean[,1]-2*N.est_mean[,2])), col = "gray90", border = "gray90")
#lines (N.est_mean[,1]+2*N.est_mean[,2]~Popdata$year[cond], col="red", lty=2)
#lines (N.est_mean[,1]-2*N.est_mean[,2]~Popdata$year[cond], col="red", lty=2)
#legend("topleft", legend = c("Observed", "Estimated", "sd Estimated", "95% CRI"), lty = c(1, 1, 2, 1), lwd = c(2, 2, 1, 2), col = c("black", "red", "red", "grey"), bty = "n", cex = 1)
# save parameter estimates
parinfo[,i] <- format(c(mean.rmax_mean[,1], mean.rmax_mean[,2],mean.rmax_mean[,4],mean.rmax_quant[,3],K_mean[,1],K_mean[,2],K_mean[,4],K_quant[,3], sigmas_mean[,1], mean(N.est_mean[,2]),mean(N.est_mean[,4]),pH_mean[,1], pH_mean[,2],pH_mean[,4],pH_quant[1:5],MSE),scientific=FALSE)
txtname <- paste(c("StateSpace2_30000_60000_summary_results_sss_",i,".txt"),collapse="")
sink(txtname,type = c("output", "message"))
print(summary(result_sss))
sink()
#save N means and median to list
N_list <- append(N_list, list(N.est_mean[,1]))
N_list <- append(N_list, list(N.est_quant[,3]))
}
mtext("Year", 1, 1, outer=TRUE, cex=3)
mtext("Population Density", 2, 1, outer=TRUE, las=0, cex=3)
mtext("StateSpace2", 3, 1, outer=TRUE, cex=3.5)
parinfo <- format(parinfo, scientific=FALSE)
parinfo
dev.off()
#save Gelman plots
m=0
for (k in c(1,4,7,10)){
m<- m+1
name <- paste(c("StateSpace2_30000_60000_Diag_",m,".png"),collapse="")
png(name, width=2200, height=1500)
par(mfrow=c(2,3),oma=c(5,5,5,5),mar=c(10, 10, 10, 10))
gelman.plot(result_final[k:(k+2)], auto.layout=FALSE, cex.axis=2.5,cex.main=3,cex=5)
mtext(paste(c("Gelman Diagnostics: StateSpace2 - MU", as.character(m)), collapse = " "), 3, 1, outer=TRUE, cex=3)
dev.off()
}
#save histogramm of pH (always 1st chain)
m=0
png("StateSpace2_30000_60000_pH_histo.png", width=2200, height=1500)
par(mfrow=c(2,2),oma=c(5,5,5,5))
for (k in c(1,4,7,10)){
m<- m+1
xmin <- as.numeric(parinfo[16,m])-0.1
xmax <- as.numeric(parinfo[20,m])+0.1
hist(result_final[[k:k+2]][,"pH"],breaks=200, main=m,xlab="",cex.axis=2.5,cex.main=3,ylab="",xlim=c(xmin,xmax))
abline(v=as.numeric(parinfo[16,m]), col="red", lwd=3)
abline(v=as.numeric(parinfo[20,m]), col="red", lwd=3)
}
mtext("pH", 3, 1, outer=TRUE, cex=3)
dev.off()
#save density plot of pH
m=0
png("StateSpace2_30000_60000_pH_den_poly_2.png", width=4000, height=4000)
par(mfrow=c(2,2),oma=c(10,10,10,10),mar=c(10,10,10,10))
for (k in c(1,4,7,10)){
m<- m+1
d <- density(result_final[[k:k+2]][,"pH"])
xmin <- as.numeric(parinfo[16,m])-0.1
xmax <- as.numeric(parinfo[20,m])+0.1
plot(d, main=m,,cex.axis=6,cex.main=5,lwd=3,ylab="",xlab="",xlim=c(xmin,xmax))
polygon(x = c(as.numeric(parinfo[16,m]),as.numeric(parinfo[20,m]),as.numeric(parinfo[20,m]),as.numeric(parinfo[16,m])), y = c(min(d$y),min(d$y),max(d$y),max(d$y)), col = "gray90", border = "gray90")
lines(d, lwd=3)
# abline(v=as.numeric(parinfo[16,m]), col="red", lwd=3)
# abline(v=as.numeric(parinfo[20,m]), col="red", lwd=3)
}
mtext("pH", 3, 1, outer=TRUE, cex=6)
mtext("Value", 1, 1, outer=TRUE, cex=6)
mtext("Density", 2, 1, outer=TRUE, las=0, cex=6)
dev.off()
#save histogramm of K
m=0
png("StateSpace1_30000_60000_K_histo.png", width=2200, height=1500)
par(mfrow=c(2,2),oma=c(5,5,5,5))
for (k in c(1,4,7,10)){
m<- m+1
hist(result_final[[k:k+2]][,"K"],breaks=300, main=m,xlab="",cex.axis=2.5,cex.main=3,ylab="")
abline(v=as.numeric(parinfo[5,m]), col="red", lwd=3)#mean
abline(v=as.numeric(parinfo[8,m]), col="blue", lwd=3)#median
}
mtext("K in StateSpace2", 3, 1, outer=TRUE, cex=3)
dev.off()
#save histogramm of rmax
m=0
png("StateSpace1_30000_60000_rmax_histo_all 3chains.png", width=2200, height=1500)
par(mfrow=c(2,2),oma=c(5,5,5,5))
for (k in c(1,4,7,10)){
m<- m+1
hist(result_final[[k:k+2]][,"mean.rmax"],breaks=200, main=m,xlab="",cex.axis=2.5,cex.main=3,ylab="")
abline(v=as.numeric(parinfo[1,m]), col="red", lwd=3)#mean
abline(v=as.numeric(parinfo[4,m]), col="blue", lwd=3)#median
}
mtext("mean.rmax in StateSpace2", 3, 1, outer=TRUE, cex=3)
dev.off()
#save Gelman Diagnostics + parameter values
name2 <-paste(c("StateSpace2_30000_60000_GelmanDiag",".txt"),collapse="")
sink(name2, type=c("output","message"))
print(parinfo)
print(GelmanDiag)
sink()
#save traceplots
m=0
for (k in c(1,4,7,10)){
m<- m+1
name5 <- paste(c("StateSpace2_30000_60000_traceplots_margden_",m,".png"),collapse="")
png(name5, width=4000, height=5000)
par(mfrow=c(5,2),oma=c(5,5,5,5))
plot(result_final[[k:k+2]])
mtext(paste(c("Traceplots_MU ",m),""), 3, 1, outer=TRUE, cex=3)
dev.off()
}
print("DO YOU WANT MCMCPLOT HTML-FILES?")
print("DO YOU?")
print("DO YOU?")
print("DO YOU?")
# save posterior distr+traces in HTML (messy with all 4 MUs, keps overwriting files)
# library(mcmcplots)
# m=0
# for (k in c(1,4,7,10)){
# m<- m+1
# name3 <- paste(c("StateSpace2_15000_30000_Posterior_",m),collapse="")
# dire <- paste(c("C:/Users/lschmidt/Bachelorarbeit/Mule_deer/Popmodels/StateSpace2/30000_60000_3 chains dif initial/HTML",m),collapse="")
# mcmcplot(result_final[k:(k+2)],filename=name3,style="plain",title=name3,dir=dire)
# }