# Single Species Single Season Occupancy models using JAGS packages
# Blue Gross Beaks.
#Downloaded from https://sites.google.com/site/asrworkshop/home/schedule/r-occupancy-1
#An occupancy study was made on Blue Grosbeaks (Guiraca caerulea)
# on 41 old fields planted to longleaf pines (Pinus palustris)
# in southern Georgia, USA.
# Surveys were 500 m transects across each field
# and were completed three times during the breeding season in 2001.
# Columns in the file are:
# field - field number
# v1, v2, v3 - detection histories for each site on each of 3 visit during the 2001 breeding season.
# field.size - size of the files
# bqi - unknown
# crop.hist - crop history
# crop1, crop2 - indicator variables for the crop history
# count1, count2, count3 - are actual counts of birds detected in each visit
#
# Bayesian model using JAGS with NO COVARIATES, either for psi or detection
library("R2jags") # used for call to JAGS
## Loading required package: rjags
## Loading required package: coda
## Linked to JAGS 4.3.0
## Loaded modules: basemod,bugs
##
## Attaching package: 'R2jags'
## The following object is masked from 'package:coda':
##
## traceplot
library(coda)
library(ggplot2)
library(reshape2)
# The BUGS model is specified as a text file.
# The model file.
# The cat() command is used to save the model to the working directory.
# Notice that you CANNOT have any " (double quotes) in the bugs code
# between the start and end of the cat("...",) command.
# Inputs to the model are
# Nsites - number of sites
# Nvisits - (max) number of visits over all sites.
# Nsites.visits - number of sites x number of visits
# if there is missing data (no visits), simply drop the corresponding row
# History - vector of 1 or 0 corresponding to Site-Visit pair
# Site - vector indicating which site the row corresponds to
# Visit - vector indicating which visit the row corresponds to
#
# psi - occupancy parameter
# p - common detection probability
#
cat(file="model.txt", "
############################################################
model {
# set up the state model, i.e. is the site actually occupied or not
for(i in 1:Nsites){
z[i] ~ dbern(psi)
}
# the observation model.
for(j in 1:Nsites.visits){
p.z[j] <- z[Site[j]]*p
History[j] ~ dbern(p.z[j])
}
# priors
psi ~ dbeta(1,1)
p ~ dbeta(1,1)
# derived variables
# number of occupied sites
occ.sites <- sum(z[1:Nsites])
# belief that psi is above some value
prob.psi.greater.50 <- ifelse( psi > 0.5, 1, 0)
}
") # End of the model
# Next create the data.txt file.
# Initialize the data values using standard R code by either reading
# in from an external file, or plain assignment.
input.data <- read.csv(file.path("..","blgr.csv"),
header=TRUE, as.is=TRUE, strip.white=TRUE)
head(input.data)
## field v1 v2 v3 field.size bqi crop.hist crop1 crop2 count1 count2 count3
## 1 1 1 1 1 14.0 1 crop 1 0 1 2 2
## 2 2 1 1 0 12.7 1 crop 1 0 2 2 0
## 3 3 0 0 0 15.7 0 grass 0 1 0 0 0
## 4 4 0 1 0 19.5 0 grass 0 1 0 2 0
## 5 5 1 0 1 13.5 0 crop 1 0 1 0 1
## 6 6 0 0 1 9.6 0 mixed 0 1 0 0 2
## X logFS
## 1 NA 1.1461280
## 2 NA 1.1038037
## 3 NA 1.1958997
## 4 NA 1.2900346
## 5 NA 1.1303338
## 6 NA 0.9822712
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.data)
## [1] 41
range(input.data[, c("v1","v2","v3")], na.rm=TRUE)
## [1] 0 1
sum(is.na(input.data[, c("v1","v2","v3")]))
## [1] 0
input.history <- input.data[, c("v1","v2","v3")]
head(input.history)
## v1 v2 v3
## 1 1 1 1
## 2 1 1 0
## 3 0 0 0
## 4 0 1 0
## 5 1 0 1
## 6 0 0 1
History <- as.vector(unlist(input.history)) # stacks the columns
Site <- rep(1:nrow(input.history), ncol(input.history))
Visit <- rep(1:ncol(input.history), each=nrow(input.history))
cbind(Site, Visit, History)[1:10,]
## Site Visit History
## [1,] 1 1 1
## [2,] 2 1 1
## [3,] 3 1 0
## [4,] 4 1 0
## [5,] 5 1 1
## [6,] 6 1 0
## [7,] 7 1 0
## [8,] 8 1 1
## [9,] 9 1 1
## [10,] 10 1 1
Nsites <- nrow(input.history)
Nvisits <- ncol(input.history)
Nsites.visits <- length(History)
# The datalist will be passed to JAGS with the names of the data
# values.
data.list <- list("Nsites","Nvisits","Nsites.visits",
"History", "Site", "Visit") # or
# check the list
data.list
## [[1]]
## [1] "Nsites"
##
## [[2]]
## [1] "Nvisits"
##
## [[3]]
## [1] "Nsites.visits"
##
## [[4]]
## [1] "History"
##
## [[5]]
## [1] "Site"
##
## [[6]]
## [1] "Visit"
# Next create the initial values.
# If you are using more than one chain, you need to create a function
# that returns initial values for each chain.
# We define the initial value of z as 1 if any visit resulted in a detection, other wise 0
init.z <- apply(input.history, 1, max, na.rm=TRUE)
# we will use the naive estimate of occupancy.
init.psi <- sum(init.z)/Nsites
# initial p will be what fraction of 1's exist/occupancy
init.p <- mean(History)/init.psi
# we will start at the same initial starting point for each chain even though this
# is not recommended.
init.list <- list(
list(z=init.z, p=init.p, psi=init.psi ),
list(z=init.z, p=init.p, psi=init.psi ),
list(z=init.z, p=init.p, psi=init.psi )
) # end of list of lists of initial values
# Next create the list of parameters to monitor.
# The deviance is automatically monitored.
#
monitor.list <- c("z","p", "psi", "occ.sites", "prob.psi.greater.50") # parameters to monitor
# Finally, the actual call to JAGS
set.seed(234234) # intitalize seed for MCMC
results <- R2jags::jags(
data =data.list, # list of data variables
inits =init.list, # list/function for initial values
parameters=monitor.list,# list of parameters to monitor
model.file="model.txt", # file with bugs model
n.chains=3,
n.iter =5000, # total iterations INCLUDING burn in
n.burnin=2000, # number of burning iterations
n.thin=2, # how much to thin
DIC=TRUE, # is DIC to be computed?
working.dir=getwd() # store results in current working directory
)
## module glm loaded
## Warning in jags.model(model.file, data = data, inits = init.values,
## n.chains = n.chains, : Unused variable "Nvisits" in data
## Warning in jags.model(model.file, data = data, inits = init.values,
## n.chains = n.chains, : Unused variable "Visit" in data
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 123
## Unobserved stochastic nodes: 43
## Total graph size: 339
##
## Initializing model
#######################################
# extract some of the usual stuff and use R code directly
# use the standard print method
names(results)
## [1] "model" "BUGSoutput" "parameters.to.save"
## [4] "model.file" "n.iter" "DIC"
names(results$BUGSoutput)
## [1] "n.chains" "n.iter" "n.burnin"
## [4] "n.thin" "n.keep" "n.sims"
## [7] "sims.array" "sims.list" "sims.matrix"
## [10] "summary" "mean" "sd"
## [13] "median" "root.short" "long.short"
## [16] "dimension.short" "indexes.short" "last.values"
## [19] "program" "model.file" "isDIC"
## [22] "DICbyR" "pD" "DIC"
# get the summary table
results$BUGSoutput$summary
## mean sd 2.5% 25%
## deviance 151.0324389 9.95001926 132.9311625 143.6208610
## occ.sites 36.4402222 2.08066490 33.0000000 35.0000000
## p 0.5503110 0.05534883 0.4435941 0.5119170
## prob.psi.greater.50 1.0000000 0.00000000 1.0000000 1.0000000
## psi 0.8696077 0.06974181 0.7201308 0.8250719
## z[1] 1.0000000 0.00000000 1.0000000 1.0000000
## z[2] 1.0000000 0.00000000 1.0000000 1.0000000
## z[3] 0.4304444 0.49519341 0.0000000 0.0000000
## z[4] 1.0000000 0.00000000 1.0000000 1.0000000
## z[5] 1.0000000 0.00000000 1.0000000 1.0000000
## z[6] 1.0000000 0.00000000 1.0000000 1.0000000
## z[7] 1.0000000 0.00000000 1.0000000 1.0000000
## z[8] 1.0000000 0.00000000 1.0000000 1.0000000
## z[9] 1.0000000 0.00000000 1.0000000 1.0000000
## z[10] 1.0000000 0.00000000 1.0000000 1.0000000
## z[11] 1.0000000 0.00000000 1.0000000 1.0000000
## z[12] 0.4357778 0.49591346 0.0000000 0.0000000
## z[13] 0.4191111 0.49346844 0.0000000 0.0000000
## z[14] 1.0000000 0.00000000 1.0000000 1.0000000
## z[15] 1.0000000 0.00000000 1.0000000 1.0000000
## z[16] 1.0000000 0.00000000 1.0000000 1.0000000
## z[17] 1.0000000 0.00000000 1.0000000 1.0000000
## z[18] 0.4324444 0.49547028 0.0000000 0.0000000
## z[19] 1.0000000 0.00000000 1.0000000 1.0000000
## z[20] 0.4271111 0.49471365 0.0000000 0.0000000
## z[21] 1.0000000 0.00000000 1.0000000 1.0000000
## z[22] 1.0000000 0.00000000 1.0000000 1.0000000
## z[23] 1.0000000 0.00000000 1.0000000 1.0000000
## z[24] 1.0000000 0.00000000 1.0000000 1.0000000
## z[25] 1.0000000 0.00000000 1.0000000 1.0000000
## z[26] 1.0000000 0.00000000 1.0000000 1.0000000
## z[27] 1.0000000 0.00000000 1.0000000 1.0000000
## z[28] 1.0000000 0.00000000 1.0000000 1.0000000
## z[29] 1.0000000 0.00000000 1.0000000 1.0000000
## z[30] 1.0000000 0.00000000 1.0000000 1.0000000
## z[31] 0.4311111 0.49528662 0.0000000 0.0000000
## z[32] 1.0000000 0.00000000 1.0000000 1.0000000
## z[33] 1.0000000 0.00000000 1.0000000 1.0000000
## z[34] 1.0000000 0.00000000 1.0000000 1.0000000
## z[35] 0.4304444 0.49519341 0.0000000 0.0000000
## z[36] 0.4337778 0.49565029 0.0000000 0.0000000
## z[37] 1.0000000 0.00000000 1.0000000 1.0000000
## z[38] 1.0000000 0.00000000 1.0000000 1.0000000
## z[39] 1.0000000 0.00000000 1.0000000 1.0000000
## z[40] 1.0000000 0.00000000 1.0000000 1.0000000
## z[41] 1.0000000 0.00000000 1.0000000 1.0000000
## 50% 75% 97.5% Rhat n.eff
## deviance 149.8072629 158.1584468 170.5667209 1.001913 1600
## occ.sites 36.0000000 38.0000000 41.0000000 1.002086 1400
## p 0.5500037 0.5885745 0.6622420 1.001336 3000
## prob.psi.greater.50 1.0000000 1.0000000 1.0000000 1.000000 1
## psi 0.8736507 0.9219870 0.9852478 1.003197 790
## z[1] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[2] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[3] 0.0000000 1.0000000 1.0000000 1.001461 2500
## z[4] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[5] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[6] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[7] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[8] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[9] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[10] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[11] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[12] 0.0000000 1.0000000 1.0000000 1.000704 4500
## z[13] 0.0000000 1.0000000 1.0000000 1.002728 970
## z[14] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[15] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[16] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[17] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[18] 0.0000000 1.0000000 1.0000000 1.002493 1100
## z[19] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[20] 0.0000000 1.0000000 1.0000000 1.000992 4500
## z[21] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[22] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[23] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[24] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[25] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[26] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[27] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[28] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[29] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[30] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[31] 0.0000000 1.0000000 1.0000000 1.001567 2200
## z[32] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[33] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[34] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[35] 0.0000000 1.0000000 1.0000000 1.000787 4500
## z[36] 0.0000000 1.0000000 1.0000000 1.000960 4500
## z[37] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[38] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[39] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[40] 1.0000000 1.0000000 1.0000000 1.000000 1
## z[41] 1.0000000 1.0000000 1.0000000 1.000000 1
results$BUGSoutput$summary[,c("mean", "sd", "2.5%","97.5%","Rhat", "n.eff")]
## mean sd 2.5% 97.5%
## deviance 151.0324389 9.95001926 132.9311625 170.5667209
## occ.sites 36.4402222 2.08066490 33.0000000 41.0000000
## p 0.5503110 0.05534883 0.4435941 0.6622420
## prob.psi.greater.50 1.0000000 0.00000000 1.0000000 1.0000000
## psi 0.8696077 0.06974181 0.7201308 0.9852478
## z[1] 1.0000000 0.00000000 1.0000000 1.0000000
## z[2] 1.0000000 0.00000000 1.0000000 1.0000000
## z[3] 0.4304444 0.49519341 0.0000000 1.0000000
## z[4] 1.0000000 0.00000000 1.0000000 1.0000000
## z[5] 1.0000000 0.00000000 1.0000000 1.0000000
## z[6] 1.0000000 0.00000000 1.0000000 1.0000000
## z[7] 1.0000000 0.00000000 1.0000000 1.0000000
## z[8] 1.0000000 0.00000000 1.0000000 1.0000000
## z[9] 1.0000000 0.00000000 1.0000000 1.0000000
## z[10] 1.0000000 0.00000000 1.0000000 1.0000000
## z[11] 1.0000000 0.00000000 1.0000000 1.0000000
## z[12] 0.4357778 0.49591346 0.0000000 1.0000000
## z[13] 0.4191111 0.49346844 0.0000000 1.0000000
## z[14] 1.0000000 0.00000000 1.0000000 1.0000000
## z[15] 1.0000000 0.00000000 1.0000000 1.0000000
## z[16] 1.0000000 0.00000000 1.0000000 1.0000000
## z[17] 1.0000000 0.00000000 1.0000000 1.0000000
## z[18] 0.4324444 0.49547028 0.0000000 1.0000000
## z[19] 1.0000000 0.00000000 1.0000000 1.0000000
## z[20] 0.4271111 0.49471365 0.0000000 1.0000000
## z[21] 1.0000000 0.00000000 1.0000000 1.0000000
## z[22] 1.0000000 0.00000000 1.0000000 1.0000000
## z[23] 1.0000000 0.00000000 1.0000000 1.0000000
## z[24] 1.0000000 0.00000000 1.0000000 1.0000000
## z[25] 1.0000000 0.00000000 1.0000000 1.0000000
## z[26] 1.0000000 0.00000000 1.0000000 1.0000000
## z[27] 1.0000000 0.00000000 1.0000000 1.0000000
## z[28] 1.0000000 0.00000000 1.0000000 1.0000000
## z[29] 1.0000000 0.00000000 1.0000000 1.0000000
## z[30] 1.0000000 0.00000000 1.0000000 1.0000000
## z[31] 0.4311111 0.49528662 0.0000000 1.0000000
## z[32] 1.0000000 0.00000000 1.0000000 1.0000000
## z[33] 1.0000000 0.00000000 1.0000000 1.0000000
## z[34] 1.0000000 0.00000000 1.0000000 1.0000000
## z[35] 0.4304444 0.49519341 0.0000000 1.0000000
## z[36] 0.4337778 0.49565029 0.0000000 1.0000000
## z[37] 1.0000000 0.00000000 1.0000000 1.0000000
## z[38] 1.0000000 0.00000000 1.0000000 1.0000000
## z[39] 1.0000000 0.00000000 1.0000000 1.0000000
## z[40] 1.0000000 0.00000000 1.0000000 1.0000000
## z[41] 1.0000000 0.00000000 1.0000000 1.0000000
## Rhat n.eff
## deviance 1.001913 1600
## occ.sites 1.002086 1400
## p 1.001336 3000
## prob.psi.greater.50 1.000000 1
## psi 1.003197 790
## z[1] 1.000000 1
## z[2] 1.000000 1
## z[3] 1.001461 2500
## z[4] 1.000000 1
## z[5] 1.000000 1
## z[6] 1.000000 1
## z[7] 1.000000 1
## z[8] 1.000000 1
## z[9] 1.000000 1
## z[10] 1.000000 1
## z[11] 1.000000 1
## z[12] 1.000704 4500
## z[13] 1.002728 970
## z[14] 1.000000 1
## z[15] 1.000000 1
## z[16] 1.000000 1
## z[17] 1.000000 1
## z[18] 1.002493 1100
## z[19] 1.000000 1
## z[20] 1.000992 4500
## z[21] 1.000000 1
## z[22] 1.000000 1
## z[23] 1.000000 1
## z[24] 1.000000 1
## z[25] 1.000000 1
## z[26] 1.000000 1
## z[27] 1.000000 1
## z[28] 1.000000 1
## z[29] 1.000000 1
## z[30] 1.000000 1
## z[31] 1.001567 2200
## z[32] 1.000000 1
## z[33] 1.000000 1
## z[34] 1.000000 1
## z[35] 1.000787 4500
## z[36] 1.000960 4500
## z[37] 1.000000 1
## z[38] 1.000000 1
## z[39] 1.000000 1
## z[40] 1.000000 1
## z[41] 1.000000 1
results$BUGSoutput$summary[,c("mean", "sd")]
## mean sd
## deviance 151.0324389 9.95001926
## occ.sites 36.4402222 2.08066490
## p 0.5503110 0.05534883
## prob.psi.greater.50 1.0000000 0.00000000
## psi 0.8696077 0.06974181
## z[1] 1.0000000 0.00000000
## z[2] 1.0000000 0.00000000
## z[3] 0.4304444 0.49519341
## z[4] 1.0000000 0.00000000
## z[5] 1.0000000 0.00000000
## z[6] 1.0000000 0.00000000
## z[7] 1.0000000 0.00000000
## z[8] 1.0000000 0.00000000
## z[9] 1.0000000 0.00000000
## z[10] 1.0000000 0.00000000
## z[11] 1.0000000 0.00000000
## z[12] 0.4357778 0.49591346
## z[13] 0.4191111 0.49346844
## z[14] 1.0000000 0.00000000
## z[15] 1.0000000 0.00000000
## z[16] 1.0000000 0.00000000
## z[17] 1.0000000 0.00000000
## z[18] 0.4324444 0.49547028
## z[19] 1.0000000 0.00000000
## z[20] 0.4271111 0.49471365
## z[21] 1.0000000 0.00000000
## z[22] 1.0000000 0.00000000
## z[23] 1.0000000 0.00000000
## z[24] 1.0000000 0.00000000
## z[25] 1.0000000 0.00000000
## z[26] 1.0000000 0.00000000
## z[27] 1.0000000 0.00000000
## z[28] 1.0000000 0.00000000
## z[29] 1.0000000 0.00000000
## z[30] 1.0000000 0.00000000
## z[31] 0.4311111 0.49528662
## z[32] 1.0000000 0.00000000
## z[33] 1.0000000 0.00000000
## z[34] 1.0000000 0.00000000
## z[35] 0.4304444 0.49519341
## z[36] 0.4337778 0.49565029
## z[37] 1.0000000 0.00000000
## z[38] 1.0000000 0.00000000
## z[39] 1.0000000 0.00000000
## z[40] 1.0000000 0.00000000
## z[41] 1.0000000 0.00000000
# get just the means
results$BUGSoutput$mean
## $deviance
## [1] 151.0324
##
## $occ.sites
## [1] 36.44022
##
## $p
## [1] 0.550311
##
## $prob.psi.greater.50
## [1] 1
##
## $psi
## [1] 0.8696077
##
## $z
## [1] 1.0000000 1.0000000 0.4304444 1.0000000 1.0000000 1.0000000 1.0000000
## [8] 1.0000000 1.0000000 1.0000000 1.0000000 0.4357778 0.4191111 1.0000000
## [15] 1.0000000 1.0000000 1.0000000 0.4324444 1.0000000 0.4271111 1.0000000
## [22] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## [29] 1.0000000 1.0000000 0.4311111 1.0000000 1.0000000 1.0000000 0.4304444
## [36] 0.4337778 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
results$BUGSoutput$mean$psi
## [1] 0.8696077
# the results$BUGSoutput$sims.array is a 3-d object [iterations, chains, variables]
dim(results$BUGSoutput$sims.array)
## [1] 1500 3 46
results$BUGSoutput$sims.array[1:5,,1:5]
## , , deviance
##
## [,1] [,2] [,3]
## [1,] 153.4604 171.4608 153.1523
## [2,] 162.9600 162.1560 157.7223
## [3,] 162.8787 163.6889 133.1059
## [4,] 167.2966 166.7140 152.6563
## [5,] 162.2269 170.6960 148.4164
##
## , , occ.sites
##
## [,1] [,2] [,3]
## [1,] 37 41 37
## [2,] 39 39 38
## [3,] 39 39 33
## [4,] 40 40 36
## [5,] 39 41 35
##
## , , p
##
## [,1] [,2] [,3]
## [1,] 0.5668788 0.4424528 0.5435832
## [2,] 0.5550481 0.5039863 0.5275552
## [3,] 0.5529624 0.4550106 0.5767290
## [4,] 0.5441958 0.5273146 0.6519774
## [5,] 0.4976729 0.5105672 0.6759793
##
## , , prob.psi.greater.50
##
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1
## [3,] 1 1 1
## [4,] 1 1 1
## [5,] 1 1 1
##
## , , psi
##
## [,1] [,2] [,3]
## [1,] 0.8378131 0.9873153 0.9030364
## [2,] 0.9211029 0.9639474 0.8884114
## [3,] 0.9172542 0.9413326 0.6936131
## [4,] 0.9539518 0.9965744 0.9358349
## [5,] 0.9438991 0.9859744 0.8571180
results$BUGSoutput$sims.array[1:5,1,"psi"]
## [1] 0.8378131 0.9211029 0.9172542 0.9539518 0.9438991
# the results$BUGSoutput$sims.matrix is a 2-d object [iterations, variables] with chains stacked
# on top of each other
dim(results$BUGSoutput$sims.matrix)
## [1] 4500 46
results$BUGSoutput$sims.matrix[1:5,1:10]
## deviance occ.sites p prob.psi.greater.50 psi z[1] z[2]
## [1,] 170.7763 41 0.4617486 1 0.9916120 1 1
## [2,] 167.4571 40 0.5477999 1 0.8988662 1 1
## [3,] 133.2396 33 0.6398758 1 0.7336665 1 1
## [4,] 139.9884 34 0.6519416 1 0.7891217 1 1
## [5,] 153.5049 37 0.5686853 1 0.9326727 1 1
## z[3] z[4] z[5]
## [1,] 1 1 1
## [2,] 1 1 1
## [3,] 0 1 1
## [4,] 0 1 1
## [5,] 0 1 1
results$BUGSoutput$sims.matrix[1:5,"psi"]
## [1] 0.9916120 0.8988662 0.7336665 0.7891217 0.9326727
# make a posterior density plot
plotdata <- data.frame(parm=results$BUGSoutput$sims.matrix[,"psi"], stringsAsFactors=FALSE)
head(plotdata)
## parm
## 1 0.9916120
## 2 0.8988662
## 3 0.7336665
## 4 0.7891217
## 5 0.9326727
## 6 0.8015004
postplot.parm <- ggplot2::ggplot( data=plotdata, aes(x=parm, y=..density..))+
geom_histogram(alpha=0.3)+
geom_density()+
ggtitle("Posterior density plot for psi")
postplot.parm
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggsave(plot=postplot.parm, file='psi-posterior-p-dot-psi-dot.png', h=4, w=6, units="in", dpi=300)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# make a trace plot (notice we use the sims.array here)
plotdata <- data.frame(psi=results$BUGSoutput$sims.array[,,"psi"], stringsAsFactors=FALSE)
plotdata$iteration <- 1:nrow(plotdata)
head(plotdata)
## psi.1 psi.2 psi.3 iteration
## 1 0.8378131 0.9873153 0.9030364 1
## 2 0.9211029 0.9639474 0.8884114 2
## 3 0.9172542 0.9413326 0.6936131 3
## 4 0.9539518 0.9965744 0.9358349 4
## 5 0.9438991 0.9859744 0.8571180 5
## 6 0.9172572 0.9537536 0.8981272 6
# convert from wide to long format
plotdata2 <- reshape2:::melt.data.frame(data=plotdata,
id.vars="iteration",
measure.vars=paste("psi",1:results$BUGSoutput$n.chains,sep="."),
variable.name="chain",
value.name='psi')
head(plotdata2)
## iteration chain psi
## 1 1 psi.1 0.8378131
## 2 2 psi.1 0.9211029
## 3 3 psi.1 0.9172542
## 4 4 psi.1 0.9539518
## 5 5 psi.1 0.9438991
## 6 6 psi.1 0.9172572
traceplot.parm <- ggplot2::ggplot(data=plotdata2, aes(x=iteration, y=psi, color=chain))+
ggtitle("Trace plot for psi")+
geom_line(alpha=.2)
traceplot.parm
ggsave(plot=traceplot.parm, file='psi-trace-p-dot-psi-dot.png', h=4, w=6, units="in", dpi=300)
# autocorrelation plot
# First compute the autocorrelation plot
acf.parm <-acf( results$BUGSoutput$sims.matrix[,"psi"], plot=FALSE)
acf.parm
##
## Autocorrelations of series 'results$BUGSoutput$sims.matrix[, "psi"]', by lag
##
## 0 1 2 3 4 5 6 7 8 9
## 1.000 -0.001 0.010 -0.011 0.040 -0.018 0.000 0.015 -0.011 0.013
## 10 11 12 13 14 15 16 17 18 19
## -0.019 0.000 0.005 -0.008 -0.013 -0.020 -0.013 0.000 -0.001 0.004
## 20 21 22 23 24 25 26 27 28 29
## 0.012 -0.002 -0.012 0.004 0.014 0.012 -0.002 -0.022 -0.018 -0.006
## 30 31 32 33 34 35 36
## 0.007 -0.005 -0.018 -0.008 0.019 -0.016 0.010
acfplot.parm <- ggplot(data=with(acf.parm, data.frame(lag, acf)), aes(x = lag, y = acf)) +
ggtitle("Autocorrelation plot for psi")+
geom_hline(aes(yintercept = 0)) +
geom_segment(aes(xend = lag, yend = 0))
acfplot.parm
ggsave(plot=acfplot.parm, file="psi-acf-p-dot-psi-dot.png",h=4, w=6, units="in", dpi=300)
#
# Bayesian model using JAGS with COVARIATES for detection
# such a time effects.
# You need to build the covariate matrix and send to JAGS
library("R2jags") # used for call to JAGS
library(coda)
library(ggplot2)
library(reshape2)
# The BUGS model is specified as a text file.
# The model file.
# The cat() command is used to save the model to the working directory.
# Notice that you CANNOT have any " (double quotes) in the bugs code
# between the start and end of the cat("...",) command.
# Inputs to the model are
# Nsites - number of sites
# Nvisits - (max) number of visits over all sites.
# Nsites.visits - number of sites x number of visits
# if there is missing data (no visits), simply drop the corresponding row
# History - vector of 1 or 0 corresponding to Site-Visit pair
# Site - vector indicating which site the row corresponds to
# Visit - vector indicating which visit the row corresponds to
#
# psi - occupancy parameter
# p - detection probability
#
# Ncovar.p - number of covariates for logit(p)
# covar.p - matrix of covariates (Nsites.visits x N.covar.p)
#
cat(file="model.txt", "
############################################################
model {
# set up the state model, i.e. is the site actually occupied or not
for(i in 1:Nsites){
z[i] ~ dbern(psi)
}
# the observation model.
for(j in 1:Nsites.visits){
logit(p.detect[j]) <- inprod(beta.p[1:Ncovar.p], covar.p[j, 1:Ncovar.p])
p.z[j] <- z[Site[j]]*p.detect[j]
History[j] ~ dbern(p.z[j])
}
# priors
psi ~ dbeta(1,1)
for(i in 1:Ncovar.p){
beta.p[i] ~ dnorm(0, .0001)
}
# derived variables
# number of occupied sites
occ.sites <- sum(z[1:Nsites])
# belief that psi is above some value
prob.psi.greater.50 <- ifelse( psi > 0.5, 1, 0)
}
") # End of the model
# Next create the data.txt file.
# Initialize the data values using standard R code by either reading
# in from an external file, or plain assignment.
input.data <- read.csv(file.path("..","blgr.csv"),
header=TRUE, as.is=TRUE, strip.white=TRUE)
head(input.data)
## field v1 v2 v3 field.size bqi crop.hist crop1 crop2 count1 count2 count3
## 1 1 1 1 1 14.0 1 crop 1 0 1 2 2
## 2 2 1 1 0 12.7 1 crop 1 0 2 2 0
## 3 3 0 0 0 15.7 0 grass 0 1 0 0 0
## 4 4 0 1 0 19.5 0 grass 0 1 0 2 0
## 5 5 1 0 1 13.5 0 crop 1 0 1 0 1
## 6 6 0 0 1 9.6 0 mixed 0 1 0 0 2
## X logFS
## 1 NA 1.1461280
## 2 NA 1.1038037
## 3 NA 1.1958997
## 4 NA 1.2900346
## 5 NA 1.1303338
## 6 NA 0.9822712
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.data)
## [1] 41
range(input.data[, c("v1","v2","v3")], na.rm=TRUE)
## [1] 0 1
sum(is.na(input.data[, c("v1","v2","v3")]))
## [1] 0
input.history <- input.data[, c("v1","v2","v3")]
head(input.history)
## v1 v2 v3
## 1 1 1 1
## 2 1 1 0
## 3 0 0 0
## 4 0 1 0
## 5 1 0 1
## 6 0 0 1
History <- as.vector(unlist(input.history)) # stacks the columns
Site <- rep(1:nrow(input.history), ncol(input.history))
Visit <- rep(1:ncol(input.history), each=nrow(input.history))
covar.p <- model.matrix( ~as.factor(Visit), data=as.data.frame(Visit))
covar.p[1:10,]
## (Intercept) as.factor(Visit)2 as.factor(Visit)3
## 1 1 0 0
## 2 1 0 0
## 3 1 0 0
## 4 1 0 0
## 5 1 0 0
## 6 1 0 0
## 7 1 0 0
## 8 1 0 0
## 9 1 0 0
## 10 1 0 0
# create a covariate matrix for time effects.
cbind(Site, Visit, History, covar.p)[1:10,]
## Site Visit History (Intercept) as.factor(Visit)2 as.factor(Visit)3
## 1 1 1 1 1 0 0
## 2 2 1 1 1 0 0
## 3 3 1 0 1 0 0
## 4 4 1 0 1 0 0
## 5 5 1 1 1 0 0
## 6 6 1 0 1 0 0
## 7 7 1 0 1 0 0
## 8 8 1 1 1 0 0
## 9 9 1 1 1 0 0
## 10 10 1 1 1 0 0
Nsites <- nrow(input.history)
Nvisits <- ncol(input.history)
Nsites.visits <- length(History)
Ncovar.p <- ncol(covar.p)
# The datalist will be passed to JAGS with the names of the data
# values.
data.list <- list("Nsites","Nvisits","Nsites.visits",
"History", "Site", "Visit",
"Ncovar.p","covar.p") # or
# check the list
data.list
## [[1]]
## [1] "Nsites"
##
## [[2]]
## [1] "Nvisits"
##
## [[3]]
## [1] "Nsites.visits"
##
## [[4]]
## [1] "History"
##
## [[5]]
## [1] "Site"
##
## [[6]]
## [1] "Visit"
##
## [[7]]
## [1] "Ncovar.p"
##
## [[8]]
## [1] "covar.p"
# Next create the initial values.
# If you are using more than one chain, you need to create a function
# that returns initial values for each chain.
# We define the initial value of z as 1 if any visit resulted in a detection, other wise 0
init.z <- apply(input.history, 1, max, na.rm=TRUE)
# we will use the naive estimate of occupancy.
init.psi <- sum(init.z)/Nsites
# initial p will be what fraction of 1's exist/occupancy
init.p <- mean(History)/init.psi
# we will start at the same initial starting point for each chain even though this
# is not recommended.
init.list <- list(
list(z=init.z, beta.p=rep(0,ncol(input.history)), psi=init.psi ),
list(z=init.z, beta.p=rep(0,ncol(input.history)), psi=init.psi ),
list(z=init.z, beta.p=rep(0,ncol(input.history)), psi=init.psi )
) # end of list of lists of initial values
# Next create the list of parameters to monitor.
# The deviance is automatically monitored.
#
monitor.list <- c("z",
"p.detect", "beta.p",
"psi", "occ.sites", "prob.psi.greater.50") # parameters to monitor
# Finally, the actual call to JAGS
set.seed(234234) # intitalize seed for MCMC
results <- R2jags::jags(
data =data.list, # list of data variables
inits =init.list, # list/function for initial values
parameters=monitor.list,# list of parameters to monitor
model.file="model.txt", # file with bugs model
n.chains=3,
n.iter =5000, # total iterations INCLUDING burn in
n.burnin=2000, # number of burning iterations
n.thin=2, # how much to thin
DIC=TRUE, # is DIC to be computed?
working.dir=getwd() # store results in current working directory
)
## Warning in jags.model(model.file, data = data, inits = init.values,
## n.chains = n.chains, : Unused variable "Nvisits" in data
## Warning in jags.model(model.file, data = data, inits = init.values,
## n.chains = n.chains, : Unused variable "Visit" in data
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 123
## Unobserved stochastic nodes: 45
## Total graph size: 924
##
## Initializing model
#######################################
# extract some of the usual stuff and use R code directly
# use the standard print method
names(results)
## [1] "model" "BUGSoutput" "parameters.to.save"
## [4] "model.file" "n.iter" "DIC"
names(results$BUGSoutput)
## [1] "n.chains" "n.iter" "n.burnin"
## [4] "n.thin" "n.keep" "n.sims"
## [7] "sims.array" "sims.list" "sims.matrix"
## [10] "summary" "mean" "sd"
## [13] "median" "root.short" "long.short"
## [16] "dimension.short" "indexes.short" "last.values"
## [19] "program" "model.file" "isDIC"
## [22] "DICbyR" "pD" "DIC"
# get the summary table
results$BUGSoutput$summary
## mean sd 2.5% 25%
## beta.p[1] 7.341136e-03 0.35027669 -0.6623809 -0.22930664
## beta.p[2] 4.570040e-01 0.48719020 -0.4838118 0.13396243
## beta.p[3] 2.295608e-01 0.47850860 -0.6929904 -0.08857968
## deviance 1.505223e+02 10.17831983 133.1999635 143.07861479
## occ.sites 3.610333e+01 2.06070088 33.0000000 35.00000000
## p.detect[1] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[2] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[3] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[4] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[5] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[6] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[7] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[8] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[9] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[10] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[11] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[12] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[13] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[14] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[15] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[16] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[17] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[18] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[19] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[20] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[21] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[22] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[23] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[24] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[25] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[26] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[27] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[28] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[29] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[30] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[31] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[32] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[33] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[34] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[35] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[36] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[37] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[38] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[39] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[40] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[41] 5.017003e-01 0.08505275 0.3402050 0.44292322
## p.detect[42] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[43] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[44] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[45] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[46] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[47] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[48] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[49] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[50] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[51] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[52] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[53] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[54] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[55] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[56] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[57] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[58] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[59] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[60] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[61] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[62] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[63] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[64] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[65] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[66] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[67] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[68] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[69] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[70] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[71] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[72] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[73] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[74] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[75] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[76] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[77] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[78] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[79] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[80] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[81] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[82] 6.102433e-01 0.08768922 0.4329100 0.55140452
## p.detect[83] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[84] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[85] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[86] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[87] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[88] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[89] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[90] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[91] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[92] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[93] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[94] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[95] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[96] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[97] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[98] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[99] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[100] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[101] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[102] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[103] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[104] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[105] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[106] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[107] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[108] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[109] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[110] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[111] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[112] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[113] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[114] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[115] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[116] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[117] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[118] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[119] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[120] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[121] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[122] 5.570885e-01 0.08618243 0.3906294 0.49531322
## p.detect[123] 5.570885e-01 0.08618243 0.3906294 0.49531322
## prob.psi.greater.50 1.000000e+00 0.00000000 1.0000000 1.00000000
## psi 8.632998e-01 0.06923007 0.7167414 0.81710865
## z[1] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[2] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[3] 3.944444e-01 0.48878535 0.0000000 0.00000000
## z[4] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[5] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[6] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[7] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[8] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[9] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[10] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[11] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[12] 3.808889e-01 0.48565930 0.0000000 0.00000000
## z[13] 3.957778e-01 0.48907145 0.0000000 0.00000000
## z[14] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[15] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[16] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[17] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[18] 3.791111e-01 0.48521974 0.0000000 0.00000000
## z[19] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[20] 3.855556e-01 0.48678037 0.0000000 0.00000000
## z[21] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[22] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[23] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[24] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[25] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[26] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[27] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[28] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[29] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[30] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[31] 3.902222e-01 0.48785421 0.0000000 0.00000000
## z[32] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[33] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[34] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[35] 3.922222e-01 0.48830005 0.0000000 0.00000000
## z[36] 3.851111e-01 0.48667564 0.0000000 0.00000000
## z[37] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[38] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[39] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[40] 1.000000e+00 0.00000000 1.0000000 1.00000000
## z[41] 1.000000e+00 0.00000000 1.0000000 1.00000000
## 50% 75% 97.5% Rhat n.eff
## beta.p[1] 1.869553e-04 0.2417988 0.7054848 1.002438 1100
## beta.p[2] 4.498199e-01 0.7815119 1.4240114 1.001731 1900
## beta.p[3] 2.257393e-01 0.5499120 1.1876976 1.001227 3600
## deviance 1.494369e+02 157.7713365 171.1245369 1.001356 2900
## occ.sites 3.600000e+01 37.0000000 41.0000000 1.001418 2700
## p.detect[1] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[2] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[3] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[4] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[5] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[6] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[7] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[8] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[9] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[10] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[11] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[12] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[13] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[14] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[15] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[16] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[17] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[18] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[19] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[20] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[21] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[22] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[23] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[24] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[25] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[26] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[27] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[28] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[29] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[30] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[31] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[32] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[33] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[34] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[35] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[36] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[37] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[38] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[39] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[40] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[41] 5.000467e-01 0.5601569 0.6694026 1.002226 1300
## p.detect[42] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[43] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[44] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[45] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[46] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[47] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[48] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[49] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[50] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[51] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[52] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[53] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[54] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[55] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[56] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[57] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[58] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[59] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[60] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[61] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[62] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[63] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[64] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[65] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[66] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[67] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[68] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[69] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[70] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[71] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[72] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[73] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[74] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[75] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[76] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[77] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[78] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[79] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[80] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[81] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[82] 6.124293e-01 0.6719637 0.7758183 1.000667 4500
## p.detect[83] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[84] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[85] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[86] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[87] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[88] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[89] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[90] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[91] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[92] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[93] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[94] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[95] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[96] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[97] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[98] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[99] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[100] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[101] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[102] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[103] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[104] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[105] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[106] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[107] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[108] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[109] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[110] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[111] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[112] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[113] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[114] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[115] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[116] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[117] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[118] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[119] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[120] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[121] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[122] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## p.detect[123] 5.564936e-01 0.6191692 0.7178190 1.001166 4000
## prob.psi.greater.50 1.000000e+00 1.0000000 1.0000000 1.000000 1
## psi 8.685032e-01 0.9140069 0.9836331 1.001179 3900
## z[1] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[2] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[3] 0.000000e+00 1.0000000 1.0000000 1.000695 4500
## z[4] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[5] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[6] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[7] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[8] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[9] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[10] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[11] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[12] 0.000000e+00 1.0000000 1.0000000 1.002014 1500
## z[13] 0.000000e+00 1.0000000 1.0000000 1.000735 4500
## z[14] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[15] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[16] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[17] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[18] 0.000000e+00 1.0000000 1.0000000 1.000693 4500
## z[19] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[20] 0.000000e+00 1.0000000 1.0000000 1.001224 3600
## z[21] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[22] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[23] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[24] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[25] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[26] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[27] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[28] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[29] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[30] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[31] 0.000000e+00 1.0000000 1.0000000 1.002157 1300
## z[32] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[33] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[34] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[35] 0.000000e+00 1.0000000 1.0000000 1.000766 4500
## z[36] 0.000000e+00 1.0000000 1.0000000 1.001324 3000
## z[37] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[38] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[39] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[40] 1.000000e+00 1.0000000 1.0000000 1.000000 1
## z[41] 1.000000e+00 1.0000000 1.0000000 1.000000 1
results$BUGSoutput$summary[,c("mean", "sd", "2.5%","97.5%","Rhat", "n.eff")]
## mean sd 2.5% 97.5%
## beta.p[1] 7.341136e-03 0.35027669 -0.6623809 0.7054848
## beta.p[2] 4.570040e-01 0.48719020 -0.4838118 1.4240114
## beta.p[3] 2.295608e-01 0.47850860 -0.6929904 1.1876976
## deviance 1.505223e+02 10.17831983 133.1999635 171.1245369
## occ.sites 3.610333e+01 2.06070088 33.0000000 41.0000000
## p.detect[1] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[2] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[3] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[4] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[5] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[6] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[7] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[8] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[9] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[10] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[11] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[12] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[13] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[14] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[15] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[16] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[17] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[18] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[19] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[20] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[21] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[22] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[23] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[24] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[25] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[26] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[27] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[28] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[29] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[30] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[31] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[32] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[33] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[34] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[35] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[36] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[37] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[38] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[39] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[40] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[41] 5.017003e-01 0.08505275 0.3402050 0.6694026
## p.detect[42] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[43] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[44] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[45] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[46] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[47] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[48] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[49] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[50] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[51] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[52] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[53] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[54] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[55] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[56] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[57] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[58] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[59] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[60] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[61] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[62] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[63] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[64] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[65] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[66] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[67] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[68] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[69] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[70] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[71] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[72] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[73] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[74] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[75] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[76] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[77] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[78] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[79] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[80] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[81] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[82] 6.102433e-01 0.08768922 0.4329100 0.7758183
## p.detect[83] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[84] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[85] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[86] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[87] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[88] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[89] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[90] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[91] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[92] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[93] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[94] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[95] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[96] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[97] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[98] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[99] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[100] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[101] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[102] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[103] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[104] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[105] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[106] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[107] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[108] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[109] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[110] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[111] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[112] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[113] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[114] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[115] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[116] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[117] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[118] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[119] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[120] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[121] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[122] 5.570885e-01 0.08618243 0.3906294 0.7178190
## p.detect[123] 5.570885e-01 0.08618243 0.3906294 0.7178190
## prob.psi.greater.50 1.000000e+00 0.00000000 1.0000000 1.0000000
## psi 8.632998e-01 0.06923007 0.7167414 0.9836331
## z[1] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[2] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[3] 3.944444e-01 0.48878535 0.0000000 1.0000000
## z[4] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[5] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[6] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[7] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[8] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[9] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[10] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[11] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[12] 3.808889e-01 0.48565930 0.0000000 1.0000000
## z[13] 3.957778e-01 0.48907145 0.0000000 1.0000000
## z[14] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[15] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[16] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[17] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[18] 3.791111e-01 0.48521974 0.0000000 1.0000000
## z[19] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[20] 3.855556e-01 0.48678037 0.0000000 1.0000000
## z[21] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[22] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[23] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[24] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[25] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[26] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[27] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[28] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[29] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[30] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[31] 3.902222e-01 0.48785421 0.0000000 1.0000000
## z[32] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[33] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[34] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[35] 3.922222e-01 0.48830005 0.0000000 1.0000000
## z[36] 3.851111e-01 0.48667564 0.0000000 1.0000000
## z[37] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[38] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[39] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[40] 1.000000e+00 0.00000000 1.0000000 1.0000000
## z[41] 1.000000e+00 0.00000000 1.0000000 1.0000000
## Rhat n.eff
## beta.p[1] 1.002438 1100
## beta.p[2] 1.001731 1900
## beta.p[3] 1.001227 3600
## deviance 1.001356 2900
## occ.sites 1.001418 2700
## p.detect[1] 1.002226 1300
## p.detect[2] 1.002226 1300
## p.detect[3] 1.002226 1300
## p.detect[4] 1.002226 1300
## p.detect[5] 1.002226 1300
## p.detect[6] 1.002226 1300
## p.detect[7] 1.002226 1300
## p.detect[8] 1.002226 1300
## p.detect[9] 1.002226 1300
## p.detect[10] 1.002226 1300
## p.detect[11] 1.002226 1300
## p.detect[12] 1.002226 1300
## p.detect[13] 1.002226 1300
## p.detect[14] 1.002226 1300
## p.detect[15] 1.002226 1300
## p.detect[16] 1.002226 1300
## p.detect[17] 1.002226 1300
## p.detect[18] 1.002226 1300
## p.detect[19] 1.002226 1300
## p.detect[20] 1.002226 1300
## p.detect[21] 1.002226 1300
## p.detect[22] 1.002226 1300
## p.detect[23] 1.002226 1300
## p.detect[24] 1.002226 1300
## p.detect[25] 1.002226 1300
## p.detect[26] 1.002226 1300
## p.detect[27] 1.002226 1300
## p.detect[28] 1.002226 1300
## p.detect[29] 1.002226 1300
## p.detect[30] 1.002226 1300
## p.detect[31] 1.002226 1300
## p.detect[32] 1.002226 1300
## p.detect[33] 1.002226 1300
## p.detect[34] 1.002226 1300
## p.detect[35] 1.002226 1300
## p.detect[36] 1.002226 1300
## p.detect[37] 1.002226 1300
## p.detect[38] 1.002226 1300
## p.detect[39] 1.002226 1300
## p.detect[40] 1.002226 1300
## p.detect[41] 1.002226 1300
## p.detect[42] 1.000667 4500
## p.detect[43] 1.000667 4500
## p.detect[44] 1.000667 4500
## p.detect[45] 1.000667 4500
## p.detect[46] 1.000667 4500
## p.detect[47] 1.000667 4500
## p.detect[48] 1.000667 4500
## p.detect[49] 1.000667 4500
## p.detect[50] 1.000667 4500
## p.detect[51] 1.000667 4500
## p.detect[52] 1.000667 4500
## p.detect[53] 1.000667 4500
## p.detect[54] 1.000667 4500
## p.detect[55] 1.000667 4500
## p.detect[56] 1.000667 4500
## p.detect[57] 1.000667 4500
## p.detect[58] 1.000667 4500
## p.detect[59] 1.000667 4500
## p.detect[60] 1.000667 4500
## p.detect[61] 1.000667 4500
## p.detect[62] 1.000667 4500
## p.detect[63] 1.000667 4500
## p.detect[64] 1.000667 4500
## p.detect[65] 1.000667 4500
## p.detect[66] 1.000667 4500
## p.detect[67] 1.000667 4500
## p.detect[68] 1.000667 4500
## p.detect[69] 1.000667 4500
## p.detect[70] 1.000667 4500
## p.detect[71] 1.000667 4500
## p.detect[72] 1.000667 4500
## p.detect[73] 1.000667 4500
## p.detect[74] 1.000667 4500
## p.detect[75] 1.000667 4500
## p.detect[76] 1.000667 4500
## p.detect[77] 1.000667 4500
## p.detect[78] 1.000667 4500
## p.detect[79] 1.000667 4500
## p.detect[80] 1.000667 4500
## p.detect[81] 1.000667 4500
## p.detect[82] 1.000667 4500
## p.detect[83] 1.001166 4000
## p.detect[84] 1.001166 4000
## p.detect[85] 1.001166 4000
## p.detect[86] 1.001166 4000
## p.detect[87] 1.001166 4000
## p.detect[88] 1.001166 4000
## p.detect[89] 1.001166 4000
## p.detect[90] 1.001166 4000
## p.detect[91] 1.001166 4000
## p.detect[92] 1.001166 4000
## p.detect[93] 1.001166 4000
## p.detect[94] 1.001166 4000
## p.detect[95] 1.001166 4000
## p.detect[96] 1.001166 4000
## p.detect[97] 1.001166 4000
## p.detect[98] 1.001166 4000
## p.detect[99] 1.001166 4000
## p.detect[100] 1.001166 4000
## p.detect[101] 1.001166 4000
## p.detect[102] 1.001166 4000
## p.detect[103] 1.001166 4000
## p.detect[104] 1.001166 4000
## p.detect[105] 1.001166 4000
## p.detect[106] 1.001166 4000
## p.detect[107] 1.001166 4000
## p.detect[108] 1.001166 4000
## p.detect[109] 1.001166 4000
## p.detect[110] 1.001166 4000
## p.detect[111] 1.001166 4000
## p.detect[112] 1.001166 4000
## p.detect[113] 1.001166 4000
## p.detect[114] 1.001166 4000
## p.detect[115] 1.001166 4000
## p.detect[116] 1.001166 4000
## p.detect[117] 1.001166 4000
## p.detect[118] 1.001166 4000
## p.detect[119] 1.001166 4000
## p.detect[120] 1.001166 4000
## p.detect[121] 1.001166 4000
## p.detect[122] 1.001166 4000
## p.detect[123] 1.001166 4000
## prob.psi.greater.50 1.000000 1
## psi 1.001179 3900
## z[1] 1.000000 1
## z[2] 1.000000 1
## z[3] 1.000695 4500
## z[4] 1.000000 1
## z[5] 1.000000 1
## z[6] 1.000000 1
## z[7] 1.000000 1
## z[8] 1.000000 1
## z[9] 1.000000 1
## z[10] 1.000000 1
## z[11] 1.000000 1
## z[12] 1.002014 1500
## z[13] 1.000735 4500
## z[14] 1.000000 1
## z[15] 1.000000 1
## z[16] 1.000000 1
## z[17] 1.000000 1
## z[18] 1.000693 4500
## z[19] 1.000000 1
## z[20] 1.001224 3600
## z[21] 1.000000 1
## z[22] 1.000000 1
## z[23] 1.000000 1
## z[24] 1.000000 1
## z[25] 1.000000 1
## z[26] 1.000000 1
## z[27] 1.000000 1
## z[28] 1.000000 1
## z[29] 1.000000 1
## z[30] 1.000000 1
## z[31] 1.002157 1300
## z[32] 1.000000 1
## z[33] 1.000000 1
## z[34] 1.000000 1
## z[35] 1.000766 4500
## z[36] 1.001324 3000
## z[37] 1.000000 1
## z[38] 1.000000 1
## z[39] 1.000000 1
## z[40] 1.000000 1
## z[41] 1.000000 1
results$BUGSoutput$summary[,c("mean", "sd")]
## mean sd
## beta.p[1] 7.341136e-03 0.35027669
## beta.p[2] 4.570040e-01 0.48719020
## beta.p[3] 2.295608e-01 0.47850860
## deviance 1.505223e+02 10.17831983
## occ.sites 3.610333e+01 2.06070088
## p.detect[1] 5.017003e-01 0.08505275
## p.detect[2] 5.017003e-01 0.08505275
## p.detect[3] 5.017003e-01 0.08505275
## p.detect[4] 5.017003e-01 0.08505275
## p.detect[5] 5.017003e-01 0.08505275
## p.detect[6] 5.017003e-01 0.08505275
## p.detect[7] 5.017003e-01 0.08505275
## p.detect[8] 5.017003e-01 0.08505275
## p.detect[9] 5.017003e-01 0.08505275
## p.detect[10] 5.017003e-01 0.08505275
## p.detect[11] 5.017003e-01 0.08505275
## p.detect[12] 5.017003e-01 0.08505275
## p.detect[13] 5.017003e-01 0.08505275
## p.detect[14] 5.017003e-01 0.08505275
## p.detect[15] 5.017003e-01 0.08505275
## p.detect[16] 5.017003e-01 0.08505275
## p.detect[17] 5.017003e-01 0.08505275
## p.detect[18] 5.017003e-01 0.08505275
## p.detect[19] 5.017003e-01 0.08505275
## p.detect[20] 5.017003e-01 0.08505275
## p.detect[21] 5.017003e-01 0.08505275
## p.detect[22] 5.017003e-01 0.08505275
## p.detect[23] 5.017003e-01 0.08505275
## p.detect[24] 5.017003e-01 0.08505275
## p.detect[25] 5.017003e-01 0.08505275
## p.detect[26] 5.017003e-01 0.08505275
## p.detect[27] 5.017003e-01 0.08505275
## p.detect[28] 5.017003e-01 0.08505275
## p.detect[29] 5.017003e-01 0.08505275
## p.detect[30] 5.017003e-01 0.08505275
## p.detect[31] 5.017003e-01 0.08505275
## p.detect[32] 5.017003e-01 0.08505275
## p.detect[33] 5.017003e-01 0.08505275
## p.detect[34] 5.017003e-01 0.08505275
## p.detect[35] 5.017003e-01 0.08505275
## p.detect[36] 5.017003e-01 0.08505275
## p.detect[37] 5.017003e-01 0.08505275
## p.detect[38] 5.017003e-01 0.08505275
## p.detect[39] 5.017003e-01 0.08505275
## p.detect[40] 5.017003e-01 0.08505275
## p.detect[41] 5.017003e-01 0.08505275
## p.detect[42] 6.102433e-01 0.08768922
## p.detect[43] 6.102433e-01 0.08768922
## p.detect[44] 6.102433e-01 0.08768922
## p.detect[45] 6.102433e-01 0.08768922
## p.detect[46] 6.102433e-01 0.08768922
## p.detect[47] 6.102433e-01 0.08768922
## p.detect[48] 6.102433e-01 0.08768922
## p.detect[49] 6.102433e-01 0.08768922
## p.detect[50] 6.102433e-01 0.08768922
## p.detect[51] 6.102433e-01 0.08768922
## p.detect[52] 6.102433e-01 0.08768922
## p.detect[53] 6.102433e-01 0.08768922
## p.detect[54] 6.102433e-01 0.08768922
## p.detect[55] 6.102433e-01 0.08768922
## p.detect[56] 6.102433e-01 0.08768922
## p.detect[57] 6.102433e-01 0.08768922
## p.detect[58] 6.102433e-01 0.08768922
## p.detect[59] 6.102433e-01 0.08768922
## p.detect[60] 6.102433e-01 0.08768922
## p.detect[61] 6.102433e-01 0.08768922
## p.detect[62] 6.102433e-01 0.08768922
## p.detect[63] 6.102433e-01 0.08768922
## p.detect[64] 6.102433e-01 0.08768922
## p.detect[65] 6.102433e-01 0.08768922
## p.detect[66] 6.102433e-01 0.08768922
## p.detect[67] 6.102433e-01 0.08768922
## p.detect[68] 6.102433e-01 0.08768922
## p.detect[69] 6.102433e-01 0.08768922
## p.detect[70] 6.102433e-01 0.08768922
## p.detect[71] 6.102433e-01 0.08768922
## p.detect[72] 6.102433e-01 0.08768922
## p.detect[73] 6.102433e-01 0.08768922
## p.detect[74] 6.102433e-01 0.08768922
## p.detect[75] 6.102433e-01 0.08768922
## p.detect[76] 6.102433e-01 0.08768922
## p.detect[77] 6.102433e-01 0.08768922
## p.detect[78] 6.102433e-01 0.08768922
## p.detect[79] 6.102433e-01 0.08768922
## p.detect[80] 6.102433e-01 0.08768922
## p.detect[81] 6.102433e-01 0.08768922
## p.detect[82] 6.102433e-01 0.08768922
## p.detect[83] 5.570885e-01 0.08618243
## p.detect[84] 5.570885e-01 0.08618243
## p.detect[85] 5.570885e-01 0.08618243
## p.detect[86] 5.570885e-01 0.08618243
## p.detect[87] 5.570885e-01 0.08618243
## p.detect[88] 5.570885e-01 0.08618243
## p.detect[89] 5.570885e-01 0.08618243
## p.detect[90] 5.570885e-01 0.08618243
## p.detect[91] 5.570885e-01 0.08618243
## p.detect[92] 5.570885e-01 0.08618243
## p.detect[93] 5.570885e-01 0.08618243
## p.detect[94] 5.570885e-01 0.08618243
## p.detect[95] 5.570885e-01 0.08618243
## p.detect[96] 5.570885e-01 0.08618243
## p.detect[97] 5.570885e-01 0.08618243
## p.detect[98] 5.570885e-01 0.08618243
## p.detect[99] 5.570885e-01 0.08618243
## p.detect[100] 5.570885e-01 0.08618243
## p.detect[101] 5.570885e-01 0.08618243
## p.detect[102] 5.570885e-01 0.08618243
## p.detect[103] 5.570885e-01 0.08618243
## p.detect[104] 5.570885e-01 0.08618243
## p.detect[105] 5.570885e-01 0.08618243
## p.detect[106] 5.570885e-01 0.08618243
## p.detect[107] 5.570885e-01 0.08618243
## p.detect[108] 5.570885e-01 0.08618243
## p.detect[109] 5.570885e-01 0.08618243
## p.detect[110] 5.570885e-01 0.08618243
## p.detect[111] 5.570885e-01 0.08618243
## p.detect[112] 5.570885e-01 0.08618243
## p.detect[113] 5.570885e-01 0.08618243
## p.detect[114] 5.570885e-01 0.08618243
## p.detect[115] 5.570885e-01 0.08618243
## p.detect[116] 5.570885e-01 0.08618243
## p.detect[117] 5.570885e-01 0.08618243
## p.detect[118] 5.570885e-01 0.08618243
## p.detect[119] 5.570885e-01 0.08618243
## p.detect[120] 5.570885e-01 0.08618243
## p.detect[121] 5.570885e-01 0.08618243
## p.detect[122] 5.570885e-01 0.08618243
## p.detect[123] 5.570885e-01 0.08618243
## prob.psi.greater.50 1.000000e+00 0.00000000
## psi 8.632998e-01 0.06923007
## z[1] 1.000000e+00 0.00000000
## z[2] 1.000000e+00 0.00000000
## z[3] 3.944444e-01 0.48878535
## z[4] 1.000000e+00 0.00000000
## z[5] 1.000000e+00 0.00000000
## z[6] 1.000000e+00 0.00000000
## z[7] 1.000000e+00 0.00000000
## z[8] 1.000000e+00 0.00000000
## z[9] 1.000000e+00 0.00000000
## z[10] 1.000000e+00 0.00000000
## z[11] 1.000000e+00 0.00000000
## z[12] 3.808889e-01 0.48565930
## z[13] 3.957778e-01 0.48907145
## z[14] 1.000000e+00 0.00000000
## z[15] 1.000000e+00 0.00000000
## z[16] 1.000000e+00 0.00000000
## z[17] 1.000000e+00 0.00000000
## z[18] 3.791111e-01 0.48521974
## z[19] 1.000000e+00 0.00000000
## z[20] 3.855556e-01 0.48678037
## z[21] 1.000000e+00 0.00000000
## z[22] 1.000000e+00 0.00000000
## z[23] 1.000000e+00 0.00000000
## z[24] 1.000000e+00 0.00000000
## z[25] 1.000000e+00 0.00000000
## z[26] 1.000000e+00 0.00000000
## z[27] 1.000000e+00 0.00000000
## z[28] 1.000000e+00 0.00000000
## z[29] 1.000000e+00 0.00000000
## z[30] 1.000000e+00 0.00000000
## z[31] 3.902222e-01 0.48785421
## z[32] 1.000000e+00 0.00000000
## z[33] 1.000000e+00 0.00000000
## z[34] 1.000000e+00 0.00000000
## z[35] 3.922222e-01 0.48830005
## z[36] 3.851111e-01 0.48667564
## z[37] 1.000000e+00 0.00000000
## z[38] 1.000000e+00 0.00000000
## z[39] 1.000000e+00 0.00000000
## z[40] 1.000000e+00 0.00000000
## z[41] 1.000000e+00 0.00000000
# get just the means
results$BUGSoutput$mean
## $beta.p
## [1] 0.007341136 0.457004050 0.229560828
##
## $deviance
## [1] 150.5223
##
## $occ.sites
## [1] 36.10333
##
## $p.detect
## [1] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003
## [8] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003
## [15] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003
## [22] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003
## [29] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003
## [36] 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.5017003 0.6102433
## [43] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433
## [50] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433
## [57] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433
## [64] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433
## [71] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433
## [78] 0.6102433 0.6102433 0.6102433 0.6102433 0.6102433 0.5570885 0.5570885
## [85] 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885
## [92] 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885
## [99] 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885
## [106] 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885
## [113] 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885 0.5570885
## [120] 0.5570885 0.5570885 0.5570885 0.5570885
##
## $prob.psi.greater.50
## [1] 1
##
## $psi
## [1] 0.8632998
##
## $z
## [1] 1.0000000 1.0000000 0.3944444 1.0000000 1.0000000 1.0000000 1.0000000
## [8] 1.0000000 1.0000000 1.0000000 1.0000000 0.3808889 0.3957778 1.0000000
## [15] 1.0000000 1.0000000 1.0000000 0.3791111 1.0000000 0.3855556 1.0000000
## [22] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## [29] 1.0000000 1.0000000 0.3902222 1.0000000 1.0000000 1.0000000 0.3922222
## [36] 0.3851111 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
results$BUGSoutput$mean$psi
## [1] 0.8632998
# the results$BUGSoutput$sims.array is a 3-d object [iterations, chains, variables]
dim(results$BUGSoutput$sims.array)
## [1] 1500 3 171
results$BUGSoutput$sims.array[1:5,,1:5]
## , , beta.p[1]
##
## [,1] [,2] [,3]
## [1,] -0.32531797 -0.31201262 0.176316153
## [2,] -0.47322175 -0.07523518 -0.074060904
## [3,] -0.41978523 0.13688101 0.170261487
## [4,] 0.04741348 -0.35102510 -0.006614073
## [5,] 0.28939496 -0.08783537 -0.264990061
##
## , , beta.p[2]
##
## [,1] [,2] [,3]
## [1,] 0.940479557 1.1543225 0.9762515
## [2,] 0.746791686 0.5912226 0.7023764
## [3,] 0.460975243 0.1183342 -0.2587394
## [4,] 0.003454781 1.1264057 0.4182297
## [5,] 0.325821815 0.5147680 1.0589265
##
## , , beta.p[3]
##
## [,1] [,2] [,3]
## [1,] -0.25771570 0.2467041 -0.024460492
## [2,] 0.36582309 -0.3488288 0.666756524
## [3,] 0.99711639 -0.1956646 0.227579034
## [4,] 0.05758707 0.4395928 -0.007287906
## [5,] 0.45371606 0.2213309 0.157285442
##
## , , deviance
##
## [,1] [,2] [,3]
## [1,] 170.7253 169.6448 145.7575
## [2,] 162.5195 172.7529 148.9843
## [3,] 160.5977 171.2673 159.9565
## [4,] 149.0355 159.3192 152.5909
## [5,] 156.8460 152.3112 159.5719
##
## , , occ.sites
##
## [,1] [,2] [,3]
## [1,] 40 40 35
## [2,] 39 41 36
## [3,] 38 41 38
## [4,] 36 38 37
## [5,] 37 37 38
results$BUGSoutput$sims.array[1:5,1,"psi"]
## [1] 0.9704670 0.9899337 0.8527430 0.8249385 0.9303492
# the results$BUGSoutput$sims.matrix is a 2-d object [iterations, variables] with chains stacked
# on top of each other
dim(results$BUGSoutput$sims.matrix)
## [1] 4500 171
results$BUGSoutput$sims.matrix[1:5,1:10]
## beta.p[1] beta.p[2] beta.p[3] deviance occ.sites p.detect[1]
## [1,] -0.08951469 0.3092667 0.48034466 138.8065 34 0.4776363
## [2,] 0.21363111 0.3073357 -0.03995562 163.4135 39 0.5532056
## [3,] -0.18455772 0.8006885 0.06779402 158.2085 38 0.4539911
## [4,] -0.03865623 0.2845696 0.18545638 143.3816 35 0.4903371
## [5,] -0.04672988 0.1926500 0.17666017 152.7937 37 0.4883197
## p.detect[2] p.detect[3] p.detect[4] p.detect[5]
## [1,] 0.4776363 0.4776363 0.4776363 0.4776363
## [2,] 0.5532056 0.5532056 0.5532056 0.5532056
## [3,] 0.4539911 0.4539911 0.4539911 0.4539911
## [4,] 0.4903371 0.4903371 0.4903371 0.4903371
## [5,] 0.4883197 0.4883197 0.4883197 0.4883197
results$BUGSoutput$sims.matrix[1:5,"psi"]
## [1] 0.8305684 0.9282073 0.9657904 0.8206742 0.9455136
# make a posterior density plot
plotdata <- data.frame(parm=results$BUGSoutput$sims.matrix[,"psi"], stringsAsFactors=FALSE)
head(plotdata)
## parm
## 1 0.8305684
## 2 0.9282073
## 3 0.9657904
## 4 0.8206742
## 5 0.9455136
## 6 0.8817393
postplot.parm <- ggplot2::ggplot( data=plotdata, aes(x=parm, y=..density..))+
geom_histogram(alpha=0.3)+
geom_density()+
ggtitle("Posterior density plot for psi")
postplot.parm
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggsave(plot=postplot.parm, file='psi-posterior-p-t-psi-dot.png', h=4, w=6, units="in", dpi=300)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# make a trace plot (notice we use the sims.array here)
plotdata <- data.frame(psi=results$BUGSoutput$sims.array[,,"psi"], stringsAsFactors=FALSE)
plotdata$iteration <- 1:nrow(plotdata)
head(plotdata)
## psi.1 psi.2 psi.3 iteration
## 1 0.9704670 0.9560543 0.8091537 1
## 2 0.9899337 0.9877420 0.8512016 2
## 3 0.8527430 0.9673665 0.8511991 3
## 4 0.8249385 0.9134451 0.9499588 4
## 5 0.9303492 0.8952087 0.8568037 5
## 6 0.7588782 0.8653957 0.7389135 6
# convert from wide to long format
plotdata2 <- reshape2:::melt.data.frame(data=plotdata,
id.vars="iteration",
measure.vars=paste("psi",1:results$BUGSoutput$n.chains,sep="."),
variable.name="chain",
value.name='psi')
head(plotdata2)
## iteration chain psi
## 1 1 psi.1 0.9704670
## 2 2 psi.1 0.9899337
## 3 3 psi.1 0.8527430
## 4 4 psi.1 0.8249385
## 5 5 psi.1 0.9303492
## 6 6 psi.1 0.7588782
traceplot.parm <- ggplot2::ggplot(data=plotdata2, aes(x=iteration, y=psi, color=chain))+
ggtitle("Trace plot for psi")+
geom_line(alpha=.2)
traceplot.parm
ggsave(plot=traceplot.parm, file='psi-trace-p-t-psi-dot.png', h=4, w=6, units="in", dpi=300)
# autocorrelation plot
# First compute the autocorrelation plot
acf.parm <-acf( results$BUGSoutput$sims.matrix[,"psi"], plot=FALSE)
acf.parm
##
## Autocorrelations of series 'results$BUGSoutput$sims.matrix[, "psi"]', by lag
##
## 0 1 2 3 4 5 6 7 8 9
## 1.000 0.014 -0.021 -0.002 0.001 0.015 -0.008 -0.006 -0.046 0.001
## 10 11 12 13 14 15 16 17 18 19
## -0.009 -0.008 0.001 0.002 0.029 0.002 -0.002 0.006 0.024 0.022
## 20 21 22 23 24 25 26 27 28 29
## -0.017 0.012 0.005 -0.020 -0.001 -0.011 -0.045 -0.001 0.000 0.032
## 30 31 32 33 34 35 36
## 0.009 0.015 0.018 0.027 -0.026 0.006 -0.019
acfplot.parm <- ggplot(data=with(acf.parm, data.frame(lag, acf)), aes(x = lag, y = acf)) +
ggtitle("Autocorrelation plot for psi")+
geom_hline(aes(yintercept = 0)) +
geom_segment(aes(xend = lag, yend = 0))
acfplot.parm
ggsave(plot=acfplot.parm, file="psi-acf-p-t-psi-dot.png",h=4, w=6, units="in", dpi=300)