# Single Species Single Season Occupancy models
# Weta Data
# using JAGS
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(car)
## Loading required package: carData
library(coda)
library(ggplot2)
library(readxl)
library(reshape2)
options(width=400) # make html output wider
# get the data read in
# Data for detections should be a data frame with rows corresponding to sites
# and columns to visits.
# The usual 1=detected; 0=not detected; NA=not visited is used.
input.history <- readxl::read_excel(file.path("..","weta.xls"),
sheet="detection_histories",
na="-",
col_names=FALSE) # notice no column names in row 1 of data file.
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.history)
## [1] 72
ncol(input.history)
## [1] 5
range(input.history, na.rm=TRUE)
## [1] 0 1
sum(is.na(input.history))
## [1] 98
head(input.history)
## # A tibble: 6 x 5
## X__1 X__2 X__3 X__4 X__5
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 NA
## 2 0 0 0 0 NA
## 3 0 0 0 1 NA
## 4 0 0 0 0 NA
## 5 0 0 0 0 NA
## 6 0 0 0 0 NA
# Get the site level covariates
site_covar <- readxl::read_excel(file.path("..","weta.xls"),
sheet="site_covar",
na="-",
col_names=TRUE) # notice col_names in row 1 of table.
# Create an alternate site level covariate that is a categorical variable rather
# than indicator variables
site_covar$BrowCat <- paste(c("","B")[1+unlist(site_covar[,1])], c("","N")[1+unlist(site_covar[,2])], sep="")
xtabs(~BrowCat, data=site_covar,exclude=NULL, na.action=na.pass)
## BrowCat
## B N
## 35 37
colSums(site_covar[,1:2])
## Browsed Unbrowsed
## 35 37
site_covar$Site <- 1:nrow(site_covar)
head(site_covar)
## # A tibble: 6 x 4
## Browsed Unbrowsed BrowCat Site
## <dbl> <dbl> <chr> <int>
## 1 1 0 B 1
## 2 1 0 B 2
## 3 1 0 B 3
## 4 0 1 N 4
## 5 1 0 B 5
## 6 0 1 N 6
# Get the individual covariates.
obs1 <- readxl::read_excel(file.path("..","weta.xls"),
sheet="Obs1",
na="-",
col_names=FALSE)
obs2 <- readxl::read_excel(file.path("..","weta.xls"),
sheet="Obs2",
na="-",
col_names=FALSE)
obs3 <- readxl::read_excel(file.path("..","weta.xls"),
sheet="Obs3",
na="-",
col_names=FALSE)
Obs <- obs1*1 + obs2*2 + obs3*3
head(Obs)
## X__1 X__2 X__3 X__4 X__5
## 1 1 3 2 3 NA
## 2 1 3 2 3 NA
## 3 1 3 2 3 NA
## 4 1 3 2 3 NA
## 5 1 3 2 3 NA
## 6 1 3 2 3 NA
# Observational covariate needs to be "stacked" so that sites1...siteS for survey occastion 1
# are then followed by covariate at survey occastion 2 for sites1...siteS, etc
survey.cov <- data.frame(site=rep(1:nrow(input.history) , ncol(input.history)),
visit=as.character(rep(1:ncol(input.history), each=nrow(input.history))), # notice we make a character
obs1 =as.vector(unlist(obs1)),
obs2 =as.vector(unlist(obs2)),
obs3 =as.vector(unlist(obs3)),
Obs =as.character(as.vector(unlist(Obs))), # notice we make a character string
stringsAsFactors=FALSE)
head(survey.cov)
## site visit obs1 obs2 obs3 Obs
## 1 1 1 1 0 0 1
## 2 2 1 1 0 0 1
## 3 3 1 1 0 0 1
## 4 4 1 1 0 0 1
## 5 5 1 1 0 0 1
## 6 6 1 1 0 0 1
str(survey.cov)
## 'data.frame': 360 obs. of 6 variables:
## $ site : int 1 2 3 4 5 6 7 8 9 10 ...
## $ visit: chr "1" "1" "1" "1" ...
## $ obs1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ obs2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ obs3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Obs : chr "1" "1" "1" "1" ...
# check that missing values in history and observer covariates align
select <- is.na(as.vector(unlist(input.history)))
survey.cov[select,]
## site visit obs1 obs2 obs3 Obs
## 16 16 1 NA NA NA <NA>
## 17 17 1 NA NA NA <NA>
## 18 18 1 NA NA NA <NA>
## 19 19 1 NA NA NA <NA>
## 38 38 1 NA NA NA <NA>
## 39 39 1 NA NA NA <NA>
## 40 40 1 NA NA NA <NA>
## 41 41 1 NA NA NA <NA>
## 42 42 1 NA NA NA <NA>
## 43 43 1 NA NA NA <NA>
## 44 44 1 NA NA NA <NA>
## 45 45 1 NA NA NA <NA>
## 46 46 1 NA NA NA <NA>
## 47 47 1 NA NA NA <NA>
## 63 63 1 NA NA NA <NA>
## 64 64 1 NA NA NA <NA>
## 65 65 1 NA NA NA <NA>
## 66 66 1 NA NA NA <NA>
## 67 67 1 NA NA NA <NA>
## 93 21 2 NA NA NA <NA>
## 94 22 2 NA NA NA <NA>
## 95 23 2 NA NA NA <NA>
## 96 24 2 NA NA NA <NA>
## 97 25 2 NA NA NA <NA>
## 115 43 2 NA NA NA <NA>
## 116 44 2 NA NA NA <NA>
## 117 45 2 NA NA NA <NA>
## 118 46 2 NA NA NA <NA>
## 119 47 2 NA NA NA <NA>
## 140 68 2 NA NA NA <NA>
## 141 69 2 NA NA NA <NA>
## 142 70 2 NA NA NA <NA>
## 143 71 2 NA NA NA <NA>
## 144 72 2 NA NA NA <NA>
## 155 11 3 NA NA NA <NA>
## 156 12 3 NA NA NA <NA>
## 157 13 3 NA NA NA <NA>
## 158 14 3 NA NA NA <NA>
## 159 15 3 NA NA NA <NA>
## 182 38 3 NA NA NA <NA>
## 183 39 3 NA NA NA <NA>
## 202 58 3 NA NA NA <NA>
## 203 59 3 NA NA NA <NA>
## 204 60 3 NA NA NA <NA>
## 205 61 3 NA NA NA <NA>
## 206 62 3 NA NA NA <NA>
## 232 16 4 NA NA NA <NA>
## 233 17 4 NA NA NA <NA>
## 234 18 4 NA NA NA <NA>
## 235 19 4 NA NA NA <NA>
## 236 20 4 NA NA NA <NA>
## 237 21 4 NA NA NA <NA>
## 238 22 4 NA NA NA <NA>
## 239 23 4 NA NA NA <NA>
## 240 24 4 NA NA NA <NA>
## 241 25 4 NA NA NA <NA>
## 242 26 4 NA NA NA <NA>
## 243 27 4 NA NA NA <NA>
## 244 28 4 NA NA NA <NA>
## 245 29 4 NA NA NA <NA>
## 279 63 4 NA NA NA <NA>
## 280 64 4 NA NA NA <NA>
## 281 65 4 NA NA NA <NA>
## 282 66 4 NA NA NA <NA>
## 283 67 4 NA NA NA <NA>
## 284 68 4 NA NA NA <NA>
## 285 69 4 NA NA NA <NA>
## 286 70 4 NA NA NA <NA>
## 287 71 4 NA NA NA <NA>
## 288 72 4 NA NA NA <NA>
## 289 1 5 NA NA NA <NA>
## 290 2 5 NA NA NA <NA>
## 291 3 5 NA NA NA <NA>
## 292 4 5 NA NA NA <NA>
## 293 5 5 NA NA NA <NA>
## 294 6 5 NA NA NA <NA>
## 295 7 5 NA NA NA <NA>
## 296 8 5 NA NA NA <NA>
## 297 9 5 NA NA NA <NA>
## 298 10 5 NA NA NA <NA>
## 314 26 5 NA NA NA <NA>
## 315 27 5 NA NA NA <NA>
## 316 28 5 NA NA NA <NA>
## 317 29 5 NA NA NA <NA>
## 318 30 5 NA NA NA <NA>
## 319 31 5 NA NA NA <NA>
## 320 32 5 NA NA NA <NA>
## 321 33 5 NA NA NA <NA>
## 336 48 5 NA NA NA <NA>
## 337 49 5 NA NA NA <NA>
## 338 50 5 NA NA NA <NA>
## 339 51 5 NA NA NA <NA>
## 340 52 5 NA NA NA <NA>
## 341 53 5 NA NA NA <NA>
## 342 54 5 NA NA NA <NA>
## 343 55 5 NA NA NA <NA>
## 344 56 5 NA NA NA <NA>
## 345 57 5 NA NA NA <NA>
sum(is.na(survey.cov[!select,]))
## [1] 0
# The missing values in the survey covariates must be filled with dummy
# values to avoid problems in fitting the models that depend on them
survey.cov[ is.na(survey.cov)] <- -1
survey.cov[select,]
## site visit obs1 obs2 obs3 Obs
## 16 16 1 -1 -1 -1 -1
## 17 17 1 -1 -1 -1 -1
## 18 18 1 -1 -1 -1 -1
## 19 19 1 -1 -1 -1 -1
## 38 38 1 -1 -1 -1 -1
## 39 39 1 -1 -1 -1 -1
## 40 40 1 -1 -1 -1 -1
## 41 41 1 -1 -1 -1 -1
## 42 42 1 -1 -1 -1 -1
## 43 43 1 -1 -1 -1 -1
## 44 44 1 -1 -1 -1 -1
## 45 45 1 -1 -1 -1 -1
## 46 46 1 -1 -1 -1 -1
## 47 47 1 -1 -1 -1 -1
## 63 63 1 -1 -1 -1 -1
## 64 64 1 -1 -1 -1 -1
## 65 65 1 -1 -1 -1 -1
## 66 66 1 -1 -1 -1 -1
## 67 67 1 -1 -1 -1 -1
## 93 21 2 -1 -1 -1 -1
## 94 22 2 -1 -1 -1 -1
## 95 23 2 -1 -1 -1 -1
## 96 24 2 -1 -1 -1 -1
## 97 25 2 -1 -1 -1 -1
## 115 43 2 -1 -1 -1 -1
## 116 44 2 -1 -1 -1 -1
## 117 45 2 -1 -1 -1 -1
## 118 46 2 -1 -1 -1 -1
## 119 47 2 -1 -1 -1 -1
## 140 68 2 -1 -1 -1 -1
## 141 69 2 -1 -1 -1 -1
## 142 70 2 -1 -1 -1 -1
## 143 71 2 -1 -1 -1 -1
## 144 72 2 -1 -1 -1 -1
## 155 11 3 -1 -1 -1 -1
## 156 12 3 -1 -1 -1 -1
## 157 13 3 -1 -1 -1 -1
## 158 14 3 -1 -1 -1 -1
## 159 15 3 -1 -1 -1 -1
## 182 38 3 -1 -1 -1 -1
## 183 39 3 -1 -1 -1 -1
## 202 58 3 -1 -1 -1 -1
## 203 59 3 -1 -1 -1 -1
## 204 60 3 -1 -1 -1 -1
## 205 61 3 -1 -1 -1 -1
## 206 62 3 -1 -1 -1 -1
## 232 16 4 -1 -1 -1 -1
## 233 17 4 -1 -1 -1 -1
## 234 18 4 -1 -1 -1 -1
## 235 19 4 -1 -1 -1 -1
## 236 20 4 -1 -1 -1 -1
## 237 21 4 -1 -1 -1 -1
## 238 22 4 -1 -1 -1 -1
## 239 23 4 -1 -1 -1 -1
## 240 24 4 -1 -1 -1 -1
## 241 25 4 -1 -1 -1 -1
## 242 26 4 -1 -1 -1 -1
## 243 27 4 -1 -1 -1 -1
## 244 28 4 -1 -1 -1 -1
## 245 29 4 -1 -1 -1 -1
## 279 63 4 -1 -1 -1 -1
## 280 64 4 -1 -1 -1 -1
## 281 65 4 -1 -1 -1 -1
## 282 66 4 -1 -1 -1 -1
## 283 67 4 -1 -1 -1 -1
## 284 68 4 -1 -1 -1 -1
## 285 69 4 -1 -1 -1 -1
## 286 70 4 -1 -1 -1 -1
## 287 71 4 -1 -1 -1 -1
## 288 72 4 -1 -1 -1 -1
## 289 1 5 -1 -1 -1 -1
## 290 2 5 -1 -1 -1 -1
## 291 3 5 -1 -1 -1 -1
## 292 4 5 -1 -1 -1 -1
## 293 5 5 -1 -1 -1 -1
## 294 6 5 -1 -1 -1 -1
## 295 7 5 -1 -1 -1 -1
## 296 8 5 -1 -1 -1 -1
## 297 9 5 -1 -1 -1 -1
## 298 10 5 -1 -1 -1 -1
## 314 26 5 -1 -1 -1 -1
## 315 27 5 -1 -1 -1 -1
## 316 28 5 -1 -1 -1 -1
## 317 29 5 -1 -1 -1 -1
## 318 30 5 -1 -1 -1 -1
## 319 31 5 -1 -1 -1 -1
## 320 32 5 -1 -1 -1 -1
## 321 33 5 -1 -1 -1 -1
## 336 48 5 -1 -1 -1 -1
## 337 49 5 -1 -1 -1 -1
## 338 50 5 -1 -1 -1 -1
## 339 51 5 -1 -1 -1 -1
## 340 52 5 -1 -1 -1 -1
## 341 53 5 -1 -1 -1 -1
## 342 54 5 -1 -1 -1 -1
## 343 55 5 -1 -1 -1 -1
## 344 56 5 -1 -1 -1 -1
## 345 57 5 -1 -1 -1 -1
sum(is.na(survey.cov[!select,]==-1))
## [1] 0
# 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
#
# dmatrix.psi - design matrix for psi
# Nbeta.psi - number of columns in design matrix for psi
# dmatrix.p - design matrix for p
# Nbeta.p - number of columns of design matrix for p
#
cat(file="model.txt", "
############################################################
model {
# estimate psi for each site from the design matrix
for(i in 1:Nsites){
logit(psi[i]) = inprod( dmatrix.psi[i, 1:Nbeta.psi], beta.psi[1:Nbeta.psi])
}
# estimate p for each observation
for(i in 1:Nsites.visits){
logit(p[i]) = inprod( dmatrix.p[i, 1:Nbeta.p], beta.p[1:Nbeta.p])
}
# set up the state model, i.e. is the site actually occupied or not
for(i in 1:Nsites){
z[i] ~ dbern(psi[i])
}
# the observation model.
for(j in 1:Nsites.visits){
p.z[j] <- z[Site[j]]*p[j]
History[j] ~ dbern(p.z[j])
}
# priors on the betas
beta.psi[1] ~ dnorm(0, .25) # intercept we want basically flat on regular scale
for(i in 2:Nbeta.psi){
beta.psi[i] ~ dnorm(0, .0001)
}
beta.p[1] ~ dnorm(0, .25)
for(i in 2:Nbeta.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[1] > 0.5, 1, 0)
}
") # End of the model
# get the data in the right format. We want all of the sites for visit 1, then all of the sites for visit 2 etc.
Survey <- data.frame(
History = as.vector(unlist(input.history)), # stacks the columns
Site = rep(1:nrow(input.history), ncol(input.history)),
Visit = as.character(rep(1:ncol(input.history), each=nrow(input.history))),
stringsAsFactors=FALSE)
Survey[1:10,]
## History Site Visit
## 1 0 1 1
## 2 0 2 1
## 3 0 3 1
## 4 0 4 1
## 5 0 5 1
## 6 0 6 1
## 7 0 7 1
## 8 0 8 1
## 9 0 9 1
## 10 1 10 1
# add in covaraites
Survey$Obs <- survey.cov$Obs # both are in correct order
Survey <- merge(Survey, site_covar[,c("Site","BrowCat")])
# re-sort
Survey <- Survey[ order(Survey$Visit, Survey$Site),]
head(Survey)
## Site History Visit Obs BrowCat
## 1 1 0 1 1 B
## 6 2 0 1 1 B
## 15 3 0 1 1 B
## 20 4 0 1 1 N
## 22 5 0 1 1 B
## 26 6 0 1 1 N
str(Survey) # be sure that all categorical variables are character or factors
## 'data.frame': 360 obs. of 5 variables:
## $ Site : int 1 2 3 4 5 6 7 8 9 10 ...
## $ History: num 0 0 0 0 0 0 0 0 0 1 ...
## $ Visit : chr "1" "1" "1" "1" ...
## $ Obs : chr "1" "1" "1" "1" ...
## $ BrowCat: chr "B" "B" "B" "N" ...
# Remove any rows with missing history value (i.e missing)
sum(is.na(Survey$History))
## [1] 98
dim(Survey)
## [1] 360 5
Survey <- Survey[!is.na(Survey$History),]
dim(Survey)
## [1] 262 5
Nsites <- nrow(input.history)
Nvisits <- ncol(input.history)
Nsites.visits <- nrow(Survey)
# Get the design matrix for model psi(BrowCat)p(visit)
dmatrix.psi <- model.matrix(~BrowCat, data=site_covar)
Nbeta.psi <- ncol(dmatrix.psi)
dmatrix.p <- model.matrix(~Visit, data=Survey)
Nbeta.p <- ncol(dmatrix.p)
model.name <- "psi(B) p(v)"
# Get the design matrix for model psi(BrowCat) p(Obs + Visit)
dmatrix.psi <- model.matrix(~BrowCat, data=site_covar) # constant psi
Nbeta.psi <- ncol(dmatrix.psi)
dmatrix.p <- model.matrix(~Visit+Obs, data=Survey)
Nbeta.p <- ncol(dmatrix.p)
model.name <- "pt-psidot"
# The datalist will be passed to JAGS with the names of the data
# values.
data.list <- list(Nsites=Nsites,
Nvisit=Nvisits,
Nsites.visits=Nsites.visits,
History = Survey$History,
Site = Survey$Site,
Visit = Survey$Visit,
dmatrix.psi=dmatrix.psi, Nbeta.psi=Nbeta.psi,
dmatrix.p =dmatrix.p, Nbeta.p =Nbeta.p)
# check the list
data.list
## $Nsites
## [1] 72
##
## $Nvisit
## [1] 5
##
## $Nsites.visits
## [1] 262
##
## $History
## [1] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [198] 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1
##
## $Site
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 68 69 70 71 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 21 22 23 24 25 26
## [132] 27 28 29 30 31 32 33 34 35 36 37 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 63 64 65 66 67 68 69 70 71 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 34 35 36 37 38 39 40 41 42 43 44 45 46 47 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
##
## $Visit
## [1] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [99] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [197] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5" "5"
##
## $dmatrix.psi
## (Intercept) BrowCatN
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 1
## 5 1 0
## 6 1 1
## 7 1 1
## 8 1 1
## 9 1 1
## 10 1 0
## 11 1 0
## 12 1 0
## 13 1 0
## 14 1 1
## 15 1 1
## 16 1 0
## 17 1 0
## 18 1 1
## 19 1 1
## 20 1 0
## 21 1 0
## 22 1 1
## 23 1 0
## 24 1 1
## 25 1 1
## 26 1 1
## 27 1 1
## 28 1 0
## 29 1 1
## 30 1 1
## 31 1 1
## 32 1 0
## 33 1 1
## 34 1 1
## 35 1 1
## 36 1 1
## 37 1 1
## 38 1 0
## 39 1 1
## 40 1 1
## 41 1 1
## 42 1 0
## 43 1 1
## 44 1 1
## 45 1 1
## 46 1 0
## 47 1 1
## 48 1 0
## 49 1 0
## 50 1 1
## 51 1 0
## 52 1 0
## 53 1 1
## 54 1 0
## 55 1 0
## 56 1 1
## 57 1 0
## 58 1 0
## 59 1 0
## 60 1 0
## 61 1 0
## 62 1 0
## 63 1 1
## 64 1 1
## 65 1 0
## 66 1 0
## 67 1 0
## 68 1 0
## 69 1 1
## 70 1 0
## 71 1 1
## 72 1 1
## attr(,"assign")
## [1] 0 1
## attr(,"contrasts")
## attr(,"contrasts")$BrowCat
## [1] "contr.treatment"
##
##
## $Nbeta.psi
## [1] 2
##
## $dmatrix.p
## (Intercept) Visit2 Visit3 Visit4 Visit5 Obs2 Obs3
## 1 1 0 0 0 0 0 0
## 6 1 0 0 0 0 0 0
## 15 1 0 0 0 0 0 0
## 20 1 0 0 0 0 0 0
## 22 1 0 0 0 0 0 0
## 26 1 0 0 0 0 0 0
## 34 1 0 0 0 0 0 0
## 38 1 0 0 0 0 0 0
## 44 1 0 0 0 0 0 0
## 47 1 0 0 0 0 0 0
## 55 1 0 0 0 0 0 0
## 60 1 0 0 0 0 0 0
## 65 1 0 0 0 0 0 0
## 67 1 0 0 0 0 0 0
## 71 1 0 0 0 0 0 0
## 100 1 0 0 0 0 0 0
## 104 1 0 0 0 0 0 0
## 108 1 0 0 0 0 0 0
## 113 1 0 0 0 0 0 0
## 120 1 0 0 0 0 0 0
## 123 1 0 0 0 0 0 0
## 129 1 0 0 0 0 1 0
## 133 1 0 0 0 0 1 0
## 137 1 0 0 0 0 1 0
## 145 1 0 0 0 0 1 0
## 149 1 0 0 0 0 1 0
## 153 1 0 0 0 0 1 0
## 158 1 0 0 0 0 1 0
## 163 1 0 0 0 0 1 0
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## attr(,"assign")
## [1] 0 1 1 1 1 2 2
## attr(,"contrasts")
## attr(,"contrasts")$Visit
## [1] "contr.treatment"
##
## attr(,"contrasts")$Obs
## [1] "contr.treatment"
##
##
## $Nbeta.p
## [1] 7
# 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 start at the same initial starting point for each chain even though this
# is not recommended.
init.list <- list(
list(z=init.z, beta.psi=rep(0,Nbeta.psi), beta.p=rep(0,Nbeta.p) ),
list(z=init.z, beta.psi=rep(0,Nbeta.psi), beta.p=rep(0,Nbeta.p) ),
list(z=init.z, beta.psi=rep(0,Nbeta.psi), beta.p=rep(0,Nbeta.p) )
) # 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","occ.sites", "prob.psi.greater.50",
"psi", "p",
"beta.psi", "beta.p") # 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?
)
## module glm loaded
## Warning in jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, : Unused variable "Nvisit" 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: 262
## Unobserved stochastic nodes: 81
## Total graph size: 3228
##
## 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" "model.file" "n.iter" "DIC"
names(results$BUGSoutput)
## [1] "n.chains" "n.iter" "n.burnin" "n.thin" "n.keep" "n.sims" "sims.array" "sims.list" "sims.matrix" "summary" "mean" "sd" "median" "root.short" "long.short" "dimension.short" "indexes.short" "last.values" "program" "model.file" "isDIC" "DICbyR"
## [23] "pD" "DIC"
# get the summary table
results$BUGSoutput$summary
## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
## beta.p[1] -1.28648826 0.50210385 -2.27075955 -1.62610410 -1.28793860 -0.9493074 -0.30189433 1.002671 1000
## beta.p[2] -0.24076473 0.54996141 -1.27820522 -0.61649516 -0.22810396 0.1297698 0.83880879 1.001518 2300
## beta.p[3] -1.07087278 0.60162468 -2.29285734 -1.46836223 -1.06507531 -0.6541845 0.05003318 1.002282 1200
## beta.p[4] -0.15771919 0.55659827 -1.26592312 -0.53297027 -0.15345809 0.2181481 0.92094627 1.001178 3900
## beta.p[5] 1.01122920 0.55404003 -0.06352737 0.63631916 1.01148821 1.3809086 2.09951188 1.001628 2100
## beta.p[6] 0.74357446 0.47805187 -0.17930336 0.42339348 0.73840956 1.0563668 1.70837352 1.002625 1000
## beta.p[7] 1.08461211 0.46615272 0.19529402 0.75995514 1.06688509 1.3979373 1.99944522 1.004918 470
## beta.psi[1] 1.34660245 0.86578879 0.18229102 0.80416706 1.19970255 1.7071364 3.34246844 1.041998 160
## beta.psi[2] -1.18292377 1.22258027 -3.31512995 -1.70532162 -1.16860699 -0.6744814 0.39724622 1.090366 110
## deviance 200.45494559 15.89471465 174.26665645 188.87135496 199.23083409 210.3887735 235.18932473 1.009177 370
## occ.sites 46.51111111 5.62115136 38.00000000 42.00000000 46.00000000 50.0000000 59.00000000 1.012942 330
## p[1] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[2] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[3] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[4] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[5] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[6] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[7] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[8] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[9] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[10] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[11] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[12] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[13] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[14] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[15] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[16] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[17] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[18] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[19] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[20] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[21] 0.22784402 0.08582972 0.09357377 0.16436476 0.21620193 0.2790241 0.42509446 1.002680 1000
## p[22] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[23] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[24] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[25] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[26] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[27] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[28] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[29] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[30] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[31] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[32] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[33] 0.37500122 0.11696783 0.17320356 0.28923530 0.36508990 0.4520737 0.62621388 1.000864 4500
## p[34] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[35] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[36] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[37] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[38] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[39] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[40] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[41] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[42] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[43] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[44] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[45] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[46] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[47] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[48] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[49] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[50] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[51] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[52] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[53] 0.45213130 0.11084316 0.24533499 0.37194265 0.44918537 0.5290100 0.66960071 1.001403 2700
## p[54] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[55] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[56] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[57] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[58] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[59] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[60] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[61] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[62] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[63] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[64] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[65] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[66] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[67] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[68] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[69] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[70] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[71] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[72] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[73] 0.39747568 0.11818822 0.18923622 0.31120975 0.39042104 0.4776863 0.63972321 1.002359 1200
## p[74] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[75] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[76] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[77] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[78] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[79] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[80] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[81] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[82] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[83] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[84] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[85] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[86] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[87] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[88] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[89] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[90] 0.19200625 0.08272862 0.06510730 0.13095168 0.17980940 0.2391891 0.38183026 1.000977 4500
## p[91] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[92] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[93] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[94] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[95] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[96] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[97] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[98] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[99] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[100] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[101] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[102] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[103] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[104] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[105] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[106] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[107] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[108] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[109] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[110] 0.32233810 0.10120878 0.14622744 0.24817880 0.31695277 0.3877725 0.53618701 1.001314 3100
## p[111] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[112] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[113] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[114] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[115] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[116] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[117] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[118] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[119] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[120] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[121] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[122] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[123] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[124] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[125] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[126] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[127] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[128] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[129] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[130] 0.18008111 0.08039099 0.05827854 0.12083231 0.16896783 0.2245155 0.37239759 1.002756 960
## p[131] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[132] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[133] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[134] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[135] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[136] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[137] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[138] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[139] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[140] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[141] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[142] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[143] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[144] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[145] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[146] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[147] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[148] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[149] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[150] 0.23220772 0.09307494 0.08393801 0.16501708 0.22021223 0.2890252 0.44319660 1.005174 460
## p[151] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[152] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[153] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[154] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[155] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[156] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[157] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[158] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[159] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[160] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[161] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[162] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[163] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[164] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[165] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[166] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[167] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[168] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[169] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[170] 0.09733179 0.04981299 0.02712114 0.06049829 0.08868028 0.1233594 0.21800016 1.001117 4400
## p[171] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[172] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[173] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[174] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[175] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[176] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[177] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[178] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[179] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[180] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[181] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[182] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[183] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[184] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[185] 0.41624212 0.12092748 0.19919566 0.32995187 0.40950411 0.4985963 0.66540760 1.002321 1200
## p[186] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[187] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[188] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[189] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[190] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[191] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[192] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[193] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[194] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[195] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[196] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[197] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[198] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[199] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[200] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[201] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[202] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[203] 0.20351781 0.08268499 0.07515674 0.14249134 0.19129409 0.2545719 0.39141302 1.001090 4500
## p[204] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[205] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[206] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[207] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[208] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[209] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[210] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[211] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[212] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[213] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[214] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[215] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[216] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[217] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[218] 0.34030010 0.10666014 0.15322672 0.26356413 0.33264734 0.4118400 0.56142938 1.001270 3300
## p[219] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[220] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[221] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[222] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[223] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[224] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[225] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[226] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[227] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[228] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[229] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[230] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[231] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[232] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[233] 0.43559764 0.12044783 0.21501548 0.35090960 0.43056665 0.5177159 0.68167099 1.002036 1500
## p[234] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[235] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[236] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[237] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[238] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[239] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[240] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[241] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[242] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[243] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[244] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[245] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[246] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[247] 0.60868564 0.11396527 0.37962262 0.53147962 0.61278752 0.6921507 0.81233950 1.001080 4500
## p[248] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[249] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[250] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[251] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[252] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[253] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[254] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[255] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[256] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[257] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[258] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[259] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[260] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[261] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## p[262] 0.68147816 0.10741422 0.45306691 0.61124873 0.68764158 0.7613090 0.87200668 1.001729 1900
## prob.psi.greater.50 0.98955556 0.10167426 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000674 4500
## psi[1] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[2] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[3] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[4] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[5] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[6] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[7] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[8] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[9] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[10] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[11] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[12] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[13] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[14] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[15] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[16] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[17] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[18] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[19] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[20] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[21] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[22] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[23] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[24] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[25] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[26] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[27] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[28] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[29] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[30] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[31] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[32] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[33] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[34] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[35] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[36] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[37] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[38] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[39] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[40] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[41] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[42] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[43] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[44] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[45] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[46] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[47] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[48] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[49] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[50] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[51] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[52] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[53] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[54] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[55] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[56] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[57] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[58] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[59] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[60] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[61] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[62] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[63] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[64] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[65] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[66] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[67] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[68] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[69] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[70] 0.76616300 0.11013951 0.54544697 0.69086515 0.76847186 0.8464645 0.96585694 1.008235 270
## psi[71] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## psi[72] 0.52097219 0.12598509 0.31072505 0.43473946 0.51017496 0.5917299 0.79322162 1.005145 800
## z[1] 0.44488889 0.49700871 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.002872 910
## z[2] 0.45222222 0.49776736 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.003016 850
## z[3] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[4] 0.20711111 0.40528089 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.002409 1100
## z[5] 0.43711111 0.49608434 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.002974 870
## z[6] 0.20711111 0.40528089 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.001794 1800
## z[7] 0.22466667 0.41740900 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.001975 1500
## z[8] 0.20977778 0.40719517 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.003001 900
## z[9] 0.21866667 0.41338787 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.001135 4300
## z[10] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[11] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[12] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[13] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[14] 0.16688889 0.37291808 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.002624 1200
## z[15] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[16] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[17] 0.49777778 0.50005063 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001103 4500
## z[18] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[19] 0.24688889 0.43124946 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.001233 3500
## z[20] 0.44111111 0.49657517 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001495 2400
## z[21] 0.54600000 0.49793483 0.00000000 0.00000000 1.00000000 1.0000000 1.00000000 1.003239 780
## z[22] 0.29622222 0.45664095 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001052 4500
## z[23] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[24] 0.28577778 0.45183427 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001277 3300
## z[25] 0.31377778 0.46407881 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.000729 4500
## z[26] 0.30822222 0.46181022 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.000924 4500
## z[27] 0.31422222 0.46425695 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001526 2300
## z[28] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[29] 0.32266667 0.46754836 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001273 3300
## z[30] 0.25666667 0.43684242 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.002538 1100
## z[31] 0.25266667 0.43458968 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001555 2200
## z[32] 0.51777778 0.49973938 0.00000000 0.00000000 1.00000000 1.0000000 1.00000000 1.004131 580
## z[33] 0.26511111 0.44144141 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001040 4500
## z[34] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[35] 0.13511111 0.34188020 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.006634 620
## z[36] 0.14022222 0.34725603 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.008233 490
## z[37] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[38] 0.46000000 0.49845282 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001963 1500
## z[39] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[40] 0.18844444 0.39111012 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.001119 4400
## z[41] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[42] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[43] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[44] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[45] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[46] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[47] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[48] 0.44577778 0.49710649 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.004186 570
## z[49] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[50] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[51] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[52] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[53] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[54] 0.44466667 0.49698401 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.004947 470
## z[55] 0.45800000 0.49828825 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001410 2700
## z[56] 0.20933333 0.40687796 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.006061 470
## z[57] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[58] 0.24933333 0.43267519 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.002650 1000
## z[59] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[60] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[61] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[62] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[63] 0.18755556 0.39040023 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.000763 4500
## z[64] 0.18288889 0.38661836 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.002129 1400
## z[65] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[66] 0.41955556 0.49354110 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.001230 3500
## z[67] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[68] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[69] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
## z[70] 0.38066667 0.48560473 0.00000000 0.00000000 0.00000000 1.0000000 1.00000000 1.002842 920
## z[71] 0.17622222 0.38105146 0.00000000 0.00000000 0.00000000 0.0000000 1.00000000 1.000984 4500
## z[72] 1.00000000 0.00000000 1.00000000 1.00000000 1.00000000 1.0000000 1.00000000 1.000000 1
#results$BUGSoutput$summary[,c("mean", "sd", "2.5%","97.5%","Rhat", "n.eff")]
#results$BUGSoutput$summary[,c("mean", "sd")]
# get just the means
results$BUGSoutput$mean
## $beta.p
## [1] -1.2864883 -0.2407647 -1.0708728 -0.1577192 1.0112292 0.7435745 1.0846121
##
## $beta.psi
## [1] 1.346602 -1.182924
##
## $deviance
## [1] 200.4549
##
## $occ.sites
## [1] 46.51111
##
## $p
## [1] 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.22784402 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.37500122 0.45213130 0.45213130
## [36] 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.45213130 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568 0.39747568
## [71] 0.39747568 0.39747568 0.39747568 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.19200625 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810
## [106] 0.32233810 0.32233810 0.32233810 0.32233810 0.32233810 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.18008111 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772
## [141] 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.23220772 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.09733179 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212
## [176] 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.41624212 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.20351781 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010
## [211] 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.34030010 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.43559764 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564 0.60868564
## [246] 0.60868564 0.60868564 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816 0.68147816
##
## $prob.psi.greater.50
## [1] 0.9895556
##
## $psi
## [1] 0.7661630 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722
## [40] 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722
##
## $z
## [1] 0.4448889 0.4522222 1.0000000 0.2071111 0.4371111 0.2071111 0.2246667 0.2097778 0.2186667 1.0000000 1.0000000 1.0000000 1.0000000 0.1668889 1.0000000 1.0000000 0.4977778 1.0000000 0.2468889 0.4411111 0.5460000 0.2962222 1.0000000 0.2857778 0.3137778 0.3082222 0.3142222 1.0000000 0.3226667 0.2566667 0.2526667 0.5177778 0.2651111 1.0000000 0.1351111 0.1402222 1.0000000 0.4600000 1.0000000
## [40] 0.1884444 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.4457778 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.4446667 0.4580000 0.2093333 1.0000000 0.2493333 1.0000000 1.0000000 1.0000000 1.0000000 0.1875556 0.1828889 1.0000000 0.4195556 1.0000000 1.0000000 1.0000000 0.3806667 0.1762222 1.0000000
results$BUGSoutput$mean$psi
## [1] 0.7661630 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722
## [40] 0.5209722 0.5209722 0.7661630 0.5209722 0.5209722 0.5209722 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.5209722 0.7661630 0.7661630 0.7661630 0.7661630 0.5209722 0.7661630 0.5209722 0.5209722
# the results$BUGSoutput$sims.array is a 3-d object [iterations, chains, variables]
dim(results$BUGSoutput$sims.array)
## [1] 1500 3 418
results$BUGSoutput$sims.array[1:5,1,1:10]
## beta.p[1] beta.p[2] beta.p[3] beta.p[4] beta.p[5] beta.p[6] beta.p[7] beta.psi[1] beta.psi[2] deviance
## [1,] -1.512230 -0.786310845 -1.7145087 -0.4619641 0.3867725 0.9955966 1.6946332 1.6756964 -1.3516317 204.1066
## [2,] -1.605319 0.121099687 -0.7712142 0.4873865 0.9391973 1.0309092 1.3237401 1.1717943 -1.2435747 183.6919
## [3,] -1.465574 -0.400248657 -0.4588490 0.4288056 0.3922997 0.9275046 0.9478107 1.8265315 -1.8881134 202.0890
## [4,] -1.642817 -0.005247888 -0.1340589 -0.9022205 0.4799133 1.2619669 1.3174393 0.4744758 0.2918069 219.9194
## [5,] -1.451131 -0.937844589 -0.3779867 -0.1897276 0.5272606 1.4491767 1.6804554 2.2184760 -2.3229250 211.8200
results$BUGSoutput$sims.array[1:5,1,"psi[1]", drop=FALSE]
## , , psi[1]
##
## [,1]
## [1,] 0.8423338
## [2,] 0.7634692
## [3,] 0.8613480
## [4,] 0.6164426
## [5,] 0.9018964
# 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 418
results$BUGSoutput$sims.matrix[1:5,1:10]
## beta.p[1] beta.p[2] beta.p[3] beta.p[4] beta.p[5] beta.p[6] beta.p[7] beta.psi[1] beta.psi[2] deviance
## [1,] -1.2828344 -0.4206127 -1.2359697 -0.7584135 1.8558444 0.5027223 1.5570419 1.4558672 -0.9309718 191.1028
## [2,] -1.9452667 0.1990594 -0.3973337 1.0838194 2.1520752 0.9349901 1.2505224 0.4360780 -0.2155436 183.4382
## [3,] -0.8407243 -0.6433530 -0.9734311 -0.1672975 1.1809176 0.2236635 0.4217458 0.8013174 -0.4197705 189.9793
## [4,] -1.7914116 -0.8721814 -0.7302754 0.2079305 1.5447251 0.7457507 0.9255172 1.3799072 -0.6528676 217.4484
## [5,] -0.7931401 -1.0454972 -1.4462531 -1.2296746 0.2790527 0.9843038 1.2264833 1.9068344 -1.9387109 200.9594
results$BUGSoutput$sims.matrix[1:5,"psi[1]", drop=FALSE]
## psi[1]
## [1,] 0.8108998
## [2,] 0.6073241
## [3,] 0.6902562
## [4,] 0.7989761
## [5,] 0.8706631
# make a posterior density plot
plotdata <- data.frame(parm=results$BUGSoutput$sims.matrix[,c("psi[1]","psi[4]")], stringsAsFactors=FALSE) # browse and unbrowsed
head(plotdata)
## parm.psi.1. parm.psi.4.
## 1 0.8108998 0.6282918
## 2 0.6073241 0.5549112
## 3 0.6902562 0.5942461
## 4 0.7989761 0.6741553
## 5 0.8706631 0.4920316
## 6 0.6765521 0.4244937
plotdata2 <- reshape2::melt(plotdata, variable.name="Site", value.name="prob")
## No id variables; using all as measure variables
head(plotdata2)
## Site prob
## 1 parm.psi.1. 0.8108998
## 2 parm.psi.1. 0.6073241
## 3 parm.psi.1. 0.6902562
## 4 parm.psi.1. 0.7989761
## 5 parm.psi.1. 0.8706631
## 6 parm.psi.1. 0.6765521
postplot.parm <- ggplot2::ggplot( data=plotdata2, aes(x=prob, y=..density..))+
geom_histogram(alpha=0.3)+
geom_density()+
ggtitle("Posterior density plot for psi[1] and psi[[4]")+
facet_wrap(~Site, ncol=1)
postplot.parm
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggsave(plot=postplot.parm,
file=paste('psi-posterior-',model.name,'.png',sep=""), h=4, w=6, units="in", dpi=300)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# Get the odds ratio for Browser vs Not Browse
plotdata <- data.frame(parm=results$BUGSoutput$sims.matrix[,c("beta.psi[2]")], stringsAsFactors=FALSE) # browse and unbrowsed
head(plotdata)
## parm
## 1 -0.9309718
## 2 -0.2155436
## 3 -0.4197705
## 4 -0.6528676
## 5 -1.9387109
## 6 -1.0423241
plotdata$odds.ratio <- exp(plotdata$parm)
range(plotdata$odds.ratio) # some very large odds ratios
## [1] 1.705940e-05 1.390323e+04
summary(plotdata$odds.ratio)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.182 0.311 18.016 0.509 13903.226
quantile(plotdata$odds.ratio, prob=.98)
## 98%
## 1.72101
plotdata$odds.ratio[ plotdata$odds.ratio > 5] <- NA
head(plotdata)
## parm odds.ratio
## 1 -0.9309718 0.3941705
## 2 -0.2155436 0.8061032
## 3 -0.4197705 0.6571976
## 4 -0.6528676 0.5205509
## 5 -1.9387109 0.1438893
## 6 -1.0423241 0.3526342
oddsplot.parm <- ggplot2::ggplot( data=plotdata, aes(x=odds.ratio, y=..density..))+
geom_histogram(alpha=0.3)+
geom_density()+
ggtitle("Odds ratio of occupancy(not browsed):occupancy(browsed)]")
oddsplot.parm
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 50 rows containing non-finite values (stat_bin).
## Warning: Removed 50 rows containing non-finite values (stat_density).
ggsave(plot=postplot.parm,
file=paste('odds-psi-posterior-',model.name,'.png',sep=""), h=4, w=6, units="in", dpi=300)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# make a trace plot (notice we use the sims.array here)
plotdata <- data.frame(psi=results$BUGSoutput$sims.array[,,"psi[1]"], stringsAsFactors=FALSE)
plotdata$iteration <- 1:nrow(plotdata)
head(plotdata)
## psi.1 psi.2 psi.3 iteration
## 1 0.8423338 0.6228555 0.7849696 1
## 2 0.7634692 0.6633186 0.8238258 2
## 3 0.8613480 0.6784891 0.8833036 3
## 4 0.6164426 0.5821840 0.9261826 4
## 5 0.9018964 0.7288919 0.9104778 5
## 6 0.7863184 0.7947837 0.9061637 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 0.8423338
## 2 2 psi.1 0.7634692
## 3 3 psi.1 0.8613480
## 4 4 psi.1 0.6164426
## 5 5 psi.1 0.9018964
## 6 6 psi.1 0.7863184
traceplot.parm <- ggplot2::ggplot(data=plotdata2, aes(x=iteration, y=psi, color=chain))+
ggtitle("Trace plot for psi[1]")+
geom_line(alpha=.2)
traceplot.parm
ggsave(plot=traceplot.parm,
file=paste('psi-trace-',model.name,'.png',sep=""), h=4, w=6, units="in", dpi=300)
# autocorrelation plot
# First compute the autocorrelation plot
acf.parm <-acf( results$BUGSoutput$sims.matrix[,"psi[1]"], plot=FALSE)
acf.parm
##
## Autocorrelations of series 'results$BUGSoutput$sims.matrix[, "psi[1]"]', by lag
##
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## 1.000 -0.004 -0.020 -0.019 0.015 0.006 -0.025 0.028 -0.008 -0.014 -0.015 -0.004 -0.020 -0.024 -0.005 0.011 -0.012 0.000 -0.006 -0.008 0.005 -0.034 0.024 0.012 0.025 0.004 0.016 0.014 0.028 0.036 0.008 -0.007 0.007 0.022 -0.009 0.002 0.001
acfplot.parm <- ggplot(data=with(acf.parm, data.frame(lag, acf)), aes(x = lag, y = acf)) +
ggtitle("Autocorrelation plot for psi[1]")+
geom_hline(aes(yintercept = 0)) +
geom_segment(aes(xend = lag, yend = 0))
acfplot.parm
ggsave(plot=acfplot.parm,
file=paste("psi-acf-", model.name,".png",sep=""),h=4, w=6, units="in", dpi=300)