# Nest survival model using JAGS
# Here we want nest survival to be a function of early vs late periods
# Notice the only change is in the definition of the fe.design matrix
#
# 2019-06-28 CHJS First Edition
#
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)
## Registered S3 methods overwritten by 'ggplot2':
## method from
## [.quosures rlang
## c.quosures rlang
## print.quosures rlang
library(reshape2)
options(width=200)
source(file.path("..","..","jags-nest-survival-fixed-effects.r"))
# The input dataframe must contain the following fields with the following names
#
# NestID: id code of the nest (alpha numeric)
# FirstFound: day the nest was first found
# LastPresent: last day that a chick was present in the nest
# LastChecked: last day the nest was checked
# Fate: fate of the nest; 0 = success; 1=fail
# AgheDay1 = age of the nest on day 1 (if you are fitting age of nest models)
#
# You could also have a nest level covariates, survey level covariates, and
# next x survey time covariates as well
nestdata <- readxl::read_excel(file.path("..","Killdeer.xlsx"),
sheet="killdeer-age")
nestdata <- plyr::rename(nestdata, c("id"="NestId"))
head(nestdata)
## # A tibble: 6 x 7
## NestId FirstFound LastPresent LastChecked Fate Freq AgeDay1
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 /*A*/ 1 9 9 0 1 0
## 2 /*B*/ 5 5 9 1 1 -2
## 3 /*C*/ 5 40 40 0 1 -3
## 4 /*D*/ 9 32 32 0 1 -4
## 5 /*E*/ 7 8 8 0 1 -4
## 6 /*F*/ 3 15 15 0 1 1
# Unfortunately, JAGS cannot deal with alpha numeric code and
# so we need to convert the alphanumberic NestID to numeric codes
# by declaring NestId as a factor and extracting the level values
nestdata$NestId.num <- as.numeric(factor(nestdata$NestId))
# We must create a file with every combination of next x day nest was "active"
# being every day from FirstCound to LastChecked-1
nesttime <- plyr::adply(nestdata, 1, function(x){
nesttime <- expand.grid(NestId.num=x$NestId.num,
Day=x$FirstFound:(x$LastChecked-1),
stringsAsFactors=FALSE)
nesttime
})
# Extract the nest level covariates (including AgeNest1)
# The next level covariates should be indexed using NestId
# If AgeNest1 variable is present then the age of the nest is computed
#
nest.covariates <- NULL
if( !is.null(nest.covariates)){
nesttime <- merge(nesttime, nest.covariates, by="NestId")
}
# Extract any survey time covariates such as time, time^2, early/late
# weather covariates ect.
# All of these covariates will affect all nests simultaneouls
nesttime $Day2 <- (nesttime$Day-20)^2 # day^2 for quadratic trends
nesttime $Period <- car::recode(nesttime$Day,
paste("lo:20='Early';",
"else='Late'"))
xtabs(~Period+Day, data=nesttime, exclude=NULL, na.action=na.pass)
## Day
## Period 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 37 38 39
## Early 1 1 2 2 4 4 5 6 5 5 5 5 6 6 6 8 7 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## Late 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 9 9 9 9 10 10 9 9 9 6 4 3 3 3 2 2 2
# if there is a AgeDay1 variable, we compute the nest age for each time for each nest
if( !is.null(nesttime$AgeDay1)){
nesttime$NestAge <- nesttime$AgeDay1 + nesttime$Day -1
}
head(nesttime)
## NestId FirstFound LastPresent LastChecked Fate Freq AgeDay1 NestId.num Day Day2 Period NestAge
## 1 /*A*/ 1 9 9 0 1 0 1 1 361 Early 0
## 2 /*A*/ 1 9 9 0 1 0 1 2 324 Early 1
## 3 /*A*/ 1 9 9 0 1 0 1 3 289 Early 2
## 4 /*A*/ 1 9 9 0 1 0 1 4 256 Early 3
## 5 /*A*/ 1 9 9 0 1 0 1 5 225 Early 4
## 6 /*A*/ 1 9 9 0 1 0 1 6 196 Early 5
# Add any next x day survey covariates to the nesttime data
#
# there is nothing here for this example
# Set up the design matrix for the fixed effects
fe.design <- model.matrix( ~ Period, data=nesttime)
head(fe.design)
## (Intercept) PeriodLate
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 1 0
# Finally, the actual call to JAGS
fitted.model <- jags.nest.survival.fixed.effects(
nestdata=nestdata, # nest data
nesttime=nesttime, # daily nest values with nest, time, nest x time covariates
fe.design=fe.design, # fixed effects design matrix
init.seed=12321312) # initial seed)
## module glm loaded
## Compiling data graph
## Declaring variables
## Resolving undeclared variables
## Allocating nodes
## Initializing
## Reading data back into data table
## Compiling model graph
## Declaring variables
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 22
## Unobserved stochastic nodes: 2
## Total graph size: 1254
##
## Initializing model
# the nesttime dataframe has the estimated DSR for every combination of NestId.num and Day
# the results list has lots of other stuff
results <- fitted.model$results
# the nesttime dataframe has the estimated DSR for every combination of NestId.num and Day
head(fitted.model$nesttime)
## NestId.num Day NestId FirstFound LastPresent LastChecked Fate Freq AgeDay1 Day2 Period NestAge mean sd X2.5. X25. X50. X75. X97.5. Rhat n.eff
## 1 1 1 /*A*/ 1 9 9 0 1 0 361 Early 0 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
## 2 1 2 /*A*/ 1 9 9 0 1 0 324 Early 1 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
## 3 1 3 /*A*/ 1 9 9 0 1 0 289 Early 2 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
## 4 1 4 /*A*/ 1 9 9 0 1 0 256 Early 3 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
## 5 1 5 /*A*/ 1 9 9 0 1 0 225 Early 4 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
## 6 1 6 /*A*/ 1 9 9 0 1 0 196 Early 5 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.9896273 0.9979615 1.002161 1300
# in this case, we fit a S~Period model, which is the same for all nests, so just extract
# days and plot
plotdata <- plyr::ddply(fitted.model$nesttime, "Day", function(x){ x[1,]})
ggplot(data=plotdata, aes(x=Day, y=mean))+
ggtitle("Estimated DSR in Early vs Late model")+
geom_line(group=1)+
geom_ribbon(aes(ymin=X2.5., ymax=X97.5.), alpha=0.2)+
ylim(0,1)
# the results list has lots of other stuff
names(results)
## [1] "model" "BUGSoutput" "parameters.to.save" "model.file" "n.iter" "DIC"
names(results$BUGSoutput)
## [1] "n.chains" "n.iter" "n.burnin" "n.thin" "n.keep" "n.sims" "sims.array" "sims.list" "sims.matrix" "summary"
## [11] "mean" "sd" "median" "root.short" "long.short" "dimension.short" "indexes.short" "last.values" "program" "model.file"
## [21] "isDIC" "DICbyR" "pD" "DIC"
# we can also look at the beta estimates
# in this case this is the logit DSR which is the same for all nest x days
results$BUGSoutput$summary[ grepl("beta", row.names(results$BUGSoutput$summary)),,drop=FALSE]
## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
## beta[1] 4.1369318 0.8434642 2.840176 3.561724 4.0340018 4.55815097 6.193585 1.013118 340
## beta[2] -0.6435272 1.0046469 -2.922889 -1.225793 -0.5636499 0.02239442 1.101678 1.018464 280
#######################################
# get the full summary table
results$BUGSoutput$summary
## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
## S[1,1] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,2] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,3] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,3] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,4] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,4] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,5] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[2,5] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,5] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,5] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,6] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[2,6] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,6] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,6] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,7] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[2,7] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,7] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[5,7] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,7] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[1,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[2,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,8] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,9] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,9] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,9] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,9] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,9] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,10] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,10] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,10] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,10] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,10] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,11] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,11] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,11] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,11] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,11] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,12] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,12] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,12] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,12] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,12] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[9,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[10,13] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[6,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[8,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,14] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[8,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,15] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[13,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[14,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[15,16] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[13,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[14,17] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[13,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[14,18] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[13,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[14,19] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[4,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[7,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[11,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[12,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[13,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[14,20] 0.9794804 0.01410726 0.9448086 0.9723939 0.9826046 0.98962730 0.9979615 1.002161 1300
## S[3,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,21] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,22] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,23] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,24] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,25] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,26] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[18,27] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[18,28] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,29] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,30] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[4,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[7,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[14,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,31] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[11,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[16,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,32] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,33] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,33] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,33] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[17,33] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,34] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,34] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,34] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,35] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,35] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,35] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,36] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[12,36] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,36] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,37] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,37] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,38] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,38] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[3,39] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## S[13,39] 0.9666730 0.01636281 0.9279712 0.9575134 0.9694467 0.97841333 0.9911513 1.000871 4500
## beta[1] 4.1369318 0.84346424 2.8401763 3.5617243 4.0340018 4.55815097 6.1935846 1.013118 340
## beta[2] -0.6435272 1.00464695 -2.9228886 -1.2257925 -0.5636499 0.02239442 1.1016778 1.018464 280
## deviance 44.3188919 2.27140073 42.2280511 42.7582402 43.6127872 45.06506746 50.6602985 1.018773 300
results$BUGSoutput$summary[grepl("beta",rownames(results$BUGSoutput$summary)),
c("mean", "sd", "2.5%","97.5%","Rhat", "n.eff")]
## mean sd 2.5% 97.5% Rhat n.eff
## beta[1] 4.1369318 0.8434642 2.840176 6.193585 1.013118 340
## beta[2] -0.6435272 1.0046469 -2.922889 1.101678 1.018464 280