# Nest survival model using JAGS
# Here we want nest survival to be a linear function of DAY only
# 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$LastChecked-1),
Survive=1-x$Fate,
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:", (max(nesttime$Day)+min(nesttime$Day))/2, "='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 Survive Day2 Period NestAge
## 1 /*A*/ 1 9 9 0 1 0 1 1 1 361 Early 0
## 2 /*A*/ 1 9 9 0 1 0 1 2 1 324 Early 1
## 3 /*A*/ 1 9 9 0 1 0 1 3 1 289 Early 2
## 4 /*A*/ 1 9 9 0 1 0 1 4 1 256 Early 3
## 5 /*A*/ 1 9 9 0 1 0 1 5 1 225 Early 4
## 6 /*A*/ 1 9 9 0 1 0 1 6 1 196 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( Survive ~ Day, data=nesttime)
head(fe.design)
## (Intercept) Day
## 1 1 1
## 2 1 2
## 3 1 3
## 4 1 4
## 5 1 5
## 6 1 6
# 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: 1330
##
## 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 Survive 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 1 361 Early 0 0.9894300 0.01389614 0.9515142 0.9863922 0.9944973 0.9978913 0.9997014 1.002285 1500
## 2 1 2 /*A*/ 1 9 9 0 1 0 1 324 Early 1 0.9892269 0.01348458 0.9515298 0.9858699 0.9940870 0.9976522 0.9996477 1.002029 1500
## 3 1 3 /*A*/ 1 9 9 0 1 0 1 289 Early 2 0.9889999 0.01310471 0.9522519 0.9853476 0.9936807 0.9973970 0.9995780 1.002044 1500
## 4 1 4 /*A*/ 1 9 9 0 1 0 1 256 Early 3 0.9887473 0.01275452 0.9531398 0.9848603 0.9932625 0.9971180 0.9995008 1.002049 1400
## 5 1 5 /*A*/ 1 9 9 0 1 0 1 225 Early 4 0.9884672 0.01243203 0.9539056 0.9844020 0.9927780 0.9968174 0.9994079 1.002043 1500
## 6 1 6 /*A*/ 1 9 9 0 1 0 1 196 Early 5 0.9881577 0.01213533 0.9546079 0.9839654 0.9922716 0.9964791 0.9993044 1.002026 1500
# in this case, we fit a S~Day model, which is the same for all nests, so just extract
# days and plot
plotdata <- plyr::ddply(fitted.model$nesttime, "Day", function(x){ x[1,]})
ggplot(data=plotdata, aes(x=Day, y=mean))+
ggtitle("Estimated DSR in linear trend")+
geom_line(group=1)+
geom_ribbon(aes(ymin=X2.5., ymax=X97.5.), alpha=0.2)+
ylim(0,1)
# the results list has lots of other stuff
names(results)
## [1] "model" "BUGSoutput" "parameters.to.save" "model.file" "n.iter" "DIC"
names(results$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] 5.35727512 1.43898795 2.9519872 4.3166322 5.25858215 6.26469962 8.28716447 1.002601 1600
## beta[2] -0.06985192 0.05365924 -0.1757258 -0.1049163 -0.06850355 -0.03237192 0.02650618 1.004691 1600
#######################################
# get the full summary table
results$BUGSoutput$summary
## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
## S[1,1] 0.98943003 0.01389614 0.9515142 0.9863922 0.99449731 0.99789125 0.99970141 1.002285 1500
## S[1,2] 0.98922694 0.01348458 0.9515298 0.9858699 0.99408704 0.99765222 0.99964774 1.002029 1500
## S[1,3] 0.98899991 0.01310471 0.9522519 0.9853476 0.99368066 0.99739701 0.99957797 1.002044 1500
## S[6,3] 0.98899991 0.01310471 0.9522519 0.9853476 0.99368066 0.99739701 0.99957797 1.002044 1500
## S[1,4] 0.98874728 0.01275452 0.9531398 0.9848603 0.99326247 0.99711796 0.99950079 1.002049 1400
## S[6,4] 0.98874728 0.01275452 0.9531398 0.9848603 0.99326247 0.99711796 0.99950079 1.002049 1400
## S[1,5] 0.98846723 0.01243203 0.9539056 0.9844020 0.99277796 0.99681742 0.99940790 1.002043 1500
## S[2,5] 0.98846723 0.01243203 0.9539056 0.9844020 0.99277796 0.99681742 0.99940790 1.002043 1500
## S[3,5] 0.98846723 0.01243203 0.9539056 0.9844020 0.99277796 0.99681742 0.99940790 1.002043 1500
## S[6,5] 0.98846723 0.01243203 0.9539056 0.9844020 0.99277796 0.99681742 0.99940790 1.002043 1500
## S[1,6] 0.98815775 0.01213533 0.9546079 0.9839654 0.99227157 0.99647914 0.99930440 1.002026 1500
## S[2,6] 0.98815775 0.01213533 0.9546079 0.9839654 0.99227157 0.99647914 0.99930440 1.002026 1500
## S[3,6] 0.98815775 0.01213533 0.9546079 0.9839654 0.99227157 0.99647914 0.99930440 1.002026 1500
## S[6,6] 0.98815775 0.01213533 0.9546079 0.9839654 0.99227157 0.99647914 0.99930440 1.002026 1500
## S[1,7] 0.98781656 0.01186266 0.9557825 0.9834316 0.99169615 0.99609594 0.99917475 1.001996 1500
## S[2,7] 0.98781656 0.01186266 0.9557825 0.9834316 0.99169615 0.99609594 0.99917475 1.001996 1500
## S[3,7] 0.98781656 0.01186266 0.9557825 0.9834316 0.99169615 0.99609594 0.99917475 1.001996 1500
## S[5,7] 0.98781656 0.01186266 0.9557825 0.9834316 0.99169615 0.99609594 0.99917475 1.001996 1500
## S[6,7] 0.98781656 0.01186266 0.9557825 0.9834316 0.99169615 0.99609594 0.99917475 1.001996 1500
## S[1,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[2,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[3,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[6,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[7,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[9,8] 0.98744115 0.01161237 0.9562738 0.9827776 0.99114387 0.99569663 0.99902227 1.001955 1600
## S[3,9] 0.98702871 0.01138306 0.9565738 0.9822150 0.99049809 0.99523174 0.99885228 1.001902 1600
## S[4,9] 0.98702871 0.01138306 0.9565738 0.9822150 0.99049809 0.99523174 0.99885228 1.001902 1600
## S[6,9] 0.98702871 0.01138306 0.9565738 0.9822150 0.99049809 0.99523174 0.99885228 1.001902 1600
## S[7,9] 0.98702871 0.01138306 0.9565738 0.9822150 0.99049809 0.99523174 0.99885228 1.001902 1600
## S[9,9] 0.98702871 0.01138306 0.9565738 0.9822150 0.99049809 0.99523174 0.99885228 1.001902 1600
## S[3,10] 0.98657611 0.01117354 0.9570114 0.9815632 0.98980810 0.99472127 0.99866820 1.001837 1700
## S[4,10] 0.98657611 0.01117354 0.9570114 0.9815632 0.98980810 0.99472127 0.99866820 1.001837 1700
## S[6,10] 0.98657611 0.01117354 0.9570114 0.9815632 0.98980810 0.99472127 0.99866820 1.001837 1700
## S[7,10] 0.98657611 0.01117354 0.9570114 0.9815632 0.98980810 0.99472127 0.99866820 1.001837 1700
## S[9,10] 0.98657611 0.01117354 0.9570114 0.9815632 0.98980810 0.99472127 0.99866820 1.001837 1700
## S[3,11] 0.98607984 0.01098296 0.9576623 0.9809393 0.98909166 0.99414498 0.99845904 1.001761 1800
## S[4,11] 0.98607984 0.01098296 0.9576623 0.9809393 0.98909166 0.99414498 0.99845904 1.001761 1800
## S[6,11] 0.98607984 0.01098296 0.9576623 0.9809393 0.98909166 0.99414498 0.99845904 1.001761 1800
## S[7,11] 0.98607984 0.01098296 0.9576623 0.9809393 0.98909166 0.99414498 0.99845904 1.001761 1800
## S[9,11] 0.98607984 0.01098296 0.9576623 0.9809393 0.98909166 0.99414498 0.99845904 1.001761 1800
## S[3,12] 0.98553601 0.01081085 0.9581506 0.9802938 0.98835431 0.99353205 0.99819480 1.001675 2000
## S[4,12] 0.98553601 0.01081085 0.9581506 0.9802938 0.98835431 0.99353205 0.99819480 1.001675 2000
## S[6,12] 0.98553601 0.01081085 0.9581506 0.9802938 0.98835431 0.99353205 0.99819480 1.001675 2000
## S[7,12] 0.98553601 0.01081085 0.9581506 0.9802938 0.98835431 0.99353205 0.99819480 1.001675 2000
## S[9,12] 0.98553601 0.01081085 0.9581506 0.9802938 0.98835431 0.99353205 0.99819480 1.001675 2000
## S[3,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[4,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[6,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[7,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[9,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[10,13] 0.98494024 0.01065726 0.9582002 0.9796105 0.98751062 0.99287956 0.99786573 1.001583 2200
## S[3,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[4,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[6,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[7,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[8,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[11,14] 0.98428766 0.01052292 0.9581602 0.9787763 0.98667804 0.99214214 0.99750804 1.001486 2400
## S[3,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[4,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[7,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[8,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[11,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[12,15] 0.98357281 0.01040938 0.9580448 0.9781822 0.98574564 0.99131187 0.99708037 1.001389 2800
## S[3,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[4,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[7,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[11,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[12,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[13,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[14,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[15,16] 0.98278959 0.01031935 0.9576475 0.9772889 0.98481784 0.99048662 0.99663724 1.001296 3200
## S[3,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[4,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[7,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[11,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[12,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[13,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[14,17] 0.98193116 0.01025697 0.9573000 0.9764662 0.98389002 0.98953459 0.99613042 1.001213 3700
## S[3,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[4,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[7,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[11,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[12,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[13,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[14,18] 0.98098988 0.01022825 0.9568592 0.9753126 0.98275016 0.98853771 0.99551484 1.001148 4100
## S[3,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[4,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[7,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[11,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[12,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[13,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[14,19] 0.97995717 0.01024159 0.9560166 0.9741995 0.98161518 0.98747264 0.99487642 1.001107 4500
## S[3,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[4,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[7,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[11,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[12,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[13,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[14,20] 0.97882345 0.01030832 0.9546889 0.9730033 0.98038474 0.98632609 0.99414583 1.001100 4500
## S[3,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[4,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[7,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[11,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[12,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[13,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[14,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[16,21] 0.97757797 0.01044331 0.9531361 0.9717658 0.97915414 0.98511173 0.99329897 1.001131 4300
## S[3,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[4,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[7,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[11,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[12,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[13,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[14,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[16,22] 0.97620869 0.01066552 0.9519324 0.9701639 0.97769399 0.98383063 0.99254076 1.001204 3700
## S[3,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[4,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[7,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[11,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[12,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[13,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[14,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[16,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[17,23] 0.97470213 0.01099836 0.9498132 0.9682789 0.97620638 0.98261158 0.99170894 1.001315 3100
## S[3,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[4,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[7,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[11,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[12,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[13,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[14,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[16,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[17,24] 0.97304322 0.01146976 0.9469169 0.9662583 0.97453909 0.98133236 0.99084858 1.001456 2500
## S[3,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[4,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[7,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[11,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[12,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[13,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[14,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[16,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[17,25] 0.97121512 0.01211199 0.9439049 0.9639588 0.97290393 0.98006773 0.99013800 1.001610 2100
## S[3,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[4,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[7,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[11,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[12,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[13,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[14,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[16,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[17,26] 0.96919901 0.01296107 0.9397846 0.9614202 0.97091171 0.97871731 0.98947024 1.001754 1800
## S[3,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[4,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[7,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[11,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[12,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[13,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[14,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[16,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[17,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[18,27] 0.96697398 0.01405631 0.9348640 0.9584942 0.96885232 0.97729968 0.98898430 1.001868 1700
## S[3,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[4,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[7,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[11,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[12,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[13,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[14,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[16,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[17,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[18,28] 0.96451677 0.01543991 0.9297491 0.9554294 0.96660006 0.97584782 0.98850037 1.001934 1600
## S[3,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[4,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[7,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[11,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[12,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[13,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[14,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[16,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[17,29] 0.96180173 0.01715724 0.9229792 0.9519346 0.96424227 0.97454927 0.98825863 1.001946 1600
## S[3,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[4,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[7,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[11,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[12,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[13,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[14,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[16,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[17,30] 0.95880066 0.01925751 0.9142769 0.9476188 0.96163088 0.97320479 0.98800066 1.001904 1600
## S[3,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[4,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[7,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[11,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[12,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[13,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[14,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[16,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[17,31] 0.95548287 0.02179495 0.9036054 0.9430302 0.95886049 0.97164394 0.98789430 1.001819 1700
## S[3,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[11,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[12,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[13,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[16,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[17,32] 0.95181537 0.02482975 0.8916186 0.9379270 0.95574133 0.97037158 0.98776741 1.001705 1900
## S[3,33] 0.94776329 0.02842829 0.8780265 0.9326219 0.95268437 0.96914983 0.98768910 1.001578 2200
## S[12,33] 0.94776329 0.02842829 0.8780265 0.9326219 0.95268437 0.96914983 0.98768910 1.001578 2200
## S[13,33] 0.94776329 0.02842829 0.8780265 0.9326219 0.95268437 0.96914983 0.98768910 1.001578 2200
## S[17,33] 0.94776329 0.02842829 0.8780265 0.9326219 0.95268437 0.96914983 0.98768910 1.001578 2200
## S[3,34] 0.94329069 0.03266155 0.8622690 0.9264359 0.94923081 0.96789924 0.98774182 1.001455 2500
## S[12,34] 0.94329069 0.03266155 0.8622690 0.9264359 0.94923081 0.96789924 0.98774182 1.001455 2500
## S[13,34] 0.94329069 0.03266155 0.8622690 0.9264359 0.94923081 0.96789924 0.98774182 1.001455 2500
## S[3,35] 0.93836174 0.03760075 0.8461267 0.9194791 0.94569238 0.96661028 0.98780575 1.001350 2900
## S[12,35] 0.93836174 0.03760075 0.8461267 0.9194791 0.94569238 0.96661028 0.98780575 1.001350 2900
## S[13,35] 0.93836174 0.03760075 0.8461267 0.9194791 0.94569238 0.96661028 0.98780575 1.001350 2900
## S[3,36] 0.93294246 0.04330932 0.8259062 0.9118177 0.94221191 0.96499738 0.98784557 1.001818 3300
## S[12,36] 0.93294246 0.04330932 0.8259062 0.9118177 0.94221191 0.96499738 0.98784557 1.001818 3300
## S[13,36] 0.93294246 0.04330932 0.8259062 0.9118177 0.94221191 0.96499738 0.98784557 1.001818 3300
## S[3,37] 0.92700271 0.04983190 0.8031810 0.9035087 0.93831368 0.96353269 0.98792541 1.003055 3500
## S[13,37] 0.92700271 0.04983190 0.8031810 0.9035087 0.93831368 0.96353269 0.98792541 1.003055 3500
## S[3,38] 0.92051835 0.05718280 0.7737472 0.8947122 0.93402574 0.96221119 0.98808159 1.004967 3500
## S[13,38] 0.92051835 0.05718280 0.7737472 0.8947122 0.93402574 0.96221119 0.98808159 1.004967 3500
## S[3,39] 0.91347296 0.06533849 0.7459431 0.8850515 0.92985588 0.96068583 0.98827237 1.007569 3300
## S[13,39] 0.91347296 0.06533849 0.7459431 0.8850515 0.92985588 0.96068583 0.98827237 1.007569 3300
## beta[1] 5.35727512 1.43898795 2.9519872 4.3166322 5.25858215 6.26469962 8.28716447 1.002601 1600
## beta[2] -0.06985192 0.05365924 -0.1757258 -0.1049163 -0.06850355 -0.03237192 0.02650618 1.004691 1600
## deviance 43.01945224 2.05971475 41.0286588 41.6027701 42.40457333 43.75860909 48.25115931 1.007572 840
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] 5.35727512 1.43898795 2.9519872 8.28716447 1.002601 1600
## beta[2] -0.06985192 0.05365924 -0.1757258 0.02650618 1.004691 1600