# Nest survival model using JAGS
# Here we want nest survival to be a function of nest age
# The variable NestAge is computed based on the Day and AgeDay1 variables
# 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: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 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 ~ NestAge, data=nesttime)
head(fe.design)
## (Intercept) NestAge
## 1 1 0
## 2 1 1
## 3 1 2
## 4 1 3
## 5 1 4
## 6 1 5
# 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: 1324
##
## Initializing model
# 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 0.9738396 0.02021652 0.9190708 0.9655924 0.9790807 0.9879974 0.9968634 1.014300 280
## 2 1 2 /*A*/ 1 9 9 0 1 0 1 324 Early 1 0.9742299 0.01865337 0.9244748 0.9661334 0.9787153 0.9875530 0.9964416 1.013300 290
## 3 1 3 /*A*/ 1 9 9 0 1 0 1 289 Early 2 0.9745562 0.01724425 0.9294622 0.9665765 0.9784623 0.9869711 0.9960018 1.012171 310
## 4 1 4 /*A*/ 1 9 9 0 1 0 1 256 Early 3 0.9748199 0.01597990 0.9343592 0.9669466 0.9781707 0.9864068 0.9955984 1.010921 330
## 5 1 5 /*A*/ 1 9 9 0 1 0 1 225 Early 4 0.9750225 0.01485262 0.9384428 0.9674183 0.9778947 0.9859641 0.9950693 1.009564 350
## 6 1 6 /*A*/ 1 9 9 0 1 0 1 196 Early 5 0.9751651 0.01385660 0.9415965 0.9676466 0.9776239 0.9854211 0.9946486 1.008123 400
# in this case, we fit a S~NestAge model, which is the same for all nests, so just extract
# DSR at each ageand plot
plotdata <- plyr::ddply(fitted.model$nesttime, "NestAge", function(x){ x[1,]})
ggplot(data=plotdata, aes(x=NestAge, y=mean))+
ggtitle("Estimated DSR as a function of NestAge")+
geom_line(group=1)+
geom_ribbon(aes(ymin=X2.5., ymax=X97.5.), alpha=0.2)+
ylim(0,1)
# the results list has lots of other stuff
names(results)
## [1] "model" "BUGSoutput" "parameters.to.save" "model.file" "n.iter" "DIC"
names(results$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] 3.90994722 0.83407749 2.429789 3.33446363 3.84593961 4.41056075 5.7614877 1.006835 330
## beta[2] -0.01470816 0.05383181 -0.118304 -0.05018079 -0.01540165 0.01973208 0.0964004 1.007686 290
#######################################
# get the full summary table
results$BUGSoutput$summary
## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
## S[1,1] 0.97383957 0.02021652 0.9190708 0.96559237 0.97908065 0.98799745 0.9968634 1.014300 280
## S[1,2] 0.97422991 0.01865337 0.9244748 0.96613339 0.97871526 0.98755295 0.9964416 1.013300 290
## S[1,3] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[6,3] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[1,4] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[6,4] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[1,5] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[2,5] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[3,5] 0.97422991 0.01865337 0.9244748 0.96613339 0.97871526 0.98755295 0.9964416 1.013300 290
## S[6,5] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[1,6] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[2,6] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[3,6] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[6,6] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[1,7] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[2,7] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[3,7] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[5,7] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[6,7] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[1,8] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[2,8] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[3,8] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[6,8] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[7,8] 0.97383957 0.02021652 0.9190708 0.96559237 0.97908065 0.98799745 0.9968634 1.014300 280
## S[9,8] 0.97383957 0.02021652 0.9190708 0.96559237 0.97908065 0.98799745 0.9968634 1.014300 280
## S[3,9] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[4,9] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[6,9] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[7,9] 0.97422991 0.01865337 0.9244748 0.96613339 0.97871526 0.98755295 0.9964416 1.013300 290
## S[9,9] 0.97422991 0.01865337 0.9244748 0.96613339 0.97871526 0.98755295 0.9964416 1.013300 290
## S[3,10] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[4,10] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[6,10] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[7,10] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[9,10] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[3,11] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[4,11] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[6,11] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[7,11] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[9,11] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[3,12] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[4,12] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[6,12] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[7,12] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[9,12] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[3,13] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[4,13] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[6,13] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[7,13] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[9,13] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[10,13] 0.97383957 0.02021652 0.9190708 0.96559237 0.97908065 0.98799745 0.9968634 1.014300 280
## S[3,14] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[4,14] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[6,14] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[7,14] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[8,14] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[11,14] 0.97383957 0.02021652 0.9190708 0.96559237 0.97908065 0.98799745 0.9968634 1.014300 280
## S[3,15] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[4,15] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[7,15] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[8,15] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[11,15] 0.97422991 0.01865337 0.9244748 0.96613339 0.97871526 0.98755295 0.9964416 1.013300 290
## S[12,15] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[3,16] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[4,16] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[7,16] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[11,16] 0.97455615 0.01724425 0.9294622 0.96657650 0.97846228 0.98697115 0.9960018 1.012171 310
## S[12,16] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[13,16] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[14,16] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[15,16] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[3,17] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[4,17] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[7,17] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[11,17] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[12,17] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[13,17] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[14,17] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[3,18] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[4,18] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[7,18] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[11,18] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[12,18] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[13,18] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[14,18] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[3,19] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[4,19] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[7,19] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[11,19] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[12,19] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[13,19] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[14,19] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[3,20] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[4,20] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[7,20] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[11,20] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[12,20] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[13,20] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[14,20] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[3,21] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[4,21] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[7,21] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[11,21] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[12,21] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[13,21] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[14,21] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[16,21] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[3,22] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[4,22] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[7,22] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[11,22] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[12,22] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[13,22] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[14,22] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[16,22] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[3,23] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[4,23] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[7,23] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[11,23] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[12,23] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[13,23] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[14,23] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[16,23] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[17,23] 0.97516506 0.01385660 0.9415965 0.96764659 0.97762387 0.98542114 0.9946486 1.008123 400
## S[3,24] 0.96990246 0.01560335 0.9319683 0.96133264 0.97209452 0.98130253 0.9926337 1.003035 850
## S[4,24] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[7,24] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[11,24] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[12,24] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[13,24] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[14,24] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[16,24] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[17,24] 0.97524843 0.01298812 0.9441429 0.96804418 0.97740985 0.98484435 0.9940749 1.006635 460
## S[3,25] 0.96897302 0.01698541 0.9278622 0.95982672 0.97173032 0.98141618 0.9930116 1.003403 730
## S[4,25] 0.96990246 0.01560335 0.9319683 0.96133264 0.97209452 0.98130253 0.9926337 1.003035 850
## S[7,25] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[11,25] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[12,25] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[13,25] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[14,25] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[16,25] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[17,25] 0.97527317 0.01224567 0.9466631 0.96798520 0.97724271 0.98426304 0.9936687 1.005150 550
## S[3,26] 0.96795086 0.01855151 0.9219906 0.95839118 0.97126363 0.98157786 0.9935259 1.003708 660
## S[4,26] 0.96897302 0.01698541 0.9278622 0.95982672 0.97173032 0.98141618 0.9930116 1.003403 730
## S[7,26] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[11,26] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[12,26] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[13,26] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[14,26] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[16,26] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[17,26] 0.97523951 0.01163000 0.9484288 0.96837683 0.97694746 0.98374818 0.9931312 1.003730 710
## S[3,27] 0.96683066 0.02031212 0.9163687 0.95669966 0.97070910 0.98163232 0.9939670 1.003949 610
## S[4,27] 0.96795086 0.01855151 0.9219906 0.95839118 0.97126363 0.98157786 0.9935259 1.003708 660
## S[7,27] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[11,27] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[12,27] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[13,27] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[14,27] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[16,27] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[17,27] 0.97514737 0.01114387 0.9497666 0.96850192 0.97667451 0.98328192 0.9924951 1.002706 980
## S[18,27] 0.97481990 0.01597990 0.9343592 0.96694662 0.97817069 0.98640684 0.9955984 1.010921 330
## S[3,28] 0.96560676 0.02227952 0.9099740 0.95487698 0.97029904 0.98177800 0.9943081 1.004131 580
## S[4,28] 0.96683066 0.02031212 0.9163687 0.95669966 0.97070910 0.98163232 0.9939670 1.003949 610
## S[7,28] 0.96990246 0.01560335 0.9319683 0.96133264 0.97209452 0.98130253 0.9926337 1.003035 850
## S[11,28] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[12,28] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[13,28] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[14,28] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[16,28] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[17,28] 0.97499635 0.01079170 0.9508896 0.96847306 0.97636036 0.98286708 0.9920307 1.001971 1500
## S[18,28] 0.97502249 0.01485262 0.9384428 0.96741830 0.97789466 0.98596412 0.9950693 1.009564 350
## S[3,29] 0.96427320 0.02446747 0.9033579 0.95294224 0.96985111 0.98205814 0.9946054 1.004259 560
## S[4,29] 0.96560676 0.02227952 0.9099740 0.95487698 0.97029904 0.98177800 0.9943081 1.004131 580
## S[7,29] 0.96897302 0.01698541 0.9278622 0.95982672 0.97173032 0.98141618 0.9930116 1.003403 730
## S[11,29] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[12,29] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[13,29] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[14,29] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[16,29] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[17,29] 0.97478570 0.01057892 0.9510086 0.96856694 0.97610783 0.98256573 0.9917346 1.001359 2900
## S[3,30] 0.96282383 0.02689086 0.8954728 0.95069877 0.96938123 0.98218645 0.9950191 1.004340 550
## S[4,30] 0.96427320 0.02446747 0.9033579 0.95294224 0.96985111 0.98205814 0.9946054 1.004259 560
## S[7,30] 0.96795086 0.01855151 0.9219906 0.95839118 0.97126363 0.98157786 0.9935259 1.003708 660
## S[11,30] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[12,30] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[13,30] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[14,30] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[16,30] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[17,30] 0.97451432 0.01051117 0.9506561 0.96842421 0.97574889 0.98220316 0.9913584 1.000927 4500
## S[3,31] 0.96125235 0.02956523 0.8858342 0.94834663 0.96904977 0.98237800 0.9954345 1.004382 540
## S[4,31] 0.96282383 0.02689086 0.8954728 0.95069877 0.96938123 0.98218645 0.9950191 1.004340 550
## S[7,31] 0.96683066 0.02031212 0.9163687 0.95669966 0.97070910 0.98163232 0.9939670 1.003949 610
## S[11,31] 0.97218231 0.01248625 0.9428015 0.96526475 0.97379201 0.98122974 0.9914843 1.001683 2000
## S[12,31] 0.96990246 0.01560335 0.9319683 0.96133264 0.97209452 0.98130253 0.9926337 1.003035 850
## S[13,31] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[14,31] 0.97074417 0.01439680 0.9363598 0.96272700 0.97269143 0.98122663 0.9921283 1.002612 1000
## S[16,31] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[17,31] 0.97418074 0.01059354 0.9495752 0.96805361 0.97538789 0.98196896 0.9910313 1.000709 4500
## S[3,32] 0.95955242 0.03250623 0.8763553 0.94569909 0.96830357 0.98269955 0.9958377 1.004392 540
## S[11,32] 0.97150272 0.01335928 0.9399174 0.96414641 0.97323188 0.98110483 0.9918187 1.002151 1300
## S[12,32] 0.96897302 0.01698541 0.9278622 0.95982672 0.97173032 0.98141618 0.9930116 1.003403 730
## S[13,32] 0.96990246 0.01560335 0.9319683 0.96133264 0.97209452 0.98130253 0.9926337 1.003035 850
## S[16,32] 0.97278672 0.01177481 0.9452478 0.96597098 0.97430086 0.98124425 0.9910692 1.001250 3400
## S[17,32] 0.97378315 0.01082998 0.9483426 0.96763139 0.97510019 0.98176139 0.9908962 1.000711 4500
## S[3,33] 0.95771781 0.03572900 0.8638914 0.94298253 0.96774859 0.98303035 0.9962093 1.004376 540
## S[12,33] 0.96795086 0.01855151 0.9219906 0.95839118 0.97126363 0.98157786 0.9935259 1.003708 660
## S[13,33] 0.96897302 0.01698541 0.9278622 0.95982672 0.97173032 0.98141618 0.9930116 1.003403 730
## S[17,33] 0.97331934 0.01122317 0.9470073 0.96680464 0.97480413 0.98143856 0.9910039 1.000907 4500
## S[3,34] 0.95574248 0.03924749 0.8523338 0.94010979 0.96707852 0.98335723 0.9965040 1.004339 550
## S[12,34] 0.96683066 0.02031212 0.9163687 0.95669966 0.97070910 0.98163232 0.9939670 1.003949 610
## S[13,34] 0.96795086 0.01855151 0.9219906 0.95839118 0.97126363 0.98157786 0.9935259 1.003708 660
## S[3,35] 0.95362083 0.04307370 0.8384427 0.93753638 0.96624335 0.98358261 0.9968649 1.004287 550
## S[12,35] 0.96560676 0.02227952 0.9099740 0.95487698 0.97029904 0.98177800 0.9943081 1.004131 580
## S[13,35] 0.96683066 0.02031212 0.9163687 0.95669966 0.97070910 0.98163232 0.9939670 1.003949 610
## S[3,36] 0.95134779 0.04721694 0.8226221 0.93483060 0.96580411 0.98377340 0.9971895 1.004409 560
## S[12,36] 0.96427320 0.02446747 0.9033579 0.95294224 0.96985111 0.98205814 0.9946054 1.004259 560
## S[13,36] 0.96560676 0.02227952 0.9099740 0.95487698 0.97029904 0.98177800 0.9943081 1.004131 580
## S[3,37] 0.94891904 0.05168310 0.8056079 0.93180456 0.96525022 0.98409776 0.9974084 1.004555 580
## S[13,37] 0.96427320 0.02446747 0.9033579 0.95294224 0.96985111 0.98205814 0.9946054 1.004259 560
## S[3,38] 0.94633118 0.05647400 0.7873182 0.92833751 0.96461730 0.98441398 0.9976301 1.004710 590
## S[13,38] 0.96282383 0.02689086 0.8954728 0.95069877 0.96938123 0.98218645 0.9950191 1.004340 550
## S[3,39] 0.94358188 0.06158685 0.7711910 0.92471204 0.96393019 0.98458925 0.9978262 1.004873 600
## S[13,39] 0.96125235 0.02956523 0.8858342 0.94834663 0.96904977 0.98237800 0.9954345 1.004382 540
## beta[1] 3.90994722 0.83407749 2.4297889 3.33446363 3.84593961 4.41056075 5.7614877 1.006835 330
## beta[2] -0.01470816 0.05383181 -0.1183040 -0.05018079 -0.01540165 0.01973208 0.0964004 1.007686 290
## deviance 44.42381116 2.05713574 42.4322338 42.95302152 43.79784018 45.19890195 49.9933623 1.001574 2200
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] 3.90994722 0.83407749 2.429789 5.7614877 1.006835 330
## beta[2] -0.01470816 0.05383181 -0.118304 0.0964004 1.007686 290