# Single Species, Multi Season Occupancy analyais
# Northern Spotted Owl (Strix occidentalis caurina) in California.
# s=55 sites visited up to K=5 times per season between 1997 and 2001 (Y=5).
# Detection probabilities relatively constant within years, but likely different among years.
# Using RMark to fit a Random Occupancy model
# 2018-08-15 Code contributed by Carl James Schwarz (cschwarz@stat.sfu.ca)
# The random occupancy model is fit in MARK as described in
# https://sites.warnercnr.colostate.edu/gwhite/occupancy-estimation-robust-design/
#
# We need to set gamma = 1-epsilon using design matrices
#
# One model often of interest is the random extinction and colonization model,
# where the probability of a site being occupied at time t+1 is the same regardless
# of whether or not the site was occupied at time t.
# You can obtain estimates for this model in MARK by clever
# coding of the design matrix.
# Suppose the epsilon of interest is parameter 2 in the PIM,
# and the gamma of interest is parameter 3 in the PIM.
# Use a common beta parameter for both epsilon and gamma,
# i.e., there will be a single column that is modeled by both rows 2 and 3 of the design matrix.
# If you specify a logit link for both epsilon and gamma, and code epsilon as -1
# in the design matrix and gamma as +1, the result is the model with 1 - epsilon = gamma.
# The design matrix looks like:
# Columns: B1 B2 B3
# Row 1: 1 0 0
# Row 2: 0 -1 0 This is epsilon
# Row 3: 0 1 0 This is gamma
#
# Unfortunately, RMark does not allow you fit this model directly because only the logit link is
# suported.
#
# You can get the equivalent of a random occupancy model by stacking the data as shown below.
# No estimates of epsilon or gamma are available as they are fixed by the psi values.
# In most cases, the random occupancy model is seldom a good fit to the data.
# Packages
library(readxl)
library(RMark)
## This is RMark 2.2.5
## Documentation available at http://www.phidot.org/software/mark/rmark/RMarkDocumentation.zip
library(ggplot2)
# Get the RPResence additional functions
source(file.path("..","..","..","AdditionalFunctions","RMark.additional.functions.R"))
# 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.data <- read.csv(file.path("..","NSO.csv"), header=FALSE, skip=2, na.strings="-")
input.data$V1 <- NULL # drop the site number
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.data)
## [1] 55
ncol(input.data)
## [1] 40
range(input.data, na.rm=TRUE)
## [1] 0 1
sum(is.na(input.data))
## [1] 752
# Extract the history records and create a capture history
input.history <- data.frame(freq=1,
ch=apply(input.data,1,paste, collapse=""), stringsAsFactors=FALSE)
head(input.history)
## freq ch
## 1 1 0111NANANANA010NANANANANA11NANANANANANA011NANANANANA0101NANANANA
## 2 1 00NANANANANANA000NANANANANA000NANANANANA000110NANA0011NANANANA
## 3 1 1000111NA0100NANANANA0001NANANANA000000NANA00000NANANA
## 4 1 111NANANANANA10NANANANANANA011NANANANANA00000100000011NANA
## 5 1 000000NANA0000000NA000000NANA000000NANA0111NANANANA
## 6 1 1NANANANANANANA000111NANA0111NANANANA01111NANANA011111NANA
# Change any NA to . in the chapter history
input.history$ch <- gsub("NA",".", input.history$ch, fixed=TRUE)
head(input.history)
## freq ch
## 1 1 0111....010.....11......011.....0101....
## 2 1 00......000.....000.....000110..0011....
## 3 1 1000111.0100....0001....000000..00000...
## 4 1 111.....10......011.....00000100000011..
## 5 1 000000..0000000.000000..000000..0111....
## 6 1 1.......000111..0111....01111...011111..
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.history)
## [1] 55
# Create the data structure
max.visit.per.year <- 8
n.season <- 5
# Creata stacked version of the data for fitting a random occupancy model
input.history.ro <- RMark.random.occup.stack(input.history, surveys.per.season=rep(max.visit.per.year,n.season))
## Loading required package: plyr
summary(input.history.ro)
## freq ch Season
## Min. :1 Length:275 Min. :1
## 1st Qu.:1 Class :character 1st Qu.:2
## Median :1 Mode :character Median :3
## Mean :1 Mean :3
## 3rd Qu.:1 3rd Qu.:4
## Max. :1 Max. :5
nso.data.ro <- process.data(data=input.history.ro, groups="Season", model="Occupancy")
## Warning in process.data(data = input.history.ro, groups = "Season", model = "Occupancy"):
## Season is not a factor variable. Coercing to factor.
summary(nso.data.ro)
## Length Class Mode
## data 4 data.frame list
## model 1 -none- character
## mixtures 1 -none- numeric
## freq 5 data.frame list
## nocc 1 -none- numeric
## nocc.secondary 0 -none- NULL
## time.intervals 40 -none- numeric
## begin.time 1 -none- numeric
## age.unit 1 -none- numeric
## initial.ages 5 -none- numeric
## group.covariates 1 data.frame list
## nstrata 1 -none- numeric
## strata.labels 0 -none- NULL
## counts 0 -none- NULL
## reverse 1 -none- logical
## areas 0 -none- NULL
## events 0 -none- NULL
# What are the parameter names for Single Season Single Species models
setup.parameters("Occupancy", check=TRUE)
## [1] "p" "Psi"
# Fit a models.
# Note that formula DO NOT HAVE AN = SIGN
mod.fit <- RMark::mark(nso.data.ro,
model="Occupancy",
model.parameters=list(
Psi =list(formula=~Season), # Occupancy eash year
p =list(formula=~1))
)
##
## Output summary for Occupancy model
## Name : p(~1)Psi(~Season)
##
## Npar : 6
## -2lnL: 1446.263
## AICc : 1458.576
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.0293390 0.0757494 -0.1778078 0.1191298
## Psi:(Intercept) 0.5706807 0.2997363 -0.0168024 1.1581638
## Psi:Season2 -0.1409865 0.4158036 -0.9559616 0.6739887
## Psi:Season3 -0.3833161 0.4105010 -1.1878981 0.4212658
## Psi:Season4 -0.2632128 0.4098293 -1.0664782 0.5400526
## Psi:Season5 -0.2614794 0.4100194 -1.0651174 0.5421586
##
##
## Real Parameter p
## 1 2 3 4 5 6
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 7 8 9 10 11 12
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 13 14 15 16 17 18
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 19 20 21 22 23 24
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 25 26 27 28 29 30
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 31 32 33 34 35 36
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 37 38 39 40
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658
##
##
## Real Parameter Psi
## 1
## Group:Season1 0.6389202
## Group:Season2 0.6058006
## Group:Season3 0.5467046
## Group:Season4 0.5762671
## Group:Season5 0.5766903
summary(mod.fit)
## Output summary for Occupancy model
## Name : p(~1)Psi(~Season)
##
## Npar : 6
## -2lnL: 1446.263
## AICc : 1458.576
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.0293390 0.0757494 -0.1778078 0.1191298
## Psi:(Intercept) 0.5706807 0.2997363 -0.0168024 1.1581638
## Psi:Season2 -0.1409865 0.4158036 -0.9559616 0.6739887
## Psi:Season3 -0.3833161 0.4105010 -1.1878981 0.4212658
## Psi:Season4 -0.2632128 0.4098293 -1.0664782 0.5400526
## Psi:Season5 -0.2614794 0.4100194 -1.0651174 0.5421586
##
##
## Real Parameter p
## 1 2 3 4 5 6
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 7 8 9 10 11 12
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 13 14 15 16 17 18
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 19 20 21 22 23 24
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 25 26 27 28 29 30
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 31 32 33 34 35 36
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658 0.4926658
## 37 38 39 40
## Group:Season1 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season2 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season3 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season4 0.4926658 0.4926658 0.4926658 0.4926658
## Group:Season5 0.4926658 0.4926658 0.4926658 0.4926658
##
##
## Real Parameter Psi
## 1
## Group:Season1 0.6389202
## Group:Season2 0.6058006
## Group:Season3 0.5467046
## Group:Season4 0.5762671
## Group:Season5 0.5766903
names(mod.fit)
## [1] "data" "model" "title"
## [4] "model.name" "links" "mixtures"
## [7] "call" "parameters" "time.intervals"
## [10] "number.of.groups" "group.labels" "nocc"
## [13] "begin.time" "covariates" "fixed"
## [16] "design.matrix" "pims" "design.data"
## [19] "strata.labels" "mlogit.list" "profile.int"
## [22] "simplify" "model.parameters" "results"
## [25] "output"
names(mod.fit$results)
## [1] "lnl" "deviance" "deviance.df"
## [4] "npar" "n" "AICc"
## [7] "beta" "real" "beta.vcv"
## [10] "derived" "derived.vcv" "covariate.values"
## [13] "singular" "real.vcv"
# Estimate of initial occupancy
names(mod.fit$results$real)
## [1] "estimate" "se" "lcl" "ucl" "fixed" "note"
mod.fit$results$real
## estimate se lcl ucl fixed note
## p g1 a0 t1 0.4926658 0.0189333 0.4556648 0.5297473
## Psi g1 a0 t1 0.6389202 0.0691495 0.4957995 0.7609989
## Psi g2 a0 t1 0.6058006 0.0690097 0.4658775 0.7302893
## Psi g3 a0 t1 0.5467046 0.0696824 0.4100510 0.6766642
## Psi g4 a0 t1 0.5762671 0.0683988 0.4399037 0.7019265
## Psi g5 a0 t1 0.5766903 0.0684535 0.4401868 0.7024113
get.real(mod.fit, parameter="Psi", se=TRUE)
## all.diff.index par.index estimate se lcl
## Psi g1 a0 t1 201 2 0.6389202 0.0691495 0.4957995
## Psi g2 a0 t1 202 3 0.6058006 0.0690097 0.4658775
## Psi g3 a0 t1 203 4 0.5467046 0.0696824 0.4100510
## Psi g4 a0 t1 204 5 0.5762671 0.0683988 0.4399037
## Psi g5 a0 t1 205 6 0.5766903 0.0684535 0.4401868
## ucl fixed note group age time Age Time Season
## Psi g1 a0 t1 0.7609989 1 0 1 0 0 1
## Psi g2 a0 t1 0.7302893 2 0 1 0 0 2
## Psi g3 a0 t1 0.6766642 3 0 1 0 0 3
## Psi g4 a0 t1 0.7019265 4 0 1 0 0 4
## Psi g5 a0 t1 0.7024113 5 0 1 0 0 5
get.real(mod.fit, parameter="p" , se=TRUE)
## all.diff.index par.index estimate se lcl
## p g1 a0 t1 1 1 0.4926658 0.0189333 0.4556648
## p g1 a1 t2 2 1 0.4926658 0.0189333 0.4556648
## p g1 a2 t3 3 1 0.4926658 0.0189333 0.4556648
## p g1 a3 t4 4 1 0.4926658 0.0189333 0.4556648
## p g1 a4 t5 5 1 0.4926658 0.0189333 0.4556648
## p g1 a5 t6 6 1 0.4926658 0.0189333 0.4556648
## p g1 a6 t7 7 1 0.4926658 0.0189333 0.4556648
## p g1 a7 t8 8 1 0.4926658 0.0189333 0.4556648
## p g1 a8 t9 9 1 0.4926658 0.0189333 0.4556648
## p g1 a9 t10 10 1 0.4926658 0.0189333 0.4556648
## p g1 a10 t11 11 1 0.4926658 0.0189333 0.4556648
## p g1 a11 t12 12 1 0.4926658 0.0189333 0.4556648
## p g1 a12 t13 13 1 0.4926658 0.0189333 0.4556648
## p g1 a13 t14 14 1 0.4926658 0.0189333 0.4556648
## p g1 a14 t15 15 1 0.4926658 0.0189333 0.4556648
## p g1 a15 t16 16 1 0.4926658 0.0189333 0.4556648
## p g1 a16 t17 17 1 0.4926658 0.0189333 0.4556648
## p g1 a17 t18 18 1 0.4926658 0.0189333 0.4556648
## p g1 a18 t19 19 1 0.4926658 0.0189333 0.4556648
## p g1 a19 t20 20 1 0.4926658 0.0189333 0.4556648
## p g1 a20 t21 21 1 0.4926658 0.0189333 0.4556648
## p g1 a21 t22 22 1 0.4926658 0.0189333 0.4556648
## p g1 a22 t23 23 1 0.4926658 0.0189333 0.4556648
## p g1 a23 t24 24 1 0.4926658 0.0189333 0.4556648
## p g1 a24 t25 25 1 0.4926658 0.0189333 0.4556648
## p g1 a25 t26 26 1 0.4926658 0.0189333 0.4556648
## p g1 a26 t27 27 1 0.4926658 0.0189333 0.4556648
## p g1 a27 t28 28 1 0.4926658 0.0189333 0.4556648
## p g1 a28 t29 29 1 0.4926658 0.0189333 0.4556648
## p g1 a29 t30 30 1 0.4926658 0.0189333 0.4556648
## p g1 a30 t31 31 1 0.4926658 0.0189333 0.4556648
## p g1 a31 t32 32 1 0.4926658 0.0189333 0.4556648
## p g1 a32 t33 33 1 0.4926658 0.0189333 0.4556648
## p g1 a33 t34 34 1 0.4926658 0.0189333 0.4556648
## p g1 a34 t35 35 1 0.4926658 0.0189333 0.4556648
## p g1 a35 t36 36 1 0.4926658 0.0189333 0.4556648
## p g1 a36 t37 37 1 0.4926658 0.0189333 0.4556648
## p g1 a37 t38 38 1 0.4926658 0.0189333 0.4556648
## p g1 a38 t39 39 1 0.4926658 0.0189333 0.4556648
## p g1 a39 t40 40 1 0.4926658 0.0189333 0.4556648
## p g2 a0 t1 41 1 0.4926658 0.0189333 0.4556648
## p g2 a1 t2 42 1 0.4926658 0.0189333 0.4556648
## p g2 a2 t3 43 1 0.4926658 0.0189333 0.4556648
## p g2 a3 t4 44 1 0.4926658 0.0189333 0.4556648
## p g2 a4 t5 45 1 0.4926658 0.0189333 0.4556648
## p g2 a5 t6 46 1 0.4926658 0.0189333 0.4556648
## p g2 a6 t7 47 1 0.4926658 0.0189333 0.4556648
## p g2 a7 t8 48 1 0.4926658 0.0189333 0.4556648
## p g2 a8 t9 49 1 0.4926658 0.0189333 0.4556648
## p g2 a9 t10 50 1 0.4926658 0.0189333 0.4556648
## p g2 a10 t11 51 1 0.4926658 0.0189333 0.4556648
## p g2 a11 t12 52 1 0.4926658 0.0189333 0.4556648
## p g2 a12 t13 53 1 0.4926658 0.0189333 0.4556648
## p g2 a13 t14 54 1 0.4926658 0.0189333 0.4556648
## p g2 a14 t15 55 1 0.4926658 0.0189333 0.4556648
## p g2 a15 t16 56 1 0.4926658 0.0189333 0.4556648
## p g2 a16 t17 57 1 0.4926658 0.0189333 0.4556648
## p g2 a17 t18 58 1 0.4926658 0.0189333 0.4556648
## p g2 a18 t19 59 1 0.4926658 0.0189333 0.4556648
## p g2 a19 t20 60 1 0.4926658 0.0189333 0.4556648
## p g2 a20 t21 61 1 0.4926658 0.0189333 0.4556648
## p g2 a21 t22 62 1 0.4926658 0.0189333 0.4556648
## p g2 a22 t23 63 1 0.4926658 0.0189333 0.4556648
## p g2 a23 t24 64 1 0.4926658 0.0189333 0.4556648
## p g2 a24 t25 65 1 0.4926658 0.0189333 0.4556648
## p g2 a25 t26 66 1 0.4926658 0.0189333 0.4556648
## p g2 a26 t27 67 1 0.4926658 0.0189333 0.4556648
## p g2 a27 t28 68 1 0.4926658 0.0189333 0.4556648
## p g2 a28 t29 69 1 0.4926658 0.0189333 0.4556648
## p g2 a29 t30 70 1 0.4926658 0.0189333 0.4556648
## p g2 a30 t31 71 1 0.4926658 0.0189333 0.4556648
## p g2 a31 t32 72 1 0.4926658 0.0189333 0.4556648
## p g2 a32 t33 73 1 0.4926658 0.0189333 0.4556648
## p g2 a33 t34 74 1 0.4926658 0.0189333 0.4556648
## p g2 a34 t35 75 1 0.4926658 0.0189333 0.4556648
## p g2 a35 t36 76 1 0.4926658 0.0189333 0.4556648
## p g2 a36 t37 77 1 0.4926658 0.0189333 0.4556648
## p g2 a37 t38 78 1 0.4926658 0.0189333 0.4556648
## p g2 a38 t39 79 1 0.4926658 0.0189333 0.4556648
## p g2 a39 t40 80 1 0.4926658 0.0189333 0.4556648
## p g3 a0 t1 81 1 0.4926658 0.0189333 0.4556648
## p g3 a1 t2 82 1 0.4926658 0.0189333 0.4556648
## p g3 a2 t3 83 1 0.4926658 0.0189333 0.4556648
## p g3 a3 t4 84 1 0.4926658 0.0189333 0.4556648
## p g3 a4 t5 85 1 0.4926658 0.0189333 0.4556648
## p g3 a5 t6 86 1 0.4926658 0.0189333 0.4556648
## p g3 a6 t7 87 1 0.4926658 0.0189333 0.4556648
## p g3 a7 t8 88 1 0.4926658 0.0189333 0.4556648
## p g3 a8 t9 89 1 0.4926658 0.0189333 0.4556648
## p g3 a9 t10 90 1 0.4926658 0.0189333 0.4556648
## p g3 a10 t11 91 1 0.4926658 0.0189333 0.4556648
## p g3 a11 t12 92 1 0.4926658 0.0189333 0.4556648
## p g3 a12 t13 93 1 0.4926658 0.0189333 0.4556648
## p g3 a13 t14 94 1 0.4926658 0.0189333 0.4556648
## p g3 a14 t15 95 1 0.4926658 0.0189333 0.4556648
## p g3 a15 t16 96 1 0.4926658 0.0189333 0.4556648
## p g3 a16 t17 97 1 0.4926658 0.0189333 0.4556648
## p g3 a17 t18 98 1 0.4926658 0.0189333 0.4556648
## p g3 a18 t19 99 1 0.4926658 0.0189333 0.4556648
## p g3 a19 t20 100 1 0.4926658 0.0189333 0.4556648
## p g3 a20 t21 101 1 0.4926658 0.0189333 0.4556648
## p g3 a21 t22 102 1 0.4926658 0.0189333 0.4556648
## p g3 a22 t23 103 1 0.4926658 0.0189333 0.4556648
## p g3 a23 t24 104 1 0.4926658 0.0189333 0.4556648
## p g3 a24 t25 105 1 0.4926658 0.0189333 0.4556648
## p g3 a25 t26 106 1 0.4926658 0.0189333 0.4556648
## p g3 a26 t27 107 1 0.4926658 0.0189333 0.4556648
## p g3 a27 t28 108 1 0.4926658 0.0189333 0.4556648
## p g3 a28 t29 109 1 0.4926658 0.0189333 0.4556648
## p g3 a29 t30 110 1 0.4926658 0.0189333 0.4556648
## p g3 a30 t31 111 1 0.4926658 0.0189333 0.4556648
## p g3 a31 t32 112 1 0.4926658 0.0189333 0.4556648
## p g3 a32 t33 113 1 0.4926658 0.0189333 0.4556648
## p g3 a33 t34 114 1 0.4926658 0.0189333 0.4556648
## p g3 a34 t35 115 1 0.4926658 0.0189333 0.4556648
## p g3 a35 t36 116 1 0.4926658 0.0189333 0.4556648
## p g3 a36 t37 117 1 0.4926658 0.0189333 0.4556648
## p g3 a37 t38 118 1 0.4926658 0.0189333 0.4556648
## p g3 a38 t39 119 1 0.4926658 0.0189333 0.4556648
## p g3 a39 t40 120 1 0.4926658 0.0189333 0.4556648
## p g4 a0 t1 121 1 0.4926658 0.0189333 0.4556648
## p g4 a1 t2 122 1 0.4926658 0.0189333 0.4556648
## p g4 a2 t3 123 1 0.4926658 0.0189333 0.4556648
## p g4 a3 t4 124 1 0.4926658 0.0189333 0.4556648
## p g4 a4 t5 125 1 0.4926658 0.0189333 0.4556648
## p g4 a5 t6 126 1 0.4926658 0.0189333 0.4556648
## p g4 a6 t7 127 1 0.4926658 0.0189333 0.4556648
## p g4 a7 t8 128 1 0.4926658 0.0189333 0.4556648
## p g4 a8 t9 129 1 0.4926658 0.0189333 0.4556648
## p g4 a9 t10 130 1 0.4926658 0.0189333 0.4556648
## p g4 a10 t11 131 1 0.4926658 0.0189333 0.4556648
## p g4 a11 t12 132 1 0.4926658 0.0189333 0.4556648
## p g4 a12 t13 133 1 0.4926658 0.0189333 0.4556648
## p g4 a13 t14 134 1 0.4926658 0.0189333 0.4556648
## p g4 a14 t15 135 1 0.4926658 0.0189333 0.4556648
## p g4 a15 t16 136 1 0.4926658 0.0189333 0.4556648
## p g4 a16 t17 137 1 0.4926658 0.0189333 0.4556648
## p g4 a17 t18 138 1 0.4926658 0.0189333 0.4556648
## p g4 a18 t19 139 1 0.4926658 0.0189333 0.4556648
## p g4 a19 t20 140 1 0.4926658 0.0189333 0.4556648
## p g4 a20 t21 141 1 0.4926658 0.0189333 0.4556648
## p g4 a21 t22 142 1 0.4926658 0.0189333 0.4556648
## p g4 a22 t23 143 1 0.4926658 0.0189333 0.4556648
## p g4 a23 t24 144 1 0.4926658 0.0189333 0.4556648
## p g4 a24 t25 145 1 0.4926658 0.0189333 0.4556648
## p g4 a25 t26 146 1 0.4926658 0.0189333 0.4556648
## p g4 a26 t27 147 1 0.4926658 0.0189333 0.4556648
## p g4 a27 t28 148 1 0.4926658 0.0189333 0.4556648
## p g4 a28 t29 149 1 0.4926658 0.0189333 0.4556648
## p g4 a29 t30 150 1 0.4926658 0.0189333 0.4556648
## p g4 a30 t31 151 1 0.4926658 0.0189333 0.4556648
## p g4 a31 t32 152 1 0.4926658 0.0189333 0.4556648
## p g4 a32 t33 153 1 0.4926658 0.0189333 0.4556648
## p g4 a33 t34 154 1 0.4926658 0.0189333 0.4556648
## p g4 a34 t35 155 1 0.4926658 0.0189333 0.4556648
## p g4 a35 t36 156 1 0.4926658 0.0189333 0.4556648
## p g4 a36 t37 157 1 0.4926658 0.0189333 0.4556648
## p g4 a37 t38 158 1 0.4926658 0.0189333 0.4556648
## p g4 a38 t39 159 1 0.4926658 0.0189333 0.4556648
## p g4 a39 t40 160 1 0.4926658 0.0189333 0.4556648
## p g5 a0 t1 161 1 0.4926658 0.0189333 0.4556648
## p g5 a1 t2 162 1 0.4926658 0.0189333 0.4556648
## p g5 a2 t3 163 1 0.4926658 0.0189333 0.4556648
## p g5 a3 t4 164 1 0.4926658 0.0189333 0.4556648
## p g5 a4 t5 165 1 0.4926658 0.0189333 0.4556648
## p g5 a5 t6 166 1 0.4926658 0.0189333 0.4556648
## p g5 a6 t7 167 1 0.4926658 0.0189333 0.4556648
## p g5 a7 t8 168 1 0.4926658 0.0189333 0.4556648
## p g5 a8 t9 169 1 0.4926658 0.0189333 0.4556648
## p g5 a9 t10 170 1 0.4926658 0.0189333 0.4556648
## p g5 a10 t11 171 1 0.4926658 0.0189333 0.4556648
## p g5 a11 t12 172 1 0.4926658 0.0189333 0.4556648
## p g5 a12 t13 173 1 0.4926658 0.0189333 0.4556648
## p g5 a13 t14 174 1 0.4926658 0.0189333 0.4556648
## p g5 a14 t15 175 1 0.4926658 0.0189333 0.4556648
## p g5 a15 t16 176 1 0.4926658 0.0189333 0.4556648
## p g5 a16 t17 177 1 0.4926658 0.0189333 0.4556648
## p g5 a17 t18 178 1 0.4926658 0.0189333 0.4556648
## p g5 a18 t19 179 1 0.4926658 0.0189333 0.4556648
## p g5 a19 t20 180 1 0.4926658 0.0189333 0.4556648
## p g5 a20 t21 181 1 0.4926658 0.0189333 0.4556648
## p g5 a21 t22 182 1 0.4926658 0.0189333 0.4556648
## p g5 a22 t23 183 1 0.4926658 0.0189333 0.4556648
## p g5 a23 t24 184 1 0.4926658 0.0189333 0.4556648
## p g5 a24 t25 185 1 0.4926658 0.0189333 0.4556648
## p g5 a25 t26 186 1 0.4926658 0.0189333 0.4556648
## p g5 a26 t27 187 1 0.4926658 0.0189333 0.4556648
## p g5 a27 t28 188 1 0.4926658 0.0189333 0.4556648
## p g5 a28 t29 189 1 0.4926658 0.0189333 0.4556648
## p g5 a29 t30 190 1 0.4926658 0.0189333 0.4556648
## p g5 a30 t31 191 1 0.4926658 0.0189333 0.4556648
## p g5 a31 t32 192 1 0.4926658 0.0189333 0.4556648
## p g5 a32 t33 193 1 0.4926658 0.0189333 0.4556648
## p g5 a33 t34 194 1 0.4926658 0.0189333 0.4556648
## p g5 a34 t35 195 1 0.4926658 0.0189333 0.4556648
## p g5 a35 t36 196 1 0.4926658 0.0189333 0.4556648
## p g5 a36 t37 197 1 0.4926658 0.0189333 0.4556648
## p g5 a37 t38 198 1 0.4926658 0.0189333 0.4556648
## p g5 a38 t39 199 1 0.4926658 0.0189333 0.4556648
## p g5 a39 t40 200 1 0.4926658 0.0189333 0.4556648
## ucl fixed note group age time Age Time Season
## p g1 a0 t1 0.5297473 1 0 1 0 0 1
## p g1 a1 t2 0.5297473 1 1 2 1 1 1
## p g1 a2 t3 0.5297473 1 2 3 2 2 1
## p g1 a3 t4 0.5297473 1 3 4 3 3 1
## p g1 a4 t5 0.5297473 1 4 5 4 4 1
## p g1 a5 t6 0.5297473 1 5 6 5 5 1
## p g1 a6 t7 0.5297473 1 6 7 6 6 1
## p g1 a7 t8 0.5297473 1 7 8 7 7 1
## p g1 a8 t9 0.5297473 1 8 9 8 8 1
## p g1 a9 t10 0.5297473 1 9 10 9 9 1
## p g1 a10 t11 0.5297473 1 10 11 10 10 1
## p g1 a11 t12 0.5297473 1 11 12 11 11 1
## p g1 a12 t13 0.5297473 1 12 13 12 12 1
## p g1 a13 t14 0.5297473 1 13 14 13 13 1
## p g1 a14 t15 0.5297473 1 14 15 14 14 1
## p g1 a15 t16 0.5297473 1 15 16 15 15 1
## p g1 a16 t17 0.5297473 1 16 17 16 16 1
## p g1 a17 t18 0.5297473 1 17 18 17 17 1
## p g1 a18 t19 0.5297473 1 18 19 18 18 1
## p g1 a19 t20 0.5297473 1 19 20 19 19 1
## p g1 a20 t21 0.5297473 1 20 21 20 20 1
## p g1 a21 t22 0.5297473 1 21 22 21 21 1
## p g1 a22 t23 0.5297473 1 22 23 22 22 1
## p g1 a23 t24 0.5297473 1 23 24 23 23 1
## p g1 a24 t25 0.5297473 1 24 25 24 24 1
## p g1 a25 t26 0.5297473 1 25 26 25 25 1
## p g1 a26 t27 0.5297473 1 26 27 26 26 1
## p g1 a27 t28 0.5297473 1 27 28 27 27 1
## p g1 a28 t29 0.5297473 1 28 29 28 28 1
## p g1 a29 t30 0.5297473 1 29 30 29 29 1
## p g1 a30 t31 0.5297473 1 30 31 30 30 1
## p g1 a31 t32 0.5297473 1 31 32 31 31 1
## p g1 a32 t33 0.5297473 1 32 33 32 32 1
## p g1 a33 t34 0.5297473 1 33 34 33 33 1
## p g1 a34 t35 0.5297473 1 34 35 34 34 1
## p g1 a35 t36 0.5297473 1 35 36 35 35 1
## p g1 a36 t37 0.5297473 1 36 37 36 36 1
## p g1 a37 t38 0.5297473 1 37 38 37 37 1
## p g1 a38 t39 0.5297473 1 38 39 38 38 1
## p g1 a39 t40 0.5297473 1 39 40 39 39 1
## p g2 a0 t1 0.5297473 2 0 1 0 0 2
## p g2 a1 t2 0.5297473 2 1 2 1 1 2
## p g2 a2 t3 0.5297473 2 2 3 2 2 2
## p g2 a3 t4 0.5297473 2 3 4 3 3 2
## p g2 a4 t5 0.5297473 2 4 5 4 4 2
## p g2 a5 t6 0.5297473 2 5 6 5 5 2
## p g2 a6 t7 0.5297473 2 6 7 6 6 2
## p g2 a7 t8 0.5297473 2 7 8 7 7 2
## p g2 a8 t9 0.5297473 2 8 9 8 8 2
## p g2 a9 t10 0.5297473 2 9 10 9 9 2
## p g2 a10 t11 0.5297473 2 10 11 10 10 2
## p g2 a11 t12 0.5297473 2 11 12 11 11 2
## p g2 a12 t13 0.5297473 2 12 13 12 12 2
## p g2 a13 t14 0.5297473 2 13 14 13 13 2
## p g2 a14 t15 0.5297473 2 14 15 14 14 2
## p g2 a15 t16 0.5297473 2 15 16 15 15 2
## p g2 a16 t17 0.5297473 2 16 17 16 16 2
## p g2 a17 t18 0.5297473 2 17 18 17 17 2
## p g2 a18 t19 0.5297473 2 18 19 18 18 2
## p g2 a19 t20 0.5297473 2 19 20 19 19 2
## p g2 a20 t21 0.5297473 2 20 21 20 20 2
## p g2 a21 t22 0.5297473 2 21 22 21 21 2
## p g2 a22 t23 0.5297473 2 22 23 22 22 2
## p g2 a23 t24 0.5297473 2 23 24 23 23 2
## p g2 a24 t25 0.5297473 2 24 25 24 24 2
## p g2 a25 t26 0.5297473 2 25 26 25 25 2
## p g2 a26 t27 0.5297473 2 26 27 26 26 2
## p g2 a27 t28 0.5297473 2 27 28 27 27 2
## p g2 a28 t29 0.5297473 2 28 29 28 28 2
## p g2 a29 t30 0.5297473 2 29 30 29 29 2
## p g2 a30 t31 0.5297473 2 30 31 30 30 2
## p g2 a31 t32 0.5297473 2 31 32 31 31 2
## p g2 a32 t33 0.5297473 2 32 33 32 32 2
## p g2 a33 t34 0.5297473 2 33 34 33 33 2
## p g2 a34 t35 0.5297473 2 34 35 34 34 2
## p g2 a35 t36 0.5297473 2 35 36 35 35 2
## p g2 a36 t37 0.5297473 2 36 37 36 36 2
## p g2 a37 t38 0.5297473 2 37 38 37 37 2
## p g2 a38 t39 0.5297473 2 38 39 38 38 2
## p g2 a39 t40 0.5297473 2 39 40 39 39 2
## p g3 a0 t1 0.5297473 3 0 1 0 0 3
## p g3 a1 t2 0.5297473 3 1 2 1 1 3
## p g3 a2 t3 0.5297473 3 2 3 2 2 3
## p g3 a3 t4 0.5297473 3 3 4 3 3 3
## p g3 a4 t5 0.5297473 3 4 5 4 4 3
## p g3 a5 t6 0.5297473 3 5 6 5 5 3
## p g3 a6 t7 0.5297473 3 6 7 6 6 3
## p g3 a7 t8 0.5297473 3 7 8 7 7 3
## p g3 a8 t9 0.5297473 3 8 9 8 8 3
## p g3 a9 t10 0.5297473 3 9 10 9 9 3
## p g3 a10 t11 0.5297473 3 10 11 10 10 3
## p g3 a11 t12 0.5297473 3 11 12 11 11 3
## p g3 a12 t13 0.5297473 3 12 13 12 12 3
## p g3 a13 t14 0.5297473 3 13 14 13 13 3
## p g3 a14 t15 0.5297473 3 14 15 14 14 3
## p g3 a15 t16 0.5297473 3 15 16 15 15 3
## p g3 a16 t17 0.5297473 3 16 17 16 16 3
## p g3 a17 t18 0.5297473 3 17 18 17 17 3
## p g3 a18 t19 0.5297473 3 18 19 18 18 3
## p g3 a19 t20 0.5297473 3 19 20 19 19 3
## p g3 a20 t21 0.5297473 3 20 21 20 20 3
## p g3 a21 t22 0.5297473 3 21 22 21 21 3
## p g3 a22 t23 0.5297473 3 22 23 22 22 3
## p g3 a23 t24 0.5297473 3 23 24 23 23 3
## p g3 a24 t25 0.5297473 3 24 25 24 24 3
## p g3 a25 t26 0.5297473 3 25 26 25 25 3
## p g3 a26 t27 0.5297473 3 26 27 26 26 3
## p g3 a27 t28 0.5297473 3 27 28 27 27 3
## p g3 a28 t29 0.5297473 3 28 29 28 28 3
## p g3 a29 t30 0.5297473 3 29 30 29 29 3
## p g3 a30 t31 0.5297473 3 30 31 30 30 3
## p g3 a31 t32 0.5297473 3 31 32 31 31 3
## p g3 a32 t33 0.5297473 3 32 33 32 32 3
## p g3 a33 t34 0.5297473 3 33 34 33 33 3
## p g3 a34 t35 0.5297473 3 34 35 34 34 3
## p g3 a35 t36 0.5297473 3 35 36 35 35 3
## p g3 a36 t37 0.5297473 3 36 37 36 36 3
## p g3 a37 t38 0.5297473 3 37 38 37 37 3
## p g3 a38 t39 0.5297473 3 38 39 38 38 3
## p g3 a39 t40 0.5297473 3 39 40 39 39 3
## p g4 a0 t1 0.5297473 4 0 1 0 0 4
## p g4 a1 t2 0.5297473 4 1 2 1 1 4
## p g4 a2 t3 0.5297473 4 2 3 2 2 4
## p g4 a3 t4 0.5297473 4 3 4 3 3 4
## p g4 a4 t5 0.5297473 4 4 5 4 4 4
## p g4 a5 t6 0.5297473 4 5 6 5 5 4
## p g4 a6 t7 0.5297473 4 6 7 6 6 4
## p g4 a7 t8 0.5297473 4 7 8 7 7 4
## p g4 a8 t9 0.5297473 4 8 9 8 8 4
## p g4 a9 t10 0.5297473 4 9 10 9 9 4
## p g4 a10 t11 0.5297473 4 10 11 10 10 4
## p g4 a11 t12 0.5297473 4 11 12 11 11 4
## p g4 a12 t13 0.5297473 4 12 13 12 12 4
## p g4 a13 t14 0.5297473 4 13 14 13 13 4
## p g4 a14 t15 0.5297473 4 14 15 14 14 4
## p g4 a15 t16 0.5297473 4 15 16 15 15 4
## p g4 a16 t17 0.5297473 4 16 17 16 16 4
## p g4 a17 t18 0.5297473 4 17 18 17 17 4
## p g4 a18 t19 0.5297473 4 18 19 18 18 4
## p g4 a19 t20 0.5297473 4 19 20 19 19 4
## p g4 a20 t21 0.5297473 4 20 21 20 20 4
## p g4 a21 t22 0.5297473 4 21 22 21 21 4
## p g4 a22 t23 0.5297473 4 22 23 22 22 4
## p g4 a23 t24 0.5297473 4 23 24 23 23 4
## p g4 a24 t25 0.5297473 4 24 25 24 24 4
## p g4 a25 t26 0.5297473 4 25 26 25 25 4
## p g4 a26 t27 0.5297473 4 26 27 26 26 4
## p g4 a27 t28 0.5297473 4 27 28 27 27 4
## p g4 a28 t29 0.5297473 4 28 29 28 28 4
## p g4 a29 t30 0.5297473 4 29 30 29 29 4
## p g4 a30 t31 0.5297473 4 30 31 30 30 4
## p g4 a31 t32 0.5297473 4 31 32 31 31 4
## p g4 a32 t33 0.5297473 4 32 33 32 32 4
## p g4 a33 t34 0.5297473 4 33 34 33 33 4
## p g4 a34 t35 0.5297473 4 34 35 34 34 4
## p g4 a35 t36 0.5297473 4 35 36 35 35 4
## p g4 a36 t37 0.5297473 4 36 37 36 36 4
## p g4 a37 t38 0.5297473 4 37 38 37 37 4
## p g4 a38 t39 0.5297473 4 38 39 38 38 4
## p g4 a39 t40 0.5297473 4 39 40 39 39 4
## p g5 a0 t1 0.5297473 5 0 1 0 0 5
## p g5 a1 t2 0.5297473 5 1 2 1 1 5
## p g5 a2 t3 0.5297473 5 2 3 2 2 5
## p g5 a3 t4 0.5297473 5 3 4 3 3 5
## p g5 a4 t5 0.5297473 5 4 5 4 4 5
## p g5 a5 t6 0.5297473 5 5 6 5 5 5
## p g5 a6 t7 0.5297473 5 6 7 6 6 5
## p g5 a7 t8 0.5297473 5 7 8 7 7 5
## p g5 a8 t9 0.5297473 5 8 9 8 8 5
## p g5 a9 t10 0.5297473 5 9 10 9 9 5
## p g5 a10 t11 0.5297473 5 10 11 10 10 5
## p g5 a11 t12 0.5297473 5 11 12 11 11 5
## p g5 a12 t13 0.5297473 5 12 13 12 12 5
## p g5 a13 t14 0.5297473 5 13 14 13 13 5
## p g5 a14 t15 0.5297473 5 14 15 14 14 5
## p g5 a15 t16 0.5297473 5 15 16 15 15 5
## p g5 a16 t17 0.5297473 5 16 17 16 16 5
## p g5 a17 t18 0.5297473 5 17 18 17 17 5
## p g5 a18 t19 0.5297473 5 18 19 18 18 5
## p g5 a19 t20 0.5297473 5 19 20 19 19 5
## p g5 a20 t21 0.5297473 5 20 21 20 20 5
## p g5 a21 t22 0.5297473 5 21 22 21 21 5
## p g5 a22 t23 0.5297473 5 22 23 22 22 5
## p g5 a23 t24 0.5297473 5 23 24 23 23 5
## p g5 a24 t25 0.5297473 5 24 25 24 24 5
## p g5 a25 t26 0.5297473 5 25 26 25 25 5
## p g5 a26 t27 0.5297473 5 26 27 26 26 5
## p g5 a27 t28 0.5297473 5 27 28 27 27 5
## p g5 a28 t29 0.5297473 5 28 29 28 28 5
## p g5 a29 t30 0.5297473 5 29 30 29 29 5
## p g5 a30 t31 0.5297473 5 30 31 30 30 5
## p g5 a31 t32 0.5297473 5 31 32 31 31 5
## p g5 a32 t33 0.5297473 5 32 33 32 32 5
## p g5 a33 t34 0.5297473 5 33 34 33 33 5
## p g5 a34 t35 0.5297473 5 34 35 34 34 5
## p g5 a35 t36 0.5297473 5 35 36 35 35 5
## p g5 a36 t37 0.5297473 5 36 37 36 36 5
## p g5 a37 t38 0.5297473 5 37 38 37 37 5
## p g5 a38 t39 0.5297473 5 38 39 38 38 5
## p g5 a39 t40 0.5297473 5 39 40 39 39 5
# Derived parameters - estimated occupancy for each unit in years 2....
names(mod.fit$results$derived)
## [1] "Occupancy"
mod.fit$results$derived$Occupancy
## estimate se lcl ucl
## 1 0.6389202 0.06914951 0.4957995 0.7609989
## 2 0.6058006 0.06900974 0.4658775 0.7302893
## 3 0.5467046 0.06968245 0.4100510 0.6766642
## 4 0.5762671 0.06839883 0.4399037 0.7019265
## 5 0.5766903 0.06845351 0.4401868 0.7024113
cleanup(ask=FALSE)