# American Toad
# Extracted from
# Darryl I. MacKenzie, et al. 2002.
# Estimating site occupancy rates when detection probabilities are less than one.
# Ecology 83:2248-2255.
# doi:10.1890/0012-9658(2002)083[2248:ESORWD]2.0.CO;2]
# 29 sites with 82 sampling occasions in 2000.
# Volunteers visited sites and recorded presence/absence of toads by calls.
# Habitat (type of pond, permanent or ephemeral) and temperature at visit recorded.
# Single Species Single Season Occupancy
# Fitting models using RMark
# 2018-08-15 Code contributed by Carl James Schwarz (cschwarz.stat.sfu.cs@gmail.com)
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 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 <- readxl::read_excel("../AmericanToad.xls",
sheet="AmToadDetectionHistories",
na="-",
col_names=FALSE) # notice no column names in row 1 of data file.
head(input.data)
## # A tibble: 6 x 82
## X__1 X__2 X__3 X__4 X__5 X__6 X__7 X__8 X__9 X__10 X__11 X__12
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NA NA NA NA NA NA NA NA NA NA NA NA
## 2 NA NA NA NA NA 0 NA NA 0 NA NA NA
## 3 NA NA NA NA NA NA NA NA NA NA NA NA
## 4 NA NA NA 0 NA NA NA NA NA NA 0 NA
## 5 NA NA NA NA NA NA NA NA NA NA NA NA
## 6 NA NA NA NA NA NA NA NA NA NA NA NA
## # ... with 70 more variables: X__13 <dbl>, X__14 <dbl>, X__15 <dbl>, X__16
## # <dbl>, X__17 <dbl>, X__18 <dbl>, X__19 <dbl>, X__20 <dbl>, X__21
## # <dbl>, X__22 <dbl>, X__23 <dbl>, X__24 <dbl>, X__25 <dbl>, X__26
## # <dbl>, X__27 <dbl>, X__28 <dbl>, X__29 <dbl>, X__30 <dbl>, X__31
## # <dbl>, X__32 <dbl>, X__33 <dbl>, X__34 <dbl>, X__35 <dbl>, X__36
## # <dbl>, X__37 <dbl>, X__38 <dbl>, X__39 <dbl>, X__40 <dbl>, X__41
## # <dbl>, X__42 <dbl>, X__43 <dbl>, X__44 <dbl>, X__45 <dbl>, X__46
## # <dbl>, X__47 <dbl>, X__48 <dbl>, X__49 <dbl>, X__50 <dbl>, X__51
## # <dbl>, X__52 <dbl>, X__53 <dbl>, X__54 <dbl>, X__55 <dbl>, X__56
## # <dbl>, X__57 <dbl>, X__58 <dbl>, X__59 <dbl>, X__60 <dbl>, X__61
## # <dbl>, X__62 <dbl>, X__63 <dbl>, X__64 <dbl>, X__65 <dbl>, X__66
## # <dbl>, X__67 <dbl>, X__68 <dbl>, X__69 <dbl>, X__70 <dbl>, X__71
## # <dbl>, X__72 <dbl>, X__73 <dbl>, X__74 <dbl>, X__75 <dbl>, X__76
## # <dbl>, X__77 <dbl>, X__78 <dbl>, X__79 <dbl>, X__80 <dbl>, X__81
## # <dbl>, X__82 <dbl>
# Extract the history records
# 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
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1
## ch
## 1 NANANANANANANANANANANANANANANANANANANANANA0NANANA0NANANANANANANANANANANANANANANANANA0NANANA0NANANANANANANANANANANA0NANANANANANANANANANANANANANANANA0NANANANANA
## 2 NANANANANA0NANA0NANANANANANANANANANANANANA1NANANANANANANANANANANANANANANANANANANANANANANANANANANA0NANANANANANANANANANANANANANANANANANANANANANANANANA0NANANANANA
## 3 NANANANANANANANANANANANANANANANANANANANANANANA0NANANANANANANANANANANANANANANANANANANA0NANANA0NANANANANANANANANANANA0NANANANANANANANANANANANANANANANA0NANANANANA
## 4 NANANA0NANANANANANA0NANANANANANA1NANANANANANA1NANANANANANA0NANANA0NANANANANANANANA0NANANANANANA0NANANANANANANA0NANANA0NANANANANANANANA0NANANANA0NANANANA
## 5 NANANANANANANANANANANANANANANANANA0NANANANANANANANANANANANANANA0NANANANANANANANANANANANA0NANANANANANA0NANANANANANANANANANANANANA00NANANANANANANANANANANANANANA
## 6 NANANANANANANANANANANANANANANANANANANANANANANANANA1NANANANANANANANANANANANANANANANANANANANANANA0NANANANANANANANANANANANANANANANANANANANANANANANANANA0NANANANANANA
# Change any NA to . in the chapter history
input.history$ch <- gsub("NA",".", input.history$ch, fixed=TRUE)
head(input.history)
## freq
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1
## ch
## 1 .....................0...0.................0...0...........0................0.....
## 2 .....0..0.............1...........................0.........................0.....
## 3 .......................0...................0...0...........0................0.....
## 4 ...0......0......1......1......0...0........0......0.......0...0........0....0....
## 5 .................0..............0............0......0.............00..............
## 6 .........................1......................0..........................0......
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.history)
## [1] 29
# Get the pond information
pond.data <- readxl::read_excel("../AmericanToad.xls",
sheet="Pond",
na="-",
col_names=TRUE)
head(pond.data)
## # A tibble: 6 x 1
## Pond
## <dbl>
## 1 1.00
## 2 1.00
## 3 1.00
## 4 1.00
## 5 0
## 6 0
input.history$Pond <- as.factor(car::recode(pond.data$Pond,
"1='P'; 0='E'; " ))
head(input.history)
## freq
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1
## ch
## 1 .....................0...0.................0...0...........0................0.....
## 2 .....0..0.............1...........................0.........................0.....
## 3 .......................0...................0...0...........0................0.....
## 4 ...0......0......1......1......0...0........0......0.......0...0........0....0....
## 5 .................0..............0............0......0.............00..............
## 6 .........................1......................0..........................0......
## Pond
## 1 P
## 2 P
## 3 P
## 4 P
## 5 E
## 6 E
# Get the temperature data
temp.data <- readxl::read_excel("../AmericanToad.xls",
sheet="AmToadTemperature",
na="-",
col_names=FALSE) # notice no column names in row 1 of data file.
head(temp.data)
## # A tibble: 6 x 82
## X__1 X__2 X__3 X__4 X__5 X__6 X__7 X__8 X__9 X__10 X__11 X__12
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 7.00 0 0 3.00 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 3.00 0 0 0 0 0 0 6.00 0
## 5 0 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0 0 0
## # ... with 70 more variables: X__13 <dbl>, X__14 <dbl>, X__15 <dbl>, X__16
## # <dbl>, X__17 <dbl>, X__18 <dbl>, X__19 <dbl>, X__20 <dbl>, X__21
## # <dbl>, X__22 <dbl>, X__23 <dbl>, X__24 <dbl>, X__25 <dbl>, X__26
## # <dbl>, X__27 <dbl>, X__28 <dbl>, X__29 <dbl>, X__30 <dbl>, X__31
## # <dbl>, X__32 <dbl>, X__33 <dbl>, X__34 <dbl>, X__35 <dbl>, X__36
## # <dbl>, X__37 <dbl>, X__38 <dbl>, X__39 <dbl>, X__40 <dbl>, X__41
## # <dbl>, X__42 <dbl>, X__43 <dbl>, X__44 <dbl>, X__45 <dbl>, X__46
## # <dbl>, X__47 <dbl>, X__48 <dbl>, X__49 <dbl>, X__50 <dbl>, X__51
## # <dbl>, X__52 <dbl>, X__53 <dbl>, X__54 <dbl>, X__55 <dbl>, X__56
## # <dbl>, X__57 <dbl>, X__58 <dbl>, X__59 <dbl>, X__60 <dbl>, X__61
## # <dbl>, X__62 <dbl>, X__63 <dbl>, X__64 <dbl>, X__65 <dbl>, X__66
## # <dbl>, X__67 <dbl>, X__68 <dbl>, X__69 <dbl>, X__70 <dbl>, X__71
## # <dbl>, X__72 <dbl>, X__73 <dbl>, X__74 <dbl>, X__75 <dbl>, X__76
## # <dbl>, X__77 <dbl>, X__78 <dbl>, X__79 <dbl>, X__80 <dbl>, X__81
## # <dbl>, X__82 <dbl>
# Notice that RMark does not allow missing values in time-varying covariates, even when visits are not made
# so do not set these to missing as in RPresence
# temp.data[ is.na(input.data)] <- NA
colnames(temp.data) = paste("Temp", 1:ncol(temp.data), sep="") # assign the observer at each time point
head(temp.data)
## # A tibble: 6 x 82
## Temp1 Temp2 Temp3 Temp4 Temp5 Temp6 Temp7 Temp8 Temp9 Temp10 Temp~ Temp~
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 7.00 0 0 3.00 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 3.00 0 0 0 0 0 0 6.00 0
## 5 0 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0 0 0
## # ... with 70 more variables: Temp13 <dbl>, Temp14 <dbl>, Temp15 <dbl>,
## # Temp16 <dbl>, Temp17 <dbl>, Temp18 <dbl>, Temp19 <dbl>, Temp20 <dbl>,
## # Temp21 <dbl>, Temp22 <dbl>, Temp23 <dbl>, Temp24 <dbl>, Temp25 <dbl>,
## # Temp26 <dbl>, Temp27 <dbl>, Temp28 <dbl>, Temp29 <dbl>, Temp30 <dbl>,
## # Temp31 <dbl>, Temp32 <dbl>, Temp33 <dbl>, Temp34 <dbl>, Temp35 <dbl>,
## # Temp36 <dbl>, Temp37 <dbl>, Temp38 <dbl>, Temp39 <dbl>, Temp40 <dbl>,
## # Temp41 <dbl>, Temp42 <dbl>, Temp43 <dbl>, Temp44 <dbl>, Temp45 <dbl>,
## # Temp46 <dbl>, Temp47 <dbl>, Temp48 <dbl>, Temp49 <dbl>, Temp50 <dbl>,
## # Temp51 <dbl>, Temp52 <dbl>, Temp53 <dbl>, Temp54 <dbl>, Temp55 <dbl>,
## # Temp56 <dbl>, Temp57 <dbl>, Temp58 <dbl>, Temp59 <dbl>, Temp60 <dbl>,
## # Temp61 <dbl>, Temp62 <dbl>, Temp63 <dbl>, Temp64 <dbl>, Temp65 <dbl>,
## # Temp66 <dbl>, Temp67 <dbl>, Temp68 <dbl>, Temp69 <dbl>, Temp70 <dbl>,
## # Temp71 <dbl>, Temp72 <dbl>, Temp73 <dbl>, Temp74 <dbl>, Temp75 <dbl>,
## # Temp76 <dbl>, Temp77 <dbl>, Temp78 <dbl>, Temp79 <dbl>, Temp80 <dbl>,
## # Temp81 <dbl>, Temp82 <dbl>
input.history <- cbind(input.history, temp.data)
head(input.history)
## freq
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1
## ch
## 1 .....................0...0.................0...0...........0................0.....
## 2 .....0..0.............1...........................0.........................0.....
## 3 .......................0...................0...0...........0................0.....
## 4 ...0......0......1......1......0...0........0......0.......0...0........0....0....
## 5 .................0..............0............0......0.............00..............
## 6 .........................1......................0..........................0......
## Pond Temp1 Temp2 Temp3 Temp4 Temp5 Temp6 Temp7 Temp8 Temp9 Temp10 Temp11
## 1 P 0 0 0 0 0 0 0 0 0 0 0
## 2 P 0 0 0 0 0 7 0 0 3 0 0
## 3 P 0 0 0 0 0 0 0 0 0 0 0
## 4 P 0 0 0 3 0 0 0 0 0 0 6
## 5 E 0 0 0 0 0 0 0 0 0 0 0
## 6 E 0 0 0 0 0 0 0 0 0 0 0
## Temp12 Temp13 Temp14 Temp15 Temp16 Temp17 Temp18 Temp19 Temp20 Temp21
## 1 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 10 0 0 0
## 5 0 0 0 0 0 0 14 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0
## Temp22 Temp23 Temp24 Temp25 Temp26 Temp27 Temp28 Temp29 Temp30 Temp31
## 1 13 0 0 0 15 0 0 0 0 0
## 2 0 5 0 0 0 0 0 0 0 0
## 3 0 0 16 0 0 0 0 0 0 0
## 4 0 0 0 15 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 18 0 0 0 0 0
## Temp32 Temp33 Temp34 Temp35 Temp36 Temp37 Temp38 Temp39 Temp40 Temp41
## 1 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0
## 4 6 0 0 0 7 0 0 0 0 0
## 5 0 13 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0
## Temp42 Temp43 Temp44 Temp45 Temp46 Temp47 Temp48 Temp49 Temp50 Temp51
## 1 0 0 5 0 0 0 8 0 0 0
## 2 0 0 0 0 0 0 0 0 0 12
## 3 0 0 16 0 0 0 8 0 0 0
## 4 0 0 0 12 0 0 0 0 0 0
## 5 0 0 0 0 10 0 0 0 0 0
## 6 0 0 0 0 0 0 0 7 0 0
## Temp52 Temp53 Temp54 Temp55 Temp56 Temp57 Temp58 Temp59 Temp60 Temp61
## 1 0 0 0 0 0 0 0 0 27 0
## 2 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 27 0
## 4 11 0 0 0 0 0 0 0 23 0
## 5 0 12 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0
## Temp62 Temp63 Temp64 Temp65 Temp66 Temp67 Temp68 Temp69 Temp70 Temp71
## 1 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0
## 4 0 0 19 0 0 0 0 0 0 0
## 5 0 0 0 0 0 14 10 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0
## Temp72 Temp73 Temp74 Temp75 Temp76 Temp77 Temp78 Temp79 Temp80 Temp81
## 1 0 0 0 0 0 18 0 0 0 0
## 2 0 0 0 0 0 16 0 0 0 0
## 3 0 0 0 0 0 18 0 0 0 0
## 4 0 14 0 0 0 0 18 0 0 0
## 5 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 15 0 0 0 0 0
## Temp82
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
# Illustration of using categorical covariate in the modelling process by creating groups
amtoad.data <- process.data(data=input.history, group="Pond",
model="Occupancy")
summary(amtoad.data)
## Length Class Mode
## data 86 data.frame list
## model 1 -none- character
## mixtures 1 -none- numeric
## freq 2 data.frame list
## nocc 1 -none- numeric
## nocc.secondary 0 -none- NULL
## time.intervals 82 -none- numeric
## begin.time 1 -none- numeric
## age.unit 1 -none- numeric
## initial.ages 2 -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
# If survey covariates are present, modify the ddl
amtoad.ddl <- make.design.data(amtoad.data)
amtoad.ddl
## $p
## par.index model.index group age time Age Time Pond
## 1 1 1 E 0 1 0 0 E
## 2 2 2 E 1 2 1 1 E
## 3 3 3 E 2 3 2 2 E
## 4 4 4 E 3 4 3 3 E
## 5 5 5 E 4 5 4 4 E
## 6 6 6 E 5 6 5 5 E
## 7 7 7 E 6 7 6 6 E
## 8 8 8 E 7 8 7 7 E
## 9 9 9 E 8 9 8 8 E
## 10 10 10 E 9 10 9 9 E
## 11 11 11 E 10 11 10 10 E
## 12 12 12 E 11 12 11 11 E
## 13 13 13 E 12 13 12 12 E
## 14 14 14 E 13 14 13 13 E
## 15 15 15 E 14 15 14 14 E
## 16 16 16 E 15 16 15 15 E
## 17 17 17 E 16 17 16 16 E
## 18 18 18 E 17 18 17 17 E
## 19 19 19 E 18 19 18 18 E
## 20 20 20 E 19 20 19 19 E
## 21 21 21 E 20 21 20 20 E
## 22 22 22 E 21 22 21 21 E
## 23 23 23 E 22 23 22 22 E
## 24 24 24 E 23 24 23 23 E
## 25 25 25 E 24 25 24 24 E
## 26 26 26 E 25 26 25 25 E
## 27 27 27 E 26 27 26 26 E
## 28 28 28 E 27 28 27 27 E
## 29 29 29 E 28 29 28 28 E
## 30 30 30 E 29 30 29 29 E
## 31 31 31 E 30 31 30 30 E
## 32 32 32 E 31 32 31 31 E
## 33 33 33 E 32 33 32 32 E
## 34 34 34 E 33 34 33 33 E
## 35 35 35 E 34 35 34 34 E
## 36 36 36 E 35 36 35 35 E
## 37 37 37 E 36 37 36 36 E
## 38 38 38 E 37 38 37 37 E
## 39 39 39 E 38 39 38 38 E
## 40 40 40 E 39 40 39 39 E
## 41 41 41 E 40 41 40 40 E
## 42 42 42 E 41 42 41 41 E
## 43 43 43 E 42 43 42 42 E
## 44 44 44 E 43 44 43 43 E
## 45 45 45 E 44 45 44 44 E
## 46 46 46 E 45 46 45 45 E
## 47 47 47 E 46 47 46 46 E
## 48 48 48 E 47 48 47 47 E
## 49 49 49 E 48 49 48 48 E
## 50 50 50 E 49 50 49 49 E
## 51 51 51 E 50 51 50 50 E
## 52 52 52 E 51 52 51 51 E
## 53 53 53 E 52 53 52 52 E
## 54 54 54 E 53 54 53 53 E
## 55 55 55 E 54 55 54 54 E
## 56 56 56 E 55 56 55 55 E
## 57 57 57 E 56 57 56 56 E
## 58 58 58 E 57 58 57 57 E
## 59 59 59 E 58 59 58 58 E
## 60 60 60 E 59 60 59 59 E
## 61 61 61 E 60 61 60 60 E
## 62 62 62 E 61 62 61 61 E
## 63 63 63 E 62 63 62 62 E
## 64 64 64 E 63 64 63 63 E
## 65 65 65 E 64 65 64 64 E
## 66 66 66 E 65 66 65 65 E
## 67 67 67 E 66 67 66 66 E
## 68 68 68 E 67 68 67 67 E
## 69 69 69 E 68 69 68 68 E
## 70 70 70 E 69 70 69 69 E
## 71 71 71 E 70 71 70 70 E
## 72 72 72 E 71 72 71 71 E
## 73 73 73 E 72 73 72 72 E
## 74 74 74 E 73 74 73 73 E
## 75 75 75 E 74 75 74 74 E
## 76 76 76 E 75 76 75 75 E
## 77 77 77 E 76 77 76 76 E
## 78 78 78 E 77 78 77 77 E
## 79 79 79 E 78 79 78 78 E
## 80 80 80 E 79 80 79 79 E
## 81 81 81 E 80 81 80 80 E
## 82 82 82 E 81 82 81 81 E
## 83 83 83 P 0 1 0 0 P
## 84 84 84 P 1 2 1 1 P
## 85 85 85 P 2 3 2 2 P
## 86 86 86 P 3 4 3 3 P
## 87 87 87 P 4 5 4 4 P
## 88 88 88 P 5 6 5 5 P
## 89 89 89 P 6 7 6 6 P
## 90 90 90 P 7 8 7 7 P
## 91 91 91 P 8 9 8 8 P
## 92 92 92 P 9 10 9 9 P
## 93 93 93 P 10 11 10 10 P
## 94 94 94 P 11 12 11 11 P
## 95 95 95 P 12 13 12 12 P
## 96 96 96 P 13 14 13 13 P
## 97 97 97 P 14 15 14 14 P
## 98 98 98 P 15 16 15 15 P
## 99 99 99 P 16 17 16 16 P
## 100 100 100 P 17 18 17 17 P
## 101 101 101 P 18 19 18 18 P
## 102 102 102 P 19 20 19 19 P
## 103 103 103 P 20 21 20 20 P
## 104 104 104 P 21 22 21 21 P
## 105 105 105 P 22 23 22 22 P
## 106 106 106 P 23 24 23 23 P
## 107 107 107 P 24 25 24 24 P
## 108 108 108 P 25 26 25 25 P
## 109 109 109 P 26 27 26 26 P
## 110 110 110 P 27 28 27 27 P
## 111 111 111 P 28 29 28 28 P
## 112 112 112 P 29 30 29 29 P
## 113 113 113 P 30 31 30 30 P
## 114 114 114 P 31 32 31 31 P
## 115 115 115 P 32 33 32 32 P
## 116 116 116 P 33 34 33 33 P
## 117 117 117 P 34 35 34 34 P
## 118 118 118 P 35 36 35 35 P
## 119 119 119 P 36 37 36 36 P
## 120 120 120 P 37 38 37 37 P
## 121 121 121 P 38 39 38 38 P
## 122 122 122 P 39 40 39 39 P
## 123 123 123 P 40 41 40 40 P
## 124 124 124 P 41 42 41 41 P
## 125 125 125 P 42 43 42 42 P
## 126 126 126 P 43 44 43 43 P
## 127 127 127 P 44 45 44 44 P
## 128 128 128 P 45 46 45 45 P
## 129 129 129 P 46 47 46 46 P
## 130 130 130 P 47 48 47 47 P
## 131 131 131 P 48 49 48 48 P
## 132 132 132 P 49 50 49 49 P
## 133 133 133 P 50 51 50 50 P
## 134 134 134 P 51 52 51 51 P
## 135 135 135 P 52 53 52 52 P
## 136 136 136 P 53 54 53 53 P
## 137 137 137 P 54 55 54 54 P
## 138 138 138 P 55 56 55 55 P
## 139 139 139 P 56 57 56 56 P
## 140 140 140 P 57 58 57 57 P
## 141 141 141 P 58 59 58 58 P
## 142 142 142 P 59 60 59 59 P
## 143 143 143 P 60 61 60 60 P
## 144 144 144 P 61 62 61 61 P
## 145 145 145 P 62 63 62 62 P
## 146 146 146 P 63 64 63 63 P
## 147 147 147 P 64 65 64 64 P
## 148 148 148 P 65 66 65 65 P
## 149 149 149 P 66 67 66 66 P
## 150 150 150 P 67 68 67 67 P
## 151 151 151 P 68 69 68 68 P
## 152 152 152 P 69 70 69 69 P
## 153 153 153 P 70 71 70 70 P
## 154 154 154 P 71 72 71 71 P
## 155 155 155 P 72 73 72 72 P
## 156 156 156 P 73 74 73 73 P
## 157 157 157 P 74 75 74 74 P
## 158 158 158 P 75 76 75 75 P
## 159 159 159 P 76 77 76 76 P
## 160 160 160 P 77 78 77 77 P
## 161 161 161 P 78 79 78 78 P
## 162 162 162 P 79 80 79 79 P
## 163 163 163 P 80 81 80 80 P
## 164 164 164 P 81 82 81 81 P
##
## $Psi
## par.index model.index group age time Age Time Pond
## 1 1 165 E 0 1 0 0 E
## 2 2 166 P 0 1 0 0 P
##
## $pimtypes
## $pimtypes$p
## $pimtypes$p$pim.type
## [1] "all"
##
##
## $pimtypes$Psi
## $pimtypes$Psi$pim.type
## [1] "all"
# What are the parameter names for Single Season Single Species models
setup.parameters("Occupancy", check=TRUE)
## [1] "p" "Psi"
# Fit a model
# Notice that RMark does not allow missing values in time-varying covariates, even when visits are not made
# Note that formula have an equal sign
mod.fit <- RMark::mark(amtoad.data, ddl=amtoad.ddl,
model="Occupancy",
model.parameters=list(
Psi =list(formula=~Pond),
p =list(formula=~Temp) # need to specify rest of obsevers after the intercept
)
)
##
## Output summary for Occupancy model
## Name : p(~Temp)Psi(~Pond)
##
## Npar : 4
## -2lnL: 175.1601
## AICc : 184.8268
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -2.2312206 0.5558228 -3.320633 -1.1418078
## p:Temp 0.0507852 0.0322792 -0.012482 0.1140524
## Psi:(Intercept) -0.5661261 0.6207633 -1.782822 0.6505701
## Psi:PondP 1.8948084 1.5894671 -1.220547 5.0101639
##
##
## Real Parameter p
## 1 2 3 4 5 6
## Group:PondE 0.1072501 0.0988377 0.0983708 0.0994634 0.0983708 0.1024836
## Group:PondP 0.1072501 0.0988377 0.0983708 0.0994634 0.0983708 0.1024836
## 7 8 9 10 11 12
## Group:PondE 0.1080914 0.0996204 0.101043 0.0975969 0.1012022 0.0979058
## Group:PondP 0.1080914 0.0996204 0.101043 0.0975969 0.1012022 0.0979058
## 13 14 15 16 17 18
## Group:PondE 0.0975969 0.0989938 0.1024836 0.1054196 0.1065813 0.1007253
## Group:PondP 0.0975969 0.0989938 0.1024836 0.1054196 0.1065813 0.1007253
## 19 20 21 22 23 24
## Group:PondE 0.0997775 0.1013616 0.1021619 0.1049252 0.1059161 0.1074179
## Group:PondP 0.0997775 0.1013616 0.1021619 0.1049252 0.1059161 0.1074179
## 25 26 27 28 29 30
## Group:PondE 0.1064146 0.1153893 0.1037795 0.1029679 0.1031298 0.1021619
## Group:PondP 0.1064146 0.1153893 0.1037795 0.1029679 0.1031298 0.1021619
## 31 32 33 34 35 36
## Group:PondE 0.0985262 0.0991501 0.106082 0.1004085 0.0989938 0.1013616
## Group:PondP 0.0985262 0.0991501 0.106082 0.1004085 0.0989938 0.1013616
## 37 38 39 40 41 42
## Group:PondE 0.0985262 0.1023227 0.1074179 0.1002504 0.1042691 0.1023227
## Group:PondP 0.0985262 0.1023227 0.1074179 0.1002504 0.1042691 0.1023227
## 43 44 45 46 47 48
## Group:PondE 0.1045967 0.1039425 0.0988377 0.1021619 0.1069152 0.1032918
## Group:PondP 0.1045967 0.1039425 0.0988377 0.1021619 0.1069152 0.1032918
## 49 50 51 52 53 54
## Group:PondE 0.106082 0.1013616 0.1054196 0.1082603 0.1079227 0.0997775
## Group:PondP 0.106082 0.1013616 0.1054196 0.1082603 0.1079227 0.0997775
## 55 56 57 58 59 60
## Group:PondE 0.1024836 0.1062482 0.1042691 0.1069152 0.1047608 0.1229231
## Group:PondP 0.1024836 0.1062482 0.1042691 0.1069152 0.1047608 0.1229231
## 61 62 63 64 65 66
## Group:PondE 0.1085989 0.1136138 0.1057504 0.1065813 0.125015 0.1004085
## Group:PondP 0.1085989 0.1136138 0.1057504 0.1065813 0.125015 0.1004085
## 67 68 69 70 71 72
## Group:PondE 0.1020014 0.1069152 0.1018411 0.1037795 0.1074179 0.1041057
## Group:PondP 0.1020014 0.1069152 0.1018411 0.1037795 0.1074179 0.1041057
## 73 74 75 76 77 78
## Group:PondE 0.0991501 0.1018411 0.1018411 0.1080914 0.125976 0.1115146
## Group:PondP 0.0991501 0.1018411 0.1018411 0.1080914 0.125976 0.1115146
## 79 80 81 82
## Group:PondE 0.1026448 0.0991501 0.1045967 0.1057504
## Group:PondP 0.1026448 0.0991501 0.1045967 0.1057504
##
##
## Real Parameter Psi
## 1
## Group:PondE 0.3621312
## Group:PondP 0.7906226
summary(mod.fit)
## Output summary for Occupancy model
## Name : p(~Temp)Psi(~Pond)
##
## Npar : 4
## -2lnL: 175.1601
## AICc : 184.8268
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -2.2312206 0.5558228 -3.320633 -1.1418078
## p:Temp 0.0507852 0.0322792 -0.012482 0.1140524
## Psi:(Intercept) -0.5661261 0.6207633 -1.782822 0.6505701
## Psi:PondP 1.8948084 1.5894671 -1.220547 5.0101639
##
##
## Real Parameter p
## 1 2 3 4 5 6
## Group:PondE 0.1072501 0.0988377 0.0983708 0.0994634 0.0983708 0.1024836
## Group:PondP 0.1072501 0.0988377 0.0983708 0.0994634 0.0983708 0.1024836
## 7 8 9 10 11 12
## Group:PondE 0.1080914 0.0996204 0.101043 0.0975969 0.1012022 0.0979058
## Group:PondP 0.1080914 0.0996204 0.101043 0.0975969 0.1012022 0.0979058
## 13 14 15 16 17 18
## Group:PondE 0.0975969 0.0989938 0.1024836 0.1054196 0.1065813 0.1007253
## Group:PondP 0.0975969 0.0989938 0.1024836 0.1054196 0.1065813 0.1007253
## 19 20 21 22 23 24
## Group:PondE 0.0997775 0.1013616 0.1021619 0.1049252 0.1059161 0.1074179
## Group:PondP 0.0997775 0.1013616 0.1021619 0.1049252 0.1059161 0.1074179
## 25 26 27 28 29 30
## Group:PondE 0.1064146 0.1153893 0.1037795 0.1029679 0.1031298 0.1021619
## Group:PondP 0.1064146 0.1153893 0.1037795 0.1029679 0.1031298 0.1021619
## 31 32 33 34 35 36
## Group:PondE 0.0985262 0.0991501 0.106082 0.1004085 0.0989938 0.1013616
## Group:PondP 0.0985262 0.0991501 0.106082 0.1004085 0.0989938 0.1013616
## 37 38 39 40 41 42
## Group:PondE 0.0985262 0.1023227 0.1074179 0.1002504 0.1042691 0.1023227
## Group:PondP 0.0985262 0.1023227 0.1074179 0.1002504 0.1042691 0.1023227
## 43 44 45 46 47 48
## Group:PondE 0.1045967 0.1039425 0.0988377 0.1021619 0.1069152 0.1032918
## Group:PondP 0.1045967 0.1039425 0.0988377 0.1021619 0.1069152 0.1032918
## 49 50 51 52 53 54
## Group:PondE 0.106082 0.1013616 0.1054196 0.1082603 0.1079227 0.0997775
## Group:PondP 0.106082 0.1013616 0.1054196 0.1082603 0.1079227 0.0997775
## 55 56 57 58 59 60
## Group:PondE 0.1024836 0.1062482 0.1042691 0.1069152 0.1047608 0.1229231
## Group:PondP 0.1024836 0.1062482 0.1042691 0.1069152 0.1047608 0.1229231
## 61 62 63 64 65 66
## Group:PondE 0.1085989 0.1136138 0.1057504 0.1065813 0.125015 0.1004085
## Group:PondP 0.1085989 0.1136138 0.1057504 0.1065813 0.125015 0.1004085
## 67 68 69 70 71 72
## Group:PondE 0.1020014 0.1069152 0.1018411 0.1037795 0.1074179 0.1041057
## Group:PondP 0.1020014 0.1069152 0.1018411 0.1037795 0.1074179 0.1041057
## 73 74 75 76 77 78
## Group:PondE 0.0991501 0.1018411 0.1018411 0.1080914 0.125976 0.1115146
## Group:PondP 0.0991501 0.1018411 0.1018411 0.1080914 0.125976 0.1115146
## 79 80 81 82
## Group:PondE 0.1026448 0.0991501 0.1045967 0.1057504
## Group:PondP 0.1026448 0.0991501 0.1045967 0.1057504
##
##
## Real Parameter Psi
## 1
## Group:PondE 0.3621312
## Group:PondP 0.7906226
# Look the objects returned in more details
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"
# look at estimates on beta and original scale
mod.fit$results$beta # on the logit scale
## estimate se lcl ucl
## p:(Intercept) -2.2312206 0.5558228 -3.320633 -1.1418078
## p:Temp 0.0507852 0.0322792 -0.012482 0.1140524
## Psi:(Intercept) -0.5661261 0.6207633 -1.782822 0.6505701
## Psi:PondP 1.8948084 1.5894671 -1.220547 5.0101639
mod.fit$results$real# on the regular 0-1 scale for each site
## estimate se lcl ucl fixed note
## p gE a0 t1 0.1072501 0.0471317 0.0437740 0.2396986
## p gE a1 t2 0.0988377 0.0484319 0.0364047 0.2415061
## p gE a2 t3 0.0983708 0.0484951 0.0360155 0.2416247
## p gE a3 t4 0.0994634 0.0483457 0.0369297 0.2413503
## p gE a4 t5 0.0983708 0.0484951 0.0360155 0.2416247
## p gE a5 t6 0.1024836 0.0479046 0.0395165 0.2406464
## p gE a6 t7 0.1080914 0.0469865 0.0445471 0.2395522
## p gE a7 t8 0.0996204 0.0483237 0.0370619 0.2413118
## p gE a8 t9 0.1010430 0.0481200 0.0382717 0.2409722
## p gE a9 t10 0.0975969 0.0485975 0.0353750 0.2418253
## p gE a10 t11 0.1012022 0.0480966 0.0384083 0.2409353
## p gE a11 t12 0.0979058 0.0485570 0.0356300 0.2417446
## p gE a12 t13 0.0975969 0.0485975 0.0353750 0.2418253
## p gE a13 t14 0.0989938 0.0484106 0.0365353 0.2414669
## p gE a14 t15 0.1024836 0.0479046 0.0395165 0.2406464
## p gE a15 t16 0.1054196 0.0474390 0.0421141 0.2400389
## p gE a16 t17 0.1065813 0.0472454 0.0431640 0.2398195
## p gE a17 t18 0.1007253 0.0481663 0.0379999 0.2410465
## p gE a18 t19 0.0997775 0.0483017 0.0371946 0.2412734
## p gE a19 t20 0.1013616 0.0480731 0.0385453 0.2408986
## p gE a20 t21 0.1021619 0.0479534 0.0392368 0.2407176
## p gE a21 t22 0.1049252 0.0475198 0.0416710 0.2401359
## p gE a22 t23 0.1059161 0.0473569 0.0425613 0.2399437
## p gE a23 t24 0.1074179 0.0471030 0.0439277 0.2396689
## p gE a24 t25 0.1064146 0.0472735 0.0430126 0.2398502
## p gE a25 t26 0.1153893 0.0456313 0.0515132 0.2385509
## p gE a26 t27 0.1037795 0.0477033 0.0406531 0.2403689
## p gE a27 t28 0.1029679 0.0478302 0.0399394 0.2405410
## p gE a28 t29 0.1031298 0.0478051 0.0400812 0.2405062
## p gE a29 t30 0.1021619 0.0479534 0.0392368 0.2407176
## p gE a30 t31 0.0985262 0.0484742 0.0361448 0.2415850
## p gE a31 t32 0.0991501 0.0483891 0.0366664 0.2414279
## p gE a32 t33 0.1060820 0.0473292 0.0427113 0.2399123
## p gE a33 t34 0.1004085 0.0482120 0.0377297 0.2411214
## p gE a34 t35 0.0989938 0.0484106 0.0365353 0.2414669
## p gE a35 t36 0.1013616 0.0480731 0.0385453 0.2408986
## p gE a36 t37 0.0985262 0.0484742 0.0361448 0.2415850
## p gE a37 t38 0.1023227 0.0479291 0.0393765 0.2406819
## p gE a38 t39 0.1074179 0.0471030 0.0439277 0.2396689
## p gE a39 t40 0.1002504 0.0482346 0.0375953 0.2411592
## p gE a40 t41 0.1042691 0.0476255 0.0410866 0.2402679
## p gE a41 t42 0.1023227 0.0479291 0.0393765 0.2406819
## p gE a42 t43 0.1045967 0.0475729 0.0413779 0.2402015
## p gE a43 t44 0.1039425 0.0476775 0.0407971 0.2403351
## p gE a44 t45 0.0988377 0.0484319 0.0364047 0.2415061
## p gE a45 t46 0.1021619 0.0479534 0.0392368 0.2407176
## p gE a46 t47 0.1069152 0.0471889 0.0434681 0.2397586
## p gE a47 t48 0.1032918 0.0477799 0.0402235 0.2404716
## p gE a48 t49 0.1060820 0.0473292 0.0427113 0.2399123
## p gE a49 t50 0.1013616 0.0480731 0.0385453 0.2408986
## p gE a50 t51 0.1054196 0.0474390 0.0421141 0.2400389
## p gE a51 t52 0.1082603 0.0469570 0.0447032 0.2395236
## p gE a52 t53 0.1079227 0.0470158 0.0443916 0.2395811
## p gE a53 t54 0.0997775 0.0483017 0.0371946 0.2412734
## p gE a54 t55 0.1024836 0.0479046 0.0395165 0.2406464
## p gE a55 t56 0.1062482 0.0473014 0.0428617 0.2398812
## p gE a56 t57 0.1042691 0.0476255 0.0410866 0.2402679
## p gE a57 t58 0.1069152 0.0471889 0.0434681 0.2397586
## p gE a58 t59 0.1047608 0.0475464 0.0415242 0.2401686
## p gE a59 t60 0.1229231 0.0440937 0.0591535 0.2380449
## p gE a60 t61 0.1085989 0.0468976 0.0450166 0.2394669
## p gE a61 t62 0.1136138 0.0459752 0.0497768 0.2387495
## p gE a62 t63 0.1057504 0.0473844 0.0424118 0.2399752
## p gE a63 t64 0.1065813 0.0472454 0.0431640 0.2398195
## p gE a64 t65 0.1250150 0.0436500 0.0613470 0.2380055
## p gE a65 t66 0.1004085 0.0482120 0.0377297 0.2411214
## p gE a66 t67 0.1020014 0.0479777 0.0390977 0.2407534
## p gE a67 t68 0.1069152 0.0471889 0.0434681 0.2397586
## p gE a68 t69 0.1018411 0.0480017 0.0389589 0.2407894
## p gE a69 t70 0.1037795 0.0477033 0.0406531 0.2403689
## p gE a70 t71 0.1074179 0.0471030 0.0439277 0.2396689
## p gE a71 t72 0.1041057 0.0476516 0.0409417 0.2403014
## p gE a72 t73 0.0991501 0.0483891 0.0366664 0.2414279
## p gE a73 t74 0.1018411 0.0480017 0.0389589 0.2407894
## p gE a74 t75 0.1018411 0.0480017 0.0389589 0.2407894
## p gE a75 t76 0.1080914 0.0469865 0.0445471 0.2395522
## p gE a76 t77 0.1259760 0.0434445 0.0623641 0.2380028
## p gE a77 t78 0.1115146 0.0463707 0.0477578 0.2390219
## p gE a78 t79 0.1026448 0.0478799 0.0396571 0.2406111
## p gE a79 t80 0.0991501 0.0483891 0.0366664 0.2414279
## p gE a80 t81 0.1045967 0.0475729 0.0413779 0.2402015
## p gE a81 t82 0.1057504 0.0473844 0.0424118 0.2399752
## Psi gE a0 t1 0.3621312 0.1433915 0.1439550 0.6571389
## Psi gP a0 t1 0.7906226 0.2510265 0.1619883 0.9866246
# derived variables is the occupancy probability
names(mod.fit$results$derived)
## [1] "Occupancy"
mod.fit$results$derived$Occupancy
## estimate se lcl ucl
## 1 0.3621312 0.1433915 0.1439550 0.6571389
## 2 0.7906226 0.2510265 0.1619883 0.9866246
# get the two psi values and their covariance
get.real(mod.fit, "Psi", se=TRUE, vcv=TRUE)
## $estimates
## all.diff.index par.index estimate se lcl
## Psi gE a0 t1 165 83 0.3621312 0.1433915 0.1439550
## Psi gP a0 t1 166 84 0.7906226 0.2510265 0.1619883
## ucl group age time Age Time Pond
## Psi gE a0 t1 0.6571389 E 0 1 0 0 E
## Psi gP a0 t1 0.9866246 P 0 1 0 0 P
##
## $vcv.real
## 83 84
## 83 0.020561117 0.003030027
## 84 0.003030027 0.063014304
get.real(mod.fit, "Psi", pim=TRUE)
## 1
## Group:PondE 0.3621312
## Group:PondP 0.7906226
# make a plot of the probability of detection as a function of temperature
Temp.df <- data.frame(Temp1=seq(min(temp.data,na.rm=TRUE),max(temp.data, na.rm=TRUE),1))
amtoad.ddl$p # see the index numbers
## par.index model.index group age time Age Time Pond
## 1 1 1 E 0 1 0 0 E
## 2 2 2 E 1 2 1 1 E
## 3 3 3 E 2 3 2 2 E
## 4 4 4 E 3 4 3 3 E
## 5 5 5 E 4 5 4 4 E
## 6 6 6 E 5 6 5 5 E
## 7 7 7 E 6 7 6 6 E
## 8 8 8 E 7 8 7 7 E
## 9 9 9 E 8 9 8 8 E
## 10 10 10 E 9 10 9 9 E
## 11 11 11 E 10 11 10 10 E
## 12 12 12 E 11 12 11 11 E
## 13 13 13 E 12 13 12 12 E
## 14 14 14 E 13 14 13 13 E
## 15 15 15 E 14 15 14 14 E
## 16 16 16 E 15 16 15 15 E
## 17 17 17 E 16 17 16 16 E
## 18 18 18 E 17 18 17 17 E
## 19 19 19 E 18 19 18 18 E
## 20 20 20 E 19 20 19 19 E
## 21 21 21 E 20 21 20 20 E
## 22 22 22 E 21 22 21 21 E
## 23 23 23 E 22 23 22 22 E
## 24 24 24 E 23 24 23 23 E
## 25 25 25 E 24 25 24 24 E
## 26 26 26 E 25 26 25 25 E
## 27 27 27 E 26 27 26 26 E
## 28 28 28 E 27 28 27 27 E
## 29 29 29 E 28 29 28 28 E
## 30 30 30 E 29 30 29 29 E
## 31 31 31 E 30 31 30 30 E
## 32 32 32 E 31 32 31 31 E
## 33 33 33 E 32 33 32 32 E
## 34 34 34 E 33 34 33 33 E
## 35 35 35 E 34 35 34 34 E
## 36 36 36 E 35 36 35 35 E
## 37 37 37 E 36 37 36 36 E
## 38 38 38 E 37 38 37 37 E
## 39 39 39 E 38 39 38 38 E
## 40 40 40 E 39 40 39 39 E
## 41 41 41 E 40 41 40 40 E
## 42 42 42 E 41 42 41 41 E
## 43 43 43 E 42 43 42 42 E
## 44 44 44 E 43 44 43 43 E
## 45 45 45 E 44 45 44 44 E
## 46 46 46 E 45 46 45 45 E
## 47 47 47 E 46 47 46 46 E
## 48 48 48 E 47 48 47 47 E
## 49 49 49 E 48 49 48 48 E
## 50 50 50 E 49 50 49 49 E
## 51 51 51 E 50 51 50 50 E
## 52 52 52 E 51 52 51 51 E
## 53 53 53 E 52 53 52 52 E
## 54 54 54 E 53 54 53 53 E
## 55 55 55 E 54 55 54 54 E
## 56 56 56 E 55 56 55 55 E
## 57 57 57 E 56 57 56 56 E
## 58 58 58 E 57 58 57 57 E
## 59 59 59 E 58 59 58 58 E
## 60 60 60 E 59 60 59 59 E
## 61 61 61 E 60 61 60 60 E
## 62 62 62 E 61 62 61 61 E
## 63 63 63 E 62 63 62 62 E
## 64 64 64 E 63 64 63 63 E
## 65 65 65 E 64 65 64 64 E
## 66 66 66 E 65 66 65 65 E
## 67 67 67 E 66 67 66 66 E
## 68 68 68 E 67 68 67 67 E
## 69 69 69 E 68 69 68 68 E
## 70 70 70 E 69 70 69 69 E
## 71 71 71 E 70 71 70 70 E
## 72 72 72 E 71 72 71 71 E
## 73 73 73 E 72 73 72 72 E
## 74 74 74 E 73 74 73 73 E
## 75 75 75 E 74 75 74 74 E
## 76 76 76 E 75 76 75 75 E
## 77 77 77 E 76 77 76 76 E
## 78 78 78 E 77 78 77 77 E
## 79 79 79 E 78 79 78 78 E
## 80 80 80 E 79 80 79 79 E
## 81 81 81 E 80 81 80 80 E
## 82 82 82 E 81 82 81 81 E
## 83 83 83 P 0 1 0 0 P
## 84 84 84 P 1 2 1 1 P
## 85 85 85 P 2 3 2 2 P
## 86 86 86 P 3 4 3 3 P
## 87 87 87 P 4 5 4 4 P
## 88 88 88 P 5 6 5 5 P
## 89 89 89 P 6 7 6 6 P
## 90 90 90 P 7 8 7 7 P
## 91 91 91 P 8 9 8 8 P
## 92 92 92 P 9 10 9 9 P
## 93 93 93 P 10 11 10 10 P
## 94 94 94 P 11 12 11 11 P
## 95 95 95 P 12 13 12 12 P
## 96 96 96 P 13 14 13 13 P
## 97 97 97 P 14 15 14 14 P
## 98 98 98 P 15 16 15 15 P
## 99 99 99 P 16 17 16 16 P
## 100 100 100 P 17 18 17 17 P
## 101 101 101 P 18 19 18 18 P
## 102 102 102 P 19 20 19 19 P
## 103 103 103 P 20 21 20 20 P
## 104 104 104 P 21 22 21 21 P
## 105 105 105 P 22 23 22 22 P
## 106 106 106 P 23 24 23 23 P
## 107 107 107 P 24 25 24 24 P
## 108 108 108 P 25 26 25 25 P
## 109 109 109 P 26 27 26 26 P
## 110 110 110 P 27 28 27 27 P
## 111 111 111 P 28 29 28 28 P
## 112 112 112 P 29 30 29 29 P
## 113 113 113 P 30 31 30 30 P
## 114 114 114 P 31 32 31 31 P
## 115 115 115 P 32 33 32 32 P
## 116 116 116 P 33 34 33 33 P
## 117 117 117 P 34 35 34 34 P
## 118 118 118 P 35 36 35 35 P
## 119 119 119 P 36 37 36 36 P
## 120 120 120 P 37 38 37 37 P
## 121 121 121 P 38 39 38 38 P
## 122 122 122 P 39 40 39 39 P
## 123 123 123 P 40 41 40 40 P
## 124 124 124 P 41 42 41 41 P
## 125 125 125 P 42 43 42 42 P
## 126 126 126 P 43 44 43 43 P
## 127 127 127 P 44 45 44 44 P
## 128 128 128 P 45 46 45 45 P
## 129 129 129 P 46 47 46 46 P
## 130 130 130 P 47 48 47 47 P
## 131 131 131 P 48 49 48 48 P
## 132 132 132 P 49 50 49 49 P
## 133 133 133 P 50 51 50 50 P
## 134 134 134 P 51 52 51 51 P
## 135 135 135 P 52 53 52 52 P
## 136 136 136 P 53 54 53 53 P
## 137 137 137 P 54 55 54 54 P
## 138 138 138 P 55 56 55 55 P
## 139 139 139 P 56 57 56 56 P
## 140 140 140 P 57 58 57 57 P
## 141 141 141 P 58 59 58 58 P
## 142 142 142 P 59 60 59 59 P
## 143 143 143 P 60 61 60 60 P
## 144 144 144 P 61 62 61 61 P
## 145 145 145 P 62 63 62 62 P
## 146 146 146 P 63 64 63 63 P
## 147 147 147 P 64 65 64 64 P
## 148 148 148 P 65 66 65 65 P
## 149 149 149 P 66 67 66 66 P
## 150 150 150 P 67 68 67 67 P
## 151 151 151 P 68 69 68 68 P
## 152 152 152 P 69 70 69 69 P
## 153 153 153 P 70 71 70 70 P
## 154 154 154 P 71 72 71 71 P
## 155 155 155 P 72 73 72 72 P
## 156 156 156 P 73 74 73 73 P
## 157 157 157 P 74 75 74 74 P
## 158 158 158 P 75 76 75 75 P
## 159 159 159 P 76 77 76 76 P
## 160 160 160 P 77 78 77 77 P
## 161 161 161 P 78 79 78 78 P
## 162 162 162 P 79 80 79 79 P
## 163 163 163 P 80 81 80 80 P
## 164 164 164 P 81 82 81 81 P
pred.p <- covariate.predictions(mod.fit, indices=1, data=Temp.df)
head(pred.p$estimates)
## vcv.index model.index par.index covdata estimate se lcl
## 1 1 1 1 0 0.09698169 0.04867688 0.03487010
## 2 2 1 1 1 0.10152121 0.04804946 0.03868274
## 3 3 1 1 2 0.10624820 0.04730143 0.04286171
## 4 4 1 1 3 0.11116807 0.04643474 0.04742818
## 5 5 1 1 4 0.11628610 0.04545448 0.05239989
## 6 6 1 1 5 0.12160753 0.04436974 0.05778932
## ucl fixed
## 1 0.2419886
## 2 0.2408620
## 3 0.2398812
## 4 0.2390708
## 5 0.2384618
## 6 0.2380928
plotdata <- cbind(Temp.df, pred.p$estimates)
head(plotdata)
## Temp1 vcv.index model.index par.index covdata estimate se
## 1 0 1 1 1 0 0.09698169 0.04867688
## 2 1 2 1 1 1 0.10152121 0.04804946
## 3 2 3 1 1 2 0.10624820 0.04730143
## 4 3 4 1 1 3 0.11116807 0.04643474
## 5 4 5 1 1 4 0.11628610 0.04545448
## 6 5 6 1 1 5 0.12160753 0.04436974
## lcl ucl fixed
## 1 0.03487010 0.2419886
## 2 0.03868274 0.2408620
## 3 0.04286171 0.2398812
## 4 0.04742818 0.2390708
## 5 0.05239989 0.2384618
## 6 0.05778932 0.2380928
ggplot(data=plotdata, aes(x=Temp1, y=estimate))+
ggtitle("Detection probability as a function of temperature")+
geom_point()+
geom_ribbon(aes(ymin=lcl, ymax=ucl), alpha=.2)+
ylim(0,1)
# covariate predictions for categorical covariates
# Occupancy predictions for different pond types
amtoad.ddl$Psi
## par.index model.index group age time Age Time Pond
## 1 1 165 E 0 1 0 0 E
## 2 2 166 P 0 1 0 0 P
fit.psi = tail(mod.fit$results$real,2)
fit.psi$pond = c("E","P")
fit.psi
## estimate se lcl ucl fixed note pond
## Psi gE a0 t1 0.3621312 0.1433915 0.1439550 0.6571389 E
## Psi gP a0 t1 0.7906226 0.2510265 0.1619883 0.9866246 P
ggplot(data=fit.psi, aes(x=pond, y=estimate))+
geom_point()+
geom_errorbar(aes(ymin=lcl,
ymax=ucl, width=0.2))+
ylim(0,1)
# cleanup
cleanup(ask=FALSE)