Formatting data for use in spOccupancy
Jeffrey W. Doser
2022
Source:vignettes/dataFormatting.Rmd
dataFormatting.RmdIntroduction
This vignette gives an example of how to take raw data and format it
for use in spOccupancy model fitting functions. This is not
an exhaustive example, as data can be recorded and stored in a variety
of ways, which requires different approaches to wrangle the data into
the necessary format for spOccupancy. However, I hope this
vignette can help provide some guidance on how to take raw data and
efficiently reformat it for use in spOccupancy. Here I will
focus solely on data preparation. For full details on the basic
spOccupancy functionality, please see the introductory
vignette.
First we load spOccupancy as well as two
tidyverse packages that we will use for manipulating our
data sets into the necessary format for spOccupancy
(dplyr and lubridate).
Raw Data: Hubbard Brook Experimental Forest
As an exmaple data set, we will use data from point count surveys on breeding birds in the Hubbard Brook Experimental Forest (HBEF). Briefly, observers performed standard point count surveys at 374 sites throughout HBEF. Typically each site was revisited three times during a given year, providing the necessary replication for occupancy modeling. During each point count survey, the observer records each individual bird they see within a pre-specified detection radius and within the 10-minute duration of the survey. This results in a number of individual birds for each species observed during each point count survey.
In the following code chunk, we read in the HBEF data set directly from the Hubbard Brook website. Note this will only work on your computer if you have an internet connection.
hb.dat <- read.csv(url("https://portal.edirepository.org/nis/dataviewer?packageid=knb-lter-hbr.178.3&entityid=eecb146279aa290af2292d75d3ba0f8b"))
# Take a look at the data set
str(hb.dat)'data.frame': 247271 obs. of 17 variables:
$ Plot : int 1 1 1 1 1 1 1 1 1 1 ...
$ Replicate : chr "1" "1" "1" "1" ...
$ Date : chr "1999-06-07" "1999-06-07" "1999-06-07" "1999-06-07" ...
$ Time : chr "05:30" "05:30" "05:30" "05:30" ...
$ Observer : chr "JRM" "JRM" "JRM" "JRM" ...
$ Sky : chr "2" "2" "2" "2" ...
$ Wind : int 0 0 0 0 0 0 0 0 0 0 ...
$ Bird.Number : int 1 2 3 4 5 6 7 8 9 10 ...
$ Period : int NA NA NA NA NA NA NA NA NA NA ...
$ Minute : int 1 1 1 1 1 1 2 3 5 5 ...
$ Species : chr "SCTA" "BTBW" "BTNW" "REVI" ...
$ Sex : chr "M" "M" "M" "M" ...
$ Detection.Method: chr "S" "S" "S" "S" ...
$ Distance : chr "2" "1" "2" "1" ...
$ New.Record : int NA NA NA NA NA NA NA NA NA NA ...
$ Counter.sing : int NA NA NA NA NA NA NA NA NA NA ...
$ Comments : chr "" "" "" "" ...We see the data set comes with a variety of auxiliary information such as the minute the species was detected, and information on the weather at the time of the survey. See the Hubbard Brook website for full metadata information on this data set.
Looking closely at the data set, we see that each row corresponds to
an individual bird that was detected during a point count survey at a
specific site (Plot) on a given date (Date).
For our example, we only want to work with data from a single year, so
we will first extract the year of each observation from the
Date column using functions from lubridate and
dplyr.
# Convert string "Date" column to Date R object
class(hb.dat$Date)[1] "character"[1] "Date"'data.frame': 247271 obs. of 18 variables:
$ Plot : int 1 1 1 1 1 1 1 1 1 1 ...
$ Replicate : chr "1" "1" "1" "1" ...
$ Date : Date, format: "1999-06-07" "1999-06-07" ...
$ Time : chr "05:30" "05:30" "05:30" "05:30" ...
$ Observer : chr "JRM" "JRM" "JRM" "JRM" ...
$ Sky : chr "2" "2" "2" "2" ...
$ Wind : int 0 0 0 0 0 0 0 0 0 0 ...
$ Bird.Number : int 1 2 3 4 5 6 7 8 9 10 ...
$ Period : int NA NA NA NA NA NA NA NA NA NA ...
$ Minute : int 1 1 1 1 1 1 2 3 5 5 ...
$ Species : chr "SCTA" "BTBW" "BTNW" "REVI" ...
$ Sex : chr "M" "M" "M" "M" ...
$ Detection.Method: chr "S" "S" "S" "S" ...
$ Distance : chr "2" "1" "2" "1" ...
$ New.Record : int NA NA NA NA NA NA NA NA NA NA ...
$ Counter.sing : int NA NA NA NA NA NA NA NA NA NA ...
$ Comments : chr "" "" "" "" ...
$ Year : num 1999 1999 1999 1999 1999 ...We will now use the dplyr::filter() function to only
select data from 2014. Additionally, I apply two further restrictions on
the data set. I only grab observations that come from the first, second,
or third replicate, and I also remove data from plot 277, as we don’t
want to include this plot in our analysis as a result of data collection
complications.
hb.2014 <- hb.dat %>%
filter(Year == 2014, # Only use data from 2014
Replicate %in% c("1", "2", "3"), # Only use data from first 3 reps
Plot != 277) # Don't use data from plot 277
str(hb.2014)'data.frame': 27141 obs. of 18 variables:
$ Plot : int 339 339 339 339 339 339 339 339 339 339 ...
$ Replicate : chr "1" "1" "1" "1" ...
$ Date : Date, format: "2014-05-29" "2014-05-29" ...
$ Time : chr "05:30" "05:30" "05:30" "05:30" ...
$ Observer : chr "NIK" "NIK" "NIK" "NIK" ...
$ Sky : chr "0" "0" "0" "0" ...
$ Wind : int 0 0 0 0 0 0 0 0 0 0 ...
$ Bird.Number : int 1 2 3 4 5 6 7 8 9 10 ...
$ Period : int 1 1 1 1 1 1 1 1 1 2 ...
$ Minute : int 1 1 1 1 1 2 2 2 2 4 ...
$ Species : chr "REVI" "HETH" "VEER" "REVI" ...
$ Sex : chr "M" "M" "M" "M" ...
$ Detection.Method: chr "S" "S" "S" "S" ...
$ Distance : chr "1" "2" "2" "2" ...
$ New.Record : int 1 1 1 1 1 1 1 1 1 1 ...
$ Counter.sing : int 1 0 0 1 1 0 1 0 0 0 ...
$ Comments : chr "" "" "" "" ...
$ Year : num 2014 2014 2014 2014 2014 ...After applying our filtering criteria, we see we have 27141 observations of individual birds.
Extract Detection-nondetection Data
Now that we have filtered the data to only contain the data we wish
to use in our analysis, our next step is to extract the
detection-nondetection data for use in spOccupancy. Let’s
suppose we are interested first in fitting a multi-species occupancy
model. All multi-species occupancy model fitting functions in
spOccupancy require the detection-nondetection data to be
in the format of a three-dimensional array, with dimensions
corresponding to species, site, and replicate.
The easiest way to think about a three-dimensional array is as a
series of stacked matrices. For a single-species, we can imagine having
a two-dimensional matrix, with the rows corresponding to sites, the
columns corresponding to replicate surveys, and the individual elements
of the matrix denoting whether or not the species was observed (1) or
not observed (0) during the specific survey at the specific site. If we
have \(N\) species, we can generate a
separate matrix for each species, giving us a total of \(N\) matrices. If we imagine “stacking”
these \(N\) species-specific matrices
on top of one another, this gives us a three-dimensional array. This is
excatly what we do to format the detection-nondetection data for use in
spOccupancy.
First, we convert the raw data into a long format, where each row
corresponds to the total number of individuals of a given species
observed at a given site during a given point count survey. We do this
using a series of dplyr functions.
y.long <- hb.2014 %>%
group_by(Plot, Date, Replicate, Species) %>%
summarize(count = n()) %>%
ungroup() %>%
glimpse()Rows: 9,090
Columns: 5
$ Plot
[3m
[38;5;246m<int>
[39m
[23m 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ Date
[3m
[38;5;246m<date>
[39m
[23m 2014-05-30, 2014-05-30, 2014-05-30, 2014-05-30, 2014-05-30,…
$ Replicate
[3m
[38;5;246m<chr>
[39m
[23m "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", …
$ Species
[3m
[38;5;246m<chr>
[39m
[23m "BLBW", "BRCR", "BTBW", "BTNW", "HETH", "OVEN", "REVI", "RTH…
$ count
[3m
[38;5;246m<int>
[39m
[23m 4, 2, 6, 2, 1, 5, 7, 1, 1, 3, 1, 4, 1, 1, 6, 4, 9, 1, 5, 4, …Next, we need to convert our y.long object into our
three-dimensional array that contains the site/replicate matrices for
each of our \(N\) species. First, I
extract the codes for each individual species and plot (site) and set up
the array (y) that will store our detection-nondetection
data.
# Species codes.
sp.codes <- sort(unique(y.long$Species))
# Plot (site) codes.
plot.codes <- sort(unique(y.long$Plot))
# Number of species
N <- length(sp.codes)
# Maximum number of replicates at a site
K <- 3
# Number of sites
J <- length(unique(y.long$Plot))
# Array for detection-nondetection data.
y <- array(NA, dim = c(N, J, K))
# Label the dimensions of y (not necessary, but helpful)
dimnames(y)[[1]] <- sp.codes
dimnames(y)[[2]] <- plot.codes
# Look at the structure of our array y
str(y) logi [1:81, 1:373, 1:3] NA NA NA NA NA NA ...
- attr(*, "dimnames")=List of 3
..$ : chr [1:81] "AMCR" "AMGO" "AMKE" "AMRE" ...
..$ : chr [1:373] "1" "2" "3" "4" ...
..$ : NULLLooking at the output from str(y), we see our
detection-nondetection array will contain data for 81 species at 373
sites across a possible 3 replicates at each site. Next we need to fill
the array with our data for each species. I do this below by using
nested for loops. Specifically, I fill in the data for each site and
each replicate one at a time. Here we need to be careful to distinguish
between site/replicate combinations where a species was not observed and
site/replicate combinations that were not sampled (e.g., a site was
sampled only twice and not three times). In this specific case here, I
make the assumption that if a site was sampled for a given replicate,
the observer will have detected at least one bird. If not, I assume the
site was not sampled. This is a valid approach for this data set, but a
different approach may need to be taken depending on the specific study
system you’re working with, and how the data were originally formatted.
Further, for this data set, there are multiple dates listed for certain
replicate surveys, and so for those cases where there are multiple dates
listed for a specific replicate, I choose here to simply use the data
that comes from the first date.
for (j in 1:J) { # Loop through sites.
for (k in 1:K) { # Loop through replicates at each site.
# Extract data for current site/replicate combination.
curr.df <- y.long %>%
filter(Plot == plot.codes[j], Replicate == k)
# Check if more than one date for a given replicate
if (n_distinct(curr.df$Date) > 1) {
# If there is more than 1 date, only use the data
# from the first date.
curr.dates <- unique(sort(curr.df$Date))
curr.df <- curr.df %>%
filter(Date == curr.dates[1])
}
# If plot j was sampled during replicate k,
# curr.df will have at least 1 row (i.e., at least
# one species will be observed). If not, assume it
# was not sampled for that replicate.
if (nrow(curr.df) > 0) {
# Extract the species that were observed during
# this site/replicate.
curr.sp <- which(sp.codes %in% curr.df$Species)
# Set value to 1 for species that were observed.
y[curr.sp, j, k] <- 1
# Set value to 0 for all other species.
y[-curr.sp, j, k] <- 0
}
} # k (replicates)
} # j (sites)
str(y) num [1:81, 1:373, 1:3] 0 0 0 0 0 0 0 0 0 0 ...
- attr(*, "dimnames")=List of 3
..$ : chr [1:81] "AMCR" "AMGO" "AMKE" "AMRE" ...
..$ : chr [1:373] "1" "2" "3" "4" ...
..$ : NULL
# Total number of observations for each species
apply(y, 1, sum, na.rm = TRUE)AMCR AMGO AMKE AMRE AMRO BANS BAOR BAWW BBCU BCCH BDOW BHVI BITH BLBW BLJA BLPW
6 5 1 21 7 1 1 45 5 254 4 114 2 703 116 79
BOCH BRCR BTBW BTNW BWHA CAGO CAWA CEDW CHSW COLO CORA COYE CSWA DOWO EACH EAPH
6 56 881 908 13 1 59 22 55 1 4 9 1 3 335 2
EAWP EVGR GCFL GCKI HAWO HETH LEFL MAWA MODO MOWA MYWA NAWA NOPA NOWA NSWO NULL
42 6 1 163 122 259 3 232 2 1 373 15 6 2 5 3
OSFL OVEN PIWA PIWO PUFI RBGR RBNU RESQ REVI RTHU RUBL RUGR SCJU SCTA SSHA SWTH
4 867 1 12 46 45 317 347 831 8 3 17 189 93 1 394
TEWA TUTI UNKN UNMA VEER WBNU WITU WIWA WIWR WOTH WTSP XXWA XXWO YBCU YBFL YBSA
1 1 53 2 24 47 4 4 286 7 56 1 2 1 90 142
YSFL
1 Not surprisingly, we see a wide range in the number of observations for the 81 species observed at HBEF in 2014.
Format detection covariates
Next, we will extract and format two observation-level covariates
that we will use to account for variation in detection probability
across the different sites and the different surveys at each site.
Specifically, we wish to extract the day of each survey and the time of
day each survey began. All spOccupancy model functions
assumes that observation-level detection covariates wil be formatted as
matrices with rows corresponding to sites and columns corresponding to
replicates. I first use a set of dplyr functions to extract
the unique date and time of day (tod) for each plot and replicate
combination in the data set.
day.time.2014 <- hb.2014 %>%
group_by(Plot, Replicate) %>%
summarize(Date = unique(Date),
tod = unique(Time)) %>%
ungroup() %>%
glimpse()Rows: 1,140
Columns: 4
$ Plot
[3m
[38;5;246m<int>
[39m
[23m 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, …
$ Replicate
[3m
[38;5;246m<chr>
[39m
[23m "1", "2", "2", "3", "1", "2", "2", "3", "1", "2", "2", "3", …
$ Date
[3m
[38;5;246m<date>
[39m
[23m 2014-05-30, 2014-06-11, 2014-06-17, 2014-06-25, 2014-05-30,…
$ tod
[3m
[38;5;246m<chr>
[39m
[23m "05:30", "09:36", "08:05", "05:30", "05:44", "09:21", "07:50…There are two things to mention. First, the date is currently stored as a date, and instead we want to extract the Julian date (i.e., the day of the year, where January first is day 1). Second, the time of day is currently stored as a character, and we want to extract the time of day as the number of minutes since midnight. Below, we use a similar nested loop statement like we used for the detection-nondetection data to extract the day and time of each survey, and convert the day and time to the desired formats.
hb.day <- matrix(NA, nrow = J, ncol = K)
hb.tod <- matrix(NA, nrow = J, ncol = K)
for (j in 1:J) { # Loop through sites
for (k in 1:K) { # Loop through replicate surveys
# Get current date and time for each survey
curr.vals <- day.time.2014 %>%
filter(Plot == plot.codes[j], Replicate == k) %>%
mutate(Date = yday(Date),
tod = period_to_seconds(hm(tod)) / 60 ) %>%
select(Date, tod) %>%
arrange(Date)
# If the site was surveyed for the given replicate,
# extract the first date and time value.
if (nrow(curr.vals) > 0) {
hb.day[j, k] <- curr.vals$Date[1]
hb.tod[j, k] <- curr.vals$tod[1]
}
} # k (replicates)
} # j (sites)
# Check out the structure of our covariates.
str(hb.day) num [1:373, 1:3] 150 150 150 150 150 150 150 150 150 150 ...
str(hb.tod) num [1:373, 1:3] 330 344 366 388 406 420 438 454 477 491 ...Format occurrence covariates
Formatting covariates for the occurrence portion of an occupancy
model in spOccupancy is straightforward, as covariates can
only vary by site. Thus, occurrence covariates simply need to be
formatted as either a data frame or a matrix, where the rows represent
the sites and the columns represent the different covariates that you
wish to include in the occupancy model.
Here we will use elevation as a site-level covariate on the
occurrence portion of the occupancy model. I extract elevation at each
of the 373 sites from the hbef2015 data object that comes
along with the spOccupancy package.
elev <- hbef2015$occ.covs[, 1]
str(elev) num [1:373] 475 494 546 587 588 ...Format site coordinates
For spatially-explicit models in spOccupancy, the model
fitting functions additionally require the site coordinates. The
coordinates should be formatted as a matrix with \(J\) rows (where \(J\) is the number of sites) and two
columns, with the horizontal component (i.e., easting) in the first
column, and the vertical component (i.e., northing) in the second
column. Note that spOccupancy assumes coordinates are
provided in a projected coordinate system. In other words, you should
not provide latitude/longitude values to spOccupancy, and
rather should convert these to some projected coordinate system. Below I
extract the coordinates for the 373 sites in the Hubbard Brook data set
from the hbef2015 data object that comes along with the
spOccupancy package. These coordinates are in UTM Zone
19N.
coords <- hbef2015$coords
str(coords) num [1:373, 1:2] 280000 280000 280000 280001 280000 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:373] "1" "2" "3" "4" ...
..$ : chr [1:2] "X" "Y"Package data into list object
We now have all the necessary components for fitting an occupancy
model in spOccupancy. Our final step for preparing the data
is to package all of the data into a list object in the specific format
that spOccupancy requires. When we fit occupancy models in
spOccupancy we need to send in a list into the
data argument that contains the detection-nondetection
data, occurrence covariates, detection covariates, and spatial
coordinates (for spatially-explicit models). The list should consist of
four objects with the following names: y (the
detection-nondetection data), det.covs (the detection
covariates), occ.covs (the occurrence covariates, and
coords (the spatial coordinates). Note that
coords is only necessary for spatially-explicit models, and
det.covs and/or occ.covs can be left out if
you are fitting models with no covariates on detection and/or
occurrence, respectively. The detection-nondetection data are in the
three-dimensional array as we previously specified. For our simple
example here, we will fit a spatially-explicit multi-species occupancy
model with ten species, and so below I subset our full
detection-nondetection data to only include ten species
# Detection-nondetection data ---------
# Species of interest
curr.birds <- c('BAWW', 'BLJA', 'BTBW', 'BTNW', 'EAWP',
'OVEN', 'VEER', 'WBNU', 'SCTA', 'GCFL')
y.msom <- y[which(sp.codes %in% curr.birds), , ]
str(y.msom) num [1:10, 1:373, 1:3] 0 0 1 1 0 0 1 0 0 0 ...
- attr(*, "dimnames")=List of 3
..$ : chr [1:10] "BAWW" "BLJA" "BTBW" "BTNW" ...
..$ : chr [1:373] "1" "2" "3" "4" ...
..$ : NULLFor the detection covariates, we need to create a list that contains
all of the detection covariates we wish to include in the model. The
individual detection covariates can be either site level covariates or
observation level covariates. Site-level covariates are specified as a
vector of length \(J\) (the number of
sites), while observation-level covariates are specified as a matrix or
data frame with the number of rows equal to \(J\) and number of columns equal to the
maximum number of replicates at a given site. Here, we have two
observation level covariates (hb.day and
hb.tod), which are formatted correctly as matrices. We put
them together in a list in the following code chunk.
List of 2
$ day: num [1:373, 1:3] 150 150 150 150 150 150 150 150 150 150 ...
$ tod: num [1:373, 1:3] 330 344 366 388 406 420 438 454 477 491 ...The occurrence covariates are stored as a matrix or data frame, with
rows corresponding to sites and columns corresponding to the different
covariates we wish to include in the model. Here, we have a single
covariate (elev) and so we convert it to a data frame in
the following code chunk.
# Occurrence covariates ---------------
occ.covs <- data.frame(elev)
str(occ.covs)'data.frame': 373 obs. of 1 variable:
$ elev: num 475 494 546 587 588 ...We already have the coordinates correctly specified as a \(J \times 2\) matrix in the
coords object, so we are now ready to package all the
objects together into a single list.
# Package all data into list object
data.msom <- list(y = y.msom,
occ.covs = occ.covs,
det.covs = det.covs,
coords = coords)Notice how we explicitly specify the name of each object
(y, occ.covs, det.covs, and
coords). The data are now ready to go, and below I fit a
spatially-explicit multi-species occupancy model to verify that (see the
introductory
vignette for more details on model-fitting functions).
out.msom <- spMsPGOcc(occ.formula = ~ scale(elev) + I(scale(elev)^2),
det.formula = ~ scale(day) + I(scale(day)^2) + scale(tod),
data = data.msom,
n.batch = 10,
batch.length = 25,
cov.model = 'exponential',
NNGP = TRUE,
verbose = FALSE)
summary(out.msom, level = 'community')
Call:
spMsPGOcc(occ.formula = ~scale(elev) + I(scale(elev)^2), det.formula = ~scale(day) +
I(scale(day)^2) + scale(tod), data = data.msom, cov.model = "exponential",
NNGP = TRUE, n.batch = 10, batch.length = 25, verbose = FALSE)
Samples per Chain: 250
Burn-in: 25
Thinning Rate: 1
Number of Chains: 1
Total Posterior Samples: 225
Run Time (min): 0.1289
----------------------------------------
Community Level
----------------------------------------
Occurrence Means (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) 0.0970 1.0553 -2.2212 0.0975 2.0290 NA 171
scale(elev) -1.0396 0.3214 -1.5938 -1.0576 -0.3014 NA 29
I(scale(elev)^2) -0.5060 0.2743 -1.0016 -0.5017 0.0231 NA 102
Occurrence Variances (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) 19.6211 9.5768 8.0161 17.7549 45.7409 NA 177
scale(elev) 0.7611 0.7439 0.1351 0.5417 2.7462 NA 16
I(scale(elev)^2) 0.6159 0.4785 0.1702 0.4924 1.5727 NA 111
Detection Means (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) -0.2500 0.5354 -1.2963 -0.2291 0.7418 NA 161
scale(day) -0.0221 0.1035 -0.2206 -0.0260 0.1705 NA 89
I(scale(day)^2) -0.0779 0.1175 -0.4007 -0.0752 0.1127 NA 76
scale(tod) -0.1475 0.1005 -0.3477 -0.1463 0.0423 NA 89
Detection Variances (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) 3.6624 2.2126 1.3730 3.0568 9.5411 NA 144
scale(day) 0.0719 0.0488 0.0200 0.0564 0.1805 NA 178
I(scale(day)^2) 0.0894 0.1432 0.0219 0.0589 0.2180 NA 66
scale(tod) 0.0727 0.0455 0.0211 0.0609 0.2002 NA 114Finally, to fit a single-species occupancy model, we only need to
make one change to the detection-nondetection data. Because we only have
a single-species, we no longer need to specify y as a
three-dimensional array, and instead it is simply a matrix with rows
corresponding to sites and columns corresponding to replicates. Below I
reformat the data for fitting a spatially-explicit occupancy model with
a single-species.
num [1:373, 1:3] 0 0 0 0 0 0 0 0 0 0 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:373] "1" "2" "3" "4" ...
..$ : NULL
data.ssom <- list(y = y.ssom,
occ.covs = occ.covs,
det.covs = det.covs,
coords = coords)
out.ssom <- spPGOcc(occ.formula = ~ scale(elev) + I(scale(elev)^2),
det.formula = ~ scale(day) + I(scale(day)^2) + scale(tod),
data = data.ssom,
n.batch = 10,
batch.length = 25,
cov.model = 'exponential',
NNGP = TRUE,
verbose = FALSE)
summary(out.ssom)
Call:
spPGOcc(occ.formula = ~scale(elev) + I(scale(elev)^2), det.formula = ~scale(day) +
I(scale(day)^2) + scale(tod), data = data.ssom, cov.model = "exponential",
NNGP = TRUE, n.batch = 10, batch.length = 25, verbose = FALSE)
Samples per Chain: 250
Burn-in: 25
Thinning Rate: 1
Number of Chains: 1
Total Posterior Samples: 225
Run Time (min): 0.0118
Occurrence (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) -3.4190 0.4964 -4.3013 -3.4111 -2.5065 NA 16
scale(elev) -1.2072 0.3424 -1.8861 -1.1833 -0.5016 NA 28
I(scale(elev)^2) -0.0973 0.2333 -0.5870 -0.1051 0.3082 NA 29
Detection (logit scale):
Mean SD 2.5% 50% 97.5% Rhat ESS
(Intercept) 0.0472 0.4106 -0.7912 0.0426 0.7307 NA 97
scale(day) 0.2832 0.2778 -0.1982 0.2552 0.7832 NA 155
I(scale(day)^2) -0.2019 0.2882 -0.6859 -0.1955 0.3597 NA 274
scale(tod) 0.1186 0.2664 -0.3760 0.1027 0.6011 NA 185
Spatial Covariance:
Mean SD 2.5% 50% 97.5% Rhat ESS
sigma.sq 2.5555 1.5014 0.6107 2.2134 6.2245 NA 4
phi 0.0115 0.0070 0.0036 0.0076 0.0261 NA 5