double_observer_analysis: Example Double Observer Data Analysis
In jlaake/DoubleObs: Analysis of double-observer survey data

An example of double observer data analysis but not using marked individuals so residual heterogeneity cannot be considered. Data were generated with the following code using simhet function.

A data frame with 129 observations of 7 variables:

ch: a character vector containing the three character encounter history; first occasion indicaes whther the group was marked or not
count: number of animals in the group
het: variable used to model heterogeneity (re-capture probability.
lngs: natural log of count
veg: random vegetation variable
type: "unmarked" or "marked"

simres=simhet(1,150,25,beta=c(-.5,-.5,-1,2,.5),data=data.frame(veg=runif(175)), gen_formula="~-1+loc+veg+cov+lngs",use_gs=TRUE,gs_param=c(1,10),seed=9234397) example_data=simres[[1]][[1]]$results[[1]]$data$data

The groups sizes were randomly generated from a gamma distribution with scale=10 and shape=1 (gs_param). The true simulated population size is 175 groups and 1732 animals. A uniform random veg variable, and unmodelled heterogeneity variable cov (uniform -1,1) and natural log of group size are used to generate p for each location(loc).

data(example_data)
df=example_data
# Only use second and third capture history positions - first position was for radio(marked)
df$ch=substr(df$ch,2,3)
# Ignore 00 values: these were marked groups that were not detected
df=df[df$ch!="00",]
# all are considered unmarked but need to create empty marked group with call to factor
df$type="unmarked"
df$type=factor(df$type,levels=c("marked","unmarked"))
# Use process.data in RMark but use groups="type" and allgroups=TRUE to create group structure
# even though it is not used. In addition, begin.time=2. These options make double observer
# analysis work with abundance estimation code Nhat functions.
dp=RMark::process.data(df,model="Huggins",groups="type",allgroups=TRUE,begin.time=2)
# Create default design data
ddl=RMark::make.design.data(dp)
# Define create rear 0/1 variable - time==3 (second occasion)
ddl$p$rear=ifelse(ddl$p$time==2,0,1)
ddl$c$rear=1
# show design data
ddl$p
ddl$c
# Create function to fit a sequence of models; must assume independence in this model
# so cannot include c:het:rear or type in models to account for residual heterogeneity
fit.models=function()
{
   p.1=list(formula=~veg+lngs,share=TRUE)
   p.2=list(formula=~lngs+rear,share=TRUE)
   p.3=list(formula=~veg+rear,share=TRUE)
   p.4=list(formula=~veg+lngs+rear,share=TRUE)
   p.5=list(formula=~rear,share=TRUE)
   cml=RMark::create.model.list("Huggins")
   results=RMark::mark.wrapper(cml,data=dp,ddl=ddl)
   return(results)
}
results=fit.models()
results
# Group abundance
Nhat_group_marklist(results,df)
# Group abundance estimate from MARK for best model
results[[1]]$results$derived[[1]][2,]
# MARK doesn't consider group size so there is no equivalent for total abundance
Nhat_marklist(results,df)