Nothing

```
#' @title Compute double observer probability of detection (No external covariates allowed)
#'
#' @description Estimates the probability of detection in a two-observer system when observations are independent.
#'
#' @param df A data frame containing the components \code{$obsby.1} and \code{$obsby.2}.
#' These components are either 0/1 (0 = missed, 1 = seen) or TRUE/FALSE (logical) vectors indicating whether
#' observer 1 (\code{obsby.1}) or observer 2 (\code{obsby.2}) spotted the target. There is
#' no flexibility
#' on naming these columns of \code{df}. They must be named \code{$obsby.1} and \code{$obsby.2}.
#' @param observer A number of text string indicating the primary observer. Primary observers can be
#' observer 1, or observer 2, or "both".
#' If, for example, observer 2 was a data recorder and part-time observer, or if observer 2
#' was the pilot, set \code{observer} = 1. This dictates which set of observations form the denominator
#' of the double observer system. For example, if \code{observer} = 1, observations by observer 1 that were not seen
#' by observer 2 are ignored. The estimate in this case uses targets seen by both observers and
#' those seen by observer 2 but not observer 1. If observer = "both", the denominator is computed twice, once
#' assuming observer 1 was the primary, once assuming observer 2 was the primary, and then computes
#' the probability of one or more observers sighting a target.
#' @details When \code{observer} = "both", the observers are assumed to be independent. In this case the estimate
#' of detection is
#' \deqn{p = p_1 + p_2 - p_1p_2}{p = p1 + p2 - p1*p2}
#' where \eqn{p_1}{p1} is the proportion of targets seen by observer 2 that were also seen by observer 1,
#' \eqn{p_2}{p2} is the proportion of targets seen by observer 1 that were also seen by observer 2.
#' This estimator is very close to unbiased when observers are actually independent.
#' @return A single scalar, the probability of detection estimate.
#'
#' @seealso \code{\link{dfuncEstim}}, \code{\link{abundEstim}}
#'
#' @examples
#' # Fake observers
#' set.seed(538392)
#' obsrv <- data.frame( obsby.1=rbinom(100,1,.75), obsby.2=rbinom(100,1,.5) )
#'
#' F.double.obs.prob( obsrv, observer=1 )
#' F.double.obs.prob( obsrv, observer=2 )
#' F.double.obs.prob( obsrv, observer="both" )
#' @keywords model
#' @export
F.double.obs.prob <- function( df, observer = "both" ){
#
# Compute the probability of detection from a double observer system.
# No external covariates allowed here.
#
# Inputs:
# df = data frame containing the components $obsby.1, $obsby.2.
# These components are TRUE/FALSE (logical) vectors indicating whether
# observer 1 (obsby.1) or observer 2 (obsby.2) spotted the target.
# observer = indicates whether observer 1 or observer 2 or both were full-time observers.
# If, for example, observer 2 was a data recorder and part-time observer, or if observer 2
# was the pilot, set "observer = 1". This dictates which set of observations form the denominator
# of the double observer system. For example, if "observer = 1", observations by observer 1 that were not seen
# by observer 2 are ignored. The estimate in this case uses targets seen by both observers and
# those seen by observer 2 but not observer 1. If observer = "both", the computation goes both directions.
if( !(all(c("obsby.1", "obsby.2") %in% names(df)))){
stop("Variables 'obsby.1' and 'obsby.2' not found in input data frame.")
}
obs1 <- as.logical( df$obsby.1 )
obs2 <- as.logical( df$obsby.2 )
obs.both <- obs1 & obs2
if( is.character( observer ) ){
if(observer == "both"){
obs.tot <- obs1 | obs2 # this should be all 1's, assuming no extra lines are input (like "unknown")
p1 <- sum( obs.both ) / sum( obs2 )
p2 <- sum( obs.both ) / sum( obs1 )
# Assume observers are independent here. This was checked via simulation. This estimator is close to unbiased when observers are actually independent.
p <- p1 + p2 - p1*p2
} else {
stop("Inappropriate 'observer' parameter")
}
} else if( observer == 1 ){
p <- sum( obs.both ) / sum( obs2 )
} else if( observer == 2 ){
p <- sum( obs.both ) / sum( obs1 )
} else {
stop("Inappropriate 'observer' parameter")
}
p
}
```

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