estimate_ehat_variance {AnglerCreelSurveySimulation}

Calculate within-day variance of estimated effort (Ehat)

Description

This function multiple outputs from simulate_bus_route to estimate the variance in estimated effort, \widehat{E}.

Usage

estimate_ehat_variance(data)

Arguments

data

A dataframe of output from simulate_bus_route.

Details

The variance in \widehat{E} is estimated from multiple simulated surveys on a single theoretical day (Within-day variance of \widehat{E}. The variance is estimated by

\frac{1}{n(n-1)}\sum(\widehat{T}_{ph}-\overline{\widehat{T}}_{ph})^2

where \widehat{T}_{ph} is the total estimated party hours for an individual survey (i.e., \widehat{E}), and \overline{\widehat{T}}_{ph} is the mean of the \widehat{E}, and n is how many simulations were run. The equation above matches the variables used in Jones et al. (1990).

Jones et al. (1990) stated that estimating within-day variance would require several crews conducting two or more randomized surveys along a given route on the same day. They use this conservative estimator of variance for building confidence intervals around the estimates of effort.

Value

The variance in estimated effort, Ehat (\widehat{E}), from Robson and Jones (1989) and Jones et al. (1990).

Author(s)

Steven H. Ranney

References

Jones, C. M., D. Robson, D. Otis, S. Gloss. 1990. Use of a computer model to determine the behavior of a new survey estimator of recreational angling. Transactions of the American Fisheries Society 119:41-54.

Robson, D., and C. M. Jones. 1989. The theoretical basis of an access site angler survey design. Biometrics 45:83-98.

Examples

#Set up a simulation to run repeatedly
## Not run: 
start_time = c(0, 1.5)
wait_time = c(1, 6.5)
fishing_day_length <- 12
n_anglers = c(50, 300)
n_sites = 2
sampling_prob <- sum(wait_time)/fishing_day_length
mean_catch_rate <- 2.5

# Simulate the creel survey n times
times <- 100

sims <- 
  matrix(data = NA, nrow = times, ncol = 5) %>% 
  as.data.frame()

names(sims) = c("Ehat", "catch_rate_ROM", "true_catch", "true_effort", "mean_lambda")

for(i in 1:times){
  
sims[i, ] <- simulate_bus_route(start_time, wait_time, n_anglers, n_sites, 
                                sampling_prob, mean_catch_rate)
  
}

estimate_ehat_variance(sims)

## End(Not run)