estimate_ehat_variance: Calculate within-day variance of estimated effort (Ehat)

In stevenranney/AnglerCreelSurveySimulation: Simulate a Bus Route Creel Survey of Anglers

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 total variance in \widehat{E} is estimated from multiple simulated surveys on a single theoretical day. 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 Robson and Jones (1989) and 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. Thus, this is total variance. They use this conservative estimator of variance for building confidence intervals around the estimates of effort.

Value

The total 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)

stevenranney/AnglerCreelSurveySimulation documentation built on May 28, 2024, 7:34 p.m.