Evidence of Absence Regression Package

These routines implement Evidence of Absence Regression (EoAR) methods described in McDonald et al. (2021, Evidence of absence regression: a binomial N-mixture model for estimating fatalities at wind energy facilities, Ecological Applications, In press, URL pending). The EoAR method estimates the number of (found + missed) entities after a series of searches by using probability of detection and covariate relationships. Special cases are the Evidence of Absence (EoA) model of Huso et al. (2015) and the Informed Evidence of Absence (IEoA) approaches.

Data

Example data analyzed in McDonald et al., (2021) are available on the Dryad digital repository: https://doi.org/10.5061/dryad.2rbnzs7jh.

Installation

EoAR uses MCMC estimation methods implemented in JAGS. Hence, EoAR requires two prerequisites.

1. Install the JAGS run time

The JAGS runtime is the program that actually performs the MCMC computations. Install the JAGS runtime by navigating here: http://www.sourceforge.net/projects/mcmc-jags/files. Download the JAGS installer. Execute it and accept all defaults.

2. Install the rjags R package

The rjags R package communicates with the JAGS runtime and makes running MCMC code in R convienient. rjags is available on R's CRAN repository. To install rjags issue the following command in R:

install.packages("rjags")

Test the JAGS installation: You can test the JAGS and rjags installation by simply attaching rjags in R. If JAGS and rjags are okay, attaching rjags using the library command will result in output similar to the following:

> library(rjags)
Loading required package: coda
Linked to JAGS 4.3.0
Loaded modules: basemod,bugs

If rjags cannot find the JAGS runtime, an error will be issued after the library(rjags) command.

3. Install the EoAR package

The easist way to install EoAR is directly from GitHub using routines in the devtools package. If you do not have devtools, install it with the following command:

install.packages("devtools")

Then, to install EoAR, issue the following command:

devtools::install_github("tmcd82070/EoAR")

Usage Example

The main routine is eoar. The eoar routine takes a count vector, a model for lambda, and g-values as inputs. Following is an eoar example on fake (simulated) data.

The following generates fake data for a three year study on seven sites. We first generate alpha and beta parameters from common normal distributions which we later use to generate site and year specific g-values.

ns <- 7  # Number of sites
ny <- 3  # Number of years
g <- data.frame(  
  alpha = rnorm(ns*ny,70,2),  
  beta = rnorm(ns*ny,700,25)  
)

In this example, we assume that the true average number of carcasses per site increases each year, but does not vary by site. We assume the true average number of carcasses per site in year 1 is 20, year 2 is 40, and year 3 is 60. We assume carcasses at each site each year are detected with probabilities equal to $\alpha / (\alpha + \beta)$, which are the means of beta distributions assumed for g-values. The following generates random observed carcasses counts, one per site per year.

meanYr1 <- 20
meanYr2 <- 40
meanYr3 <- 60
Y <- rbinom(ns*ny, c(rep(meanYr1,ns), rep(meanYr2,ns), rep(meanYr3,ns)), g$alpha/(g$alpha+g$beta))

In this example, we fit a linear trend and annual categories to the true number of carcasses.
We construct the linear Year and factor year covariates in a data frame using the following code:

df <- data.frame(year=factor(c(rep("2015",ns),rep("2016",ns),rep("2017",ns))),  
    Year=c(rep(1,ns),rep(2,ns),rep(3,ns)))

Finally, we relate true carcass deposition rates to year and Year. In this simple example, we assume that we have correctly estimated all g-values by using the generated $\alpha$ and $\beta$ parameters.
This EoAR run uses vague priors for the coefficients.

eoa.1 <- eoar(Y~year, g, df )
eoa.2 <- eoar(Y~Year, g, df )

Informed Priors

When appropriate, it is possible to inform the EoAR coefficient's prior distributios. The following assumes that the prior mean number of carcasses per site is 10 with a standard deviation of 3. The following code fits an intercept-only model.

intMean <- 2*log(10) - 0.5*log(3^2 + 10^2)  
intSd <- sqrt(-2*log(10) + log(3^2 + 10^2))  
prior <- data.frame(mean=intMean, sd=intSd, row.names="(Intercept)")  
eoa.1 <- eoa(Y~1, g, df, priors=prior )  

Model Checks

After running EoAR, you should check convergence.
We suggest running traceplots and Gelman stats. Any Rhats > 1.1 indicate suspect convergence. The following commands are useful for inspecting mixing and convergence:

library(lattice)
xyplot(ieoa.1$out[,labels(ieoa.1)])
acfplot(ieoa.1$out[,labels(ieoa.1)])   
densityplot(ieoa.1$out[,labels(ieoa.1)])  
gelman.diag(ieoa.1$out) # gelmanStats  
gelman.plot(ieoa.1$out) # gelmanPlot