unmarked (version 1.5.0)

ranef: Estimate posterior distributions of latent occupancy or abundance

Description

Estimate posterior distributions of the random variables (latent occupancy or abundance) using empirical Bayes methods. These methods return an object storing the posterior distributions of the latent variables at each site, and for each year (primary period) in the case of open population models. See unmarkedRanef-class and posteriorSamples for methods used to manipulate the returned object.

Usage

# S4 method for unmarkedFit
ranef(object, ...)

Arguments

object

A unmarkedFit object

...

Other arguments. For some abundance models you can specify K; for multi-species models you can specify species.

Warning

Empirical Bayes methods can underestimate the variance of the posterior distribution because they do not account for uncertainty in the hyperparameters (lambda or psi). Eventually, we hope to add methods to account for the uncertainty of the hyperparameters.

Note also that the posterior mode appears to exhibit some bias as an estimator or abundance. Consider using the posterior mean instead, even though it will not be an integer in general. More simulation studies are needed to evaluate the performance of empirical Bayes methods for these models.

Author

Richard Chandler

References

Laird, N.M. and T.A. Louis. 1987. Empirical Bayes confidence intervals based on bootstrap samples. Journal of the American Statistical Association 82:739--750.

Carlin, B.P and T.A Louis. 1996. Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall/CRC.

Royle, J.A and R.M. Dorazio. 2008. Hierarchical Modeling and Inference in Ecology. Academic Press.

See Also

unmarkedRanef-class, bup

Examples

# Simulate data under N-mixture model
set.seed(4564)
R <- 20
J <- 5
N <- rpois(R, 10)
y <- matrix(NA, R, J)
y[] <- rbinom(R*J, N, 0.5)

# Fit model
umf <- unmarkedFramePCount(y=y)
fm <- pcount(~1 ~1, umf, K=50)

# Estimates of conditional abundance distribution at each site
(re <- ranef(fm))
# Best Unbiased Predictors
bup(re, stat="mean")           # Posterior mean
bup(re, stat="mode")           # Posterior mode
confint(re, level=0.9) # 90% CI

# Plots
plot(re, subset=site %in% c(1:10), layout=c(5, 2), xlim=c(-1,20))

# Compare estimates to truth
sum(N)
sum(bup(re))

# Extract all values in convenient formats
post.df <- as(re, "data.frame")
head(post.df)
post.arr <- as(re, "array")

#Generate posterior predictive distribution for a function
#of random variables using predict()

#First, create a function that operates on a vector of 
#length M (if you fit a single-season model) or a matrix of 
#dimensions MxT (if a dynamic model), where
#M = nsites and T = n primary periods
#Our function will generate mean abundance for sites 1-10 and sites 11-20
myfunc <- function(x){ #x will be length 20 since M=20
  
  #Mean of first 10 sites
  group1 <- mean(x[1:10])
  #Mean of sites 11-20
  group2 <- mean(x[11:20])
  
  #Naming elements of the output is optional but helpful
  return(c(group1=group1, group2=group2))

}

#Get 100 samples of the values calculated in your function
(pr <- predict(re, func=myfunc, nsims=100))

#Summarize posterior
data.frame(mean=rowMeans(pr),
           se=apply(pr, 1, stats::sd),
           lower=apply(pr, 1, stats::quantile, 0.025),
           upper=apply(pr, 1, stats::quantile, 0.975))

#Alternatively, you can return the posterior predictive distribution
#and run operations on it separately
(ppd <- posteriorSamples(re, nsims=100))