waicOcc {spOccupancy}

Compute Widely Applicable Information Criterion for spOccupancy Model Objects

Description

Function for computing the Widely Applicable Information Criterion (WAIC; Watanabe 2010) for spOccupancy model objects.

Usage

waicOcc(object, by.sp = FALSE, ...)

Arguments

object

an object of class PGOcc, spPGOcc, msPGOcc, spMsPGOcc, intPGOcc, spIntPGOcc, lfJSDM, sfJSDM, lfMsPGOcc, sfMsPGOcc, tPGOcc, stPGOcc, svcPGBinom, svcPGOcc, svcTPGBinom, svcTPGOcc, or intMsPGOcc, svcMsPGOcc, tMsPGOcc, stMsPGOcc, svcTMsPGOcc.

by.sp

a logical value indicating whether to return a separate WAIC value for each species in a multi-species occupancy model or a single value for all species.

...

currently no additional arguments

Details

The effective number of parameters is calculated following the recommendations of Gelman et al. (2014). Note that when fitting multi-species occupancy models with the range.ind tag, it is not valid to use WAIC to compare a model that uses range.ind (i.e., restricts certain species to a subset of the locations) with a model that does not use range.ind (i.e., assumes all species can occur at all locations in the data set) or that uses different range.ind values.

Value

When object is of class PGOcc, spPGOcc, msPGOcc, spMsPGOcc, lfJSDM, sfJSDM, lfMsPGOcc, sfMsPGOcc, tPGOcc, stPGOcc, svcPGBinom, svcPGOcc, svcTPGOcc, svcTPGBinom, svcMsPGOcc, tMsPGOcc, stMsPGOcc, svcTMsPGOcc returns a vector with three elements corresponding to estimates of the expected log pointwise predictive density (elpd), the effective number of parameters (pD), and the WAIC. When by.sp = TRUE for multi-species models, object is a data frame with each row corresponding to a different species. When object is of class intPGOcc or spIntPGOcc, returns a data frame with columns elpd, pD, and WAIC, with each row corresponding to the estimated values for each data source in the integrated model.

Author(s)

Jeffrey W. Doser [e-mail],
Andrew O. Finley [e-mail]

References

Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11:3571-3594.

Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. (2013). Bayesian Data Analysis. 3rd edition. CRC Press, Taylor and Francis Group

Gelman, A., J. Hwang, and A. Vehtari (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24:997-1016.

Examples

set.seed(400)
# Simulate Data -----------------------------------------------------------
J.x <- 8
J.y <- 8
J <- J.x * J.y
n.rep <- sample(2:4, J, replace = TRUE)
beta <- c(0.5, -0.15)
p.occ <- length(beta)
alpha <- c(0.7, 0.4)
p.det <- length(alpha)
dat <- simOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, beta = beta, alpha = alpha,
              sp = FALSE)
occ.covs <- dat$X[, 2, drop = FALSE]
colnames(occ.covs) <- c('occ.cov')
det.covs <- list(det.cov = dat$X.p[, , 2])
# Data bundle
data.list <- list(y = dat$y,
                  occ.covs = occ.covs,
                  det.covs = det.covs)

# Priors
prior.list <- list(beta.normal = list(mean = rep(0, p.occ),
                                      var = rep(2.72, p.occ)),
                   alpha.normal = list(mean = rep(0, p.det),
                                       var = rep(2.72, p.det)))
# Initial values
inits.list <- list(alpha = rep(0, p.det),
                   beta = rep(0, p.occ),
                   z = apply(data.list$y, 1, max, na.rm = TRUE))

n.samples <- 5000
n.report <- 1000

out <- PGOcc(occ.formula = ~ occ.cov,
             det.formula = ~ det.cov,
             data = data.list,
             inits = inits.list,
             n.samples = n.samples,
             priors = prior.list,
             n.omp.threads = 1,
             verbose = TRUE,
             n.report = n.report, 
             n.burn = 4000, 
             n.thin = 1)

# Calculate WAIC
waicOcc(out)