waicAbund {spAbundance}

Compute Widely Applicable Information Criterion for spAbundance Model Objects

Description

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

Usage

waicAbund(object, N.max, by.species = FALSE, ...)

Arguments

object

an object of class NMix, spNMix, msNMix, lfMsNMix, sfMsNMix, abund, spAbund, msAbund, lfMsAbund, sfMsAbund, DS, spDS, msDS, lfMsDS, sfMsDS.

N.max

values indicating the upper limit on the latent abundance values when calculating WAIC for N-mixture models or hierarchical distance sampling models. For single-species models, this can be a single value or a vector of different values for each site. For multi-species models, this can be a single value, a vector of values for each species, or a species by site matrix for a separate value for each species/site combination. Defaults to ten plus the largest abundance value for each site/species in the posterior samples object$N.samples.

by.species

a logical value indicating whether or not WAIC should be reported individually for each species (TRUE) or summed across the entire community (FALSE) for multi-species models. Ignored for single species models.

...

currently no additional arguments

Details

The effective number of parameters is calculated following the recommendations of Gelman et al. (2014).

Value

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. If calculating WAIC for a multi-species model and by.species = TRUE, this will be a data frame with rows corresponding to the different species.

Note

When fitting zero-inflated Gaussian models, the WAIC is only calculated for the non-zero values. If fitting a first stage model with spOccupancy to the binary portion of the zero-inflated model, you can use the spOccupancy::waicOcc function to calculate WAIC for the binary component.

Author(s)

Jeffrey W. Doser [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(1010)
J.x <- 15
J.y <- 15
J <- J.x * J.y
n.rep <- sample(3, J, replace = TRUE)
beta <- c(0, -1.5, 0.3, -0.8)
p.abund <- length(beta)
mu.RE <- list(levels = c(30), sigma.sq.mu = c(1.3))
kappa <- 0.5
sp <- FALSE 
family <- 'NB'
dat <- simAbund(J.x = J.x, J.y = J.y, n.rep = n.rep, beta = beta, 
                kappa = kappa, mu.RE = mu.RE, sp = sp, family = 'NB')

y <- dat$y
X <- dat$X
X.re <- dat$X.re

abund.covs <- list(int = X[, , 1], 
                   abund.cov.1 = X[, , 2], 
                   abund.cov.2 = X[, , 3], 
                   abund.cov.3 = X[, , 4],
                   abund.factor.1 = X.re[, , 1])

data.list <- list(y = y, covs = abund.covs)

# Priors
prior.list <- list(beta.normal = list(mean = 0, var = 100),
                   kappa.unif = c(0.001, 10)) 
# Starting values
inits.list <- list(beta = 0, kappa = kappa)

n.batch <- 5
batch.length <- 25
n.burn <- 0
n.thin <- 1
n.chains <- 1

out <- abund(formula = ~ abund.cov.1 + abund.cov.2 + abund.cov.3 + 
                         (1 | abund.factor.1),
             data = data.list, 
             n.batch = n.batch, 
             batch.length = batch.length, 
             inits = inits.list, 
             priors = prior.list, 
             accept.rate = 0.43, 
             n.omp.threads = 1, 
             verbose = TRUE, 
             n.report = 1,
             n.burn = n.burn,
             n.thin = n.thin,
             n.chains = n.chains) 

# Calculate WAIC
waicAbund(out)