Compute Widely Applicable Information Criterion for spAbundance Model Objects
waicAbund.RdFunction for computing the Widely Applicable Information Criterion
(WAIC; Watanabe 2010) for spAbundance model objects.
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$N.samples.- by.species
a logical value indicating whether or not WAIC should be reported individually for each species (
TRUE) or summed across the entire community (FALSE) for multi-species models. Ignored for single species models.- ...
currently no additional arguments
Note
When fitting zero-inflated Gaussian models, the WAIC is only calculated for the
non-zero values. If fitting a first stage model with
spOccupancy to the binary portion of the
zero-inflated model, you can use the spOccupancy::waicOcc function to
calculate WAIC for the binary component.
References
Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11:3571-3594.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. (2013). Bayesian Data Analysis. 3rd edition. CRC Press, Taylor and Francis Group
Gelman, A., J. Hwang, and A. Vehtari (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24:997-1016.
Author
Jeffrey W. Doser doserjef@msu.edu,
Value
Returns a vector with three elements corresponding to
estimates of the expected log pointwise predictive density (elpd), the
effective number of parameters (pD), and the WAIC. If calculating WAIC
for a multi-species model and by.species = TRUE, this will be a
data frame with rows corresponding to the different species.
Details
The effective number of parameters is calculated following the recommendations of Gelman et al. (2014).
Examples
set.seed(1010)
J.x <- 15
J.y <- 15
J <- J.x * J.y
n.rep <- sample(3, J, replace = TRUE)
beta <- c(0, -1.5, 0.3, -0.8)
p.abund <- length(beta)
mu.RE <- list(levels = c(30), sigma.sq.mu = c(1.3))
kappa <- 0.5
sp <- FALSE
family <- 'NB'
dat <- simAbund(J.x = J.x, J.y = J.y, n.rep = n.rep, beta = beta,
kappa = kappa, mu.RE = mu.RE, sp = sp, family = 'NB')
y <- dat$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)
#> ----------------------------------------
#> Preparing to run the model
#> ----------------------------------------
#> No prior specified for sigma.sq.mu.ig.
#> Setting prior shape to 0.1 and prior scale to 0.1
#> sigma.sq.mu is not specified in initial values.
#> Setting initial values to random values between 0.05 and 1
#> ----------------------------------------
#> Model description
#> ----------------------------------------
#> Poisson abundance model fit with 225 sites.
#>
#> Samples per Chain: 125 (5 batches of length 25)
#> Burn-in: 0
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 125
#>
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#>
#> Adaptive Metropolis with target acceptance rate: 43.0
#> ----------------------------------------
#> Chain 1
#> ----------------------------------------
#> Sampling ...
#> Batch: 1 of 5, 20.00%
#> Parameter Acceptance Tuning
#> beta[1] 4.0 0.98020
#> beta[2] 4.0 0.98020
#> beta[3] 8.0 0.98020
#> beta[4] 8.0 0.98020
#> -------------------------------------------------
#> Batch: 2 of 5, 40.00%
#> Parameter Acceptance Tuning
#> beta[1] 4.0 0.97045
#> beta[2] 0.0 0.97045
#> beta[3] 4.0 0.97045
#> beta[4] 8.0 0.97045
#> -------------------------------------------------
#> Batch: 3 of 5, 60.00%
#> Parameter Acceptance Tuning
#> beta[1] 0.0 0.96079
#> beta[2] 4.0 0.96079
#> beta[3] 0.0 0.96079
#> beta[4] 0.0 0.96079
#> -------------------------------------------------
#> Batch: 4 of 5, 80.00%
#> Parameter Acceptance Tuning
#> beta[1] 0.0 0.95123
#> beta[2] 0.0 0.95123
#> beta[3] 4.0 0.95123
#> beta[4] 0.0 0.95123
#> -------------------------------------------------
#> Batch: 5 of 5, 100.00%
# Calculate WAIC
waicAbund(out)
#> elpd pD WAIC
#> -2260.297 11639.301 27799.197