Function for prediction at new locations for multi-species occupancy models

The function predict collects posterior predictive samples for a set of new locations given an object of class `msPGOcc`. Prediction is possible for both the latent occupancy state as well as detection.

Usage

# S3 method for msPGOcc
predict(object, X.0, ignore.RE = FALSE, type = 'occupancy', ...)

Arguments

object: an object of class msPGOcc
X.0: the design matrix of covariates at the prediction locations. This should include a column of 1s for the intercept if an intercept is included in the model. If random effects are included in the occupancy (or detection if type = 'detection') portion of the model, the levels of the random effects at the new locations should be included as a column in the design matrix. The ordering of the levels should match the ordering used to fit the data in msPGOcc. Columns should correspond to the order of how covariates were specified in the corresponding formula argument of msPGOcc. Column names of the random effects must match the name of the random effects, if specified in the corresponding formula argument of msPGOcc.
ignore.RE: a logical value indicating whether to include unstructured random effects for prediction. If TRUE, random effects will be ignored and prediction will only use the fixed effects. If FALSE, random effects will be included in the prediction for both observed and unobserved levels of the random effect.
...: currently no additional arguments
type: a quoted keyword indicating what type of prediction to produce. Valid keywords are 'occupancy' to predict latent occupancy probability and latent occupancy values (this is the default), or 'detection' to predict detection probability given new values of detection covariates.

Note

When ignore.RE = FALSE, both sampled levels and non-sampled levels of random effects are supported for prediction. For sampled levels, the posterior distribution for the random intercept corresponding to that level of the random effect will be used in the prediction. For non-sampled levels, random values are drawn from a normal distribution using the posterior samples of the random effect variance, which results in fully propagated uncertainty in predictions with models that incorporate random effects.

Author

Jeffrey W. Doser doserjef@msu.edu,
Andrew O. Finley finleya@msu.edu

Value

A list object of class predict.msPGOcc. When type = 'occupancy', the list consists of:

psi.0.samples: a three-dimensional array of posterior predictive samples for the latent occurrence probability values.
z.0.samples: a three-dimensional array of posterior predictive samples for the latent occurrence values.

When type = 'detection', the list consists of:

p.0.samples: a three-dimensional array of posterior predictive samples for the detection probability values.

The return object will include additional objects used for standard extractor functions.

Examples

set.seed(400)
J.x <- 8
J.y <- 8
J <- J.x * J.y
n.rep<- sample(2:4, size = J, replace = TRUE)
N <- 6
# Community-level covariate effects
# Occurrence
beta.mean <- c(0.2, 0.5)
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 0.3)
# Detection
alpha.mean <- c(0.5, 0.2, -0.1)
tau.sq.alpha <- c(0.2, 0.3, 1)
p.det <- length(alpha.mean)
# Draw species-level effects from community means.
beta <- matrix(NA, nrow = N, ncol = p.occ)
alpha <- matrix(NA, nrow = N, ncol = p.det)
for (i in 1:p.occ) {
  beta[, i] <- rnorm(N, beta.mean[i], sqrt(tau.sq.beta[i]))
}
for (i in 1:p.det) {
  alpha[, i] <- rnorm(N, alpha.mean[i], sqrt(tau.sq.alpha[i]))
}

dat <- simMsOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, N = N, beta = beta, alpha = alpha,
                sp = FALSE)
n.samples <- 5000
# Split into fitting and prediction data set
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[, -pred.indx, ]
# Occupancy covariates
X <- dat$X[-pred.indx, ]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , ]
# Prediction values
X.0 <- dat$X[pred.indx, ]
psi.0 <- dat$psi[, pred.indx]
# Package all data into a list
occ.covs <- X[, 2, drop = FALSE]
colnames(occ.covs) <- c('occ.cov')
det.covs <- list(det.cov.1 = X.p[, , 2], 
                 det.cov.2 = X.p[, , 3])
data.list <- list(y = y, 
                  occ.covs = occ.covs,
                  det.covs = det.covs)

# Occupancy initial values
prior.list <- list(beta.comm.normal = list(mean = 0, var = 2.72), 
                   alpha.comm.normal = list(mean = 0, var = 2.72), 
                   tau.sq.beta.ig = list(a = 0.1, b = 0.1), 
                   tau.sq.alpha.ig = list(a = 0.1, b = 0.1))
# Initial values
inits.list <- list(alpha.comm = 0, 
                   beta.comm = 0, 
                   beta = 0, 
                   alpha = 0,
                   tau.sq.beta = 1, 
                   tau.sq.alpha = 1, 
                   z = apply(y, c(1, 2), max, na.rm = TRUE))

out <- msPGOcc(occ.formula = ~ occ.cov, 
               det.formula = ~ det.cov.1 + det.cov.2, 
               data = data.list, 
               inits = inits.list, 
               n.samples = n.samples, 
               priors = prior.list, 
               n.omp.threads = 1, 
               verbose = TRUE, 
               n.report = 1000, 
               n.burn = 4000)
#> ----------------------------------------
#> 	Preparing to run the model
#> ----------------------------------------
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> Multi-species Occupancy Model with Polya-Gamma latent
#> variable fit with 48 sites and 6 species.
#> 
#> Samples per Chain: 5000 
#> Burn-in: 4000 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 1000 
#> 
#> 
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#> 
#> ----------------------------------------
#> 	Chain 1
#> ----------------------------------------
#> Sampling ... 
#> Sampled: 1000 of 5000, 20.00%
#> -------------------------------------------------
#> Sampled: 2000 of 5000, 40.00%
#> -------------------------------------------------
#> Sampled: 3000 of 5000, 60.00%
#> -------------------------------------------------
#> Sampled: 4000 of 5000, 80.00%
#> -------------------------------------------------
#> Sampled: 5000 of 5000, 100.00%

summary(out, level = 'community')
#> 
#> Call:
#> msPGOcc(occ.formula = ~occ.cov, det.formula = ~det.cov.1 + det.cov.2, 
#>     data = data.list, inits = inits.list, priors = prior.list, 
#>     n.samples = n.samples, n.omp.threads = 1, verbose = TRUE, 
#>     n.report = 1000, n.burn = 4000)
#> 
#> Samples per Chain: 5000
#> Burn-in: 4000
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 1000
#> Run Time (min): 0.0192
#> 
#> ----------------------------------------
#> 	Community Level
#> ----------------------------------------
#> Occurrence Means (logit scale): 
#>               Mean     SD    2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.1259 0.3205 -0.5543 0.1292 0.7473   NA 586
#> occ.cov     0.1703 0.2755 -0.3688 0.1679 0.7119   NA 563
#> 
#> Occurrence Variances (logit scale): 
#>               Mean     SD   2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.5821 0.6561 0.0692 0.3778 2.4334   NA 334
#> occ.cov     0.4010 0.5875 0.0430 0.2336 1.7680   NA 444
#> 
#> Detection Means (logit scale): 
#>                Mean     SD    2.5%     50%  97.5% Rhat ESS
#> (Intercept)  0.1934 0.2271 -0.2483  0.1924 0.6226   NA 373
#> det.cov.1    0.4117 0.2916 -0.1355  0.3988 1.0363   NA 637
#> det.cov.2   -0.4645 0.6105 -1.6800 -0.4799 0.7776   NA 763
#> 
#> Detection Variances (logit scale): 
#>               Mean     SD   2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.2155 0.2791 0.0287 0.1326 0.8872   NA 330
#> det.cov.1   0.4075 0.4803 0.0533 0.2625 1.7310   NA 309
#> det.cov.2   2.6993 3.0828 0.4493 1.8124 9.8362   NA 138

# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0)