Function for prediction at new locations for latent factor multi-species N-mixture models

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

Usage

# S3 method for lfMsNMix
predict(object, X.0, coords.0, ignore.RE = FALSE, 
        type = 'abundance', include.w = TRUE, ...)

Arguments

object: an object of class lfMsNMix
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 abundance (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 lfMsNMix. Columns should correspond to the order of how covariates were specified in the corresponding formula argument of lfMsNMix. Column names must match the names of the variables used to fit the model (for the intercept, use '(Intercept)').
coords.0: the spatial coordinates corresponding to X.0. Note that spOccupancy assumes coordinates are specified in a projected coordinate system. This is not a required argument, but can be used if some of the prediction sites are the same sites as those used to fit the data, in which case the latent factors estimated during model fitting can be used to improve the predictions. If predicting at different sites than those used to fit the data, this argument will not have any influence on model results.
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.
type: a quoted keyword indicating what type of prediction to produce. Valid keywords are 'abundance' to predict expected abundance and latent abundance values (this is the default), or 'detection' to predict detection probability given new values of detection covariates.
include.w: a logical value used to indicate whether the latent random effects should be included in the predictions. By default, this is set to TRUE. If set to FALSE, predictions are given using the covariates and any unstructured random effects in the model. If FALSE, the coords.0 argument is not required.
...: currently no additional arguments

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 effect 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,

Value

A list object of class predict.lfMsNMix. When type = 'abundance', the list consists of:

mu.0.samples: a three-dimensional array of posterior predictive samples for the expected abundance values. Note these will be per unit area if an offset was used when fitting the model with lfMsNMix().
N.0.samples: a three-dimensional array of posterior predictive samples for the latent abundance values. These will be in the same units as mu.0.samples.

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.sp <- 6
# Community-level covariate effects
# Abundance
beta.mean <- c(0.2, 0.5)
p.abund <- 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.sp, ncol = p.abund)
alpha <- matrix(NA, nrow = n.sp, ncol = p.det)
for (i in 1:p.abund) {
  beta[, i] <- rnorm(n.sp, beta.mean[i], sqrt(tau.sq.beta[i]))
}
for (i in 1:p.det) {
  alpha[, i] <- rnorm(n.sp, alpha.mean[i], sqrt(tau.sq.alpha[i]))
}
family <- 'Poisson'
n.factors <- 3

dat <- simMsNMix(J.x = J.x, J.y = J.y, n.rep = n.rep, n.sp = n.sp, beta = beta, alpha = alpha,
                 sp = FALSE, family = 'Poisson', factor.model = TRUE, 
                 n.factors = n.factors)
# Split into fitting and prediction data set
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[, -pred.indx, ]
# Abundance covariates
X <- dat$X[-pred.indx, ]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , ]
# Coordinates
coords <- dat$coords[-pred.indx, ]
# Prediction values
X.0 <- dat$X[pred.indx, ]
mu.0 <- dat$psi[, pred.indx]
coords.0 <- dat$coords[pred.indx, ]
# Package all data into a list
abund.covs <- X[, 2, drop = FALSE]
colnames(abund.covs) <- c('abund.cov')
det.covs <- list(det.cov.1 = X.p[, , 2], 
                 det.cov.2 = X.p[, , 3])
data.list <- list(y = y, 
                  abund.covs = abund.covs,
                  det.covs = det.covs, 
                  coords = coords)

# 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, 
                   N = apply(y, c(1, 2), max, na.rm = TRUE))
# Tuning values
tuning <- list(beta = 0.3, alpha = 0.3, lambda = 0.5, w = 0.5)
n.batch <- 4
batch.length <- 25
accept.rate <- 0.43

out <- lfMsNMix(abund.formula = ~ abund.cov, 
                det.formula = ~ det.cov.1 + det.cov.2, 
                data = data.list, 
                inits = inits.list, 
                family = 'Poisson', 
                n.factors = n.factors,
                n.batch = n.batch,
                batch.length = batch.length, 
                accept.rate = 0.43,
                tuning = tuning,
                priors = prior.list, 
                n.omp.threads = 1, 
                verbose = TRUE, 
                n.report = 1)
#> ----------------------------------------
#> 	Preparing to run the model
#> ----------------------------------------
#> lambda is not specified in initial values.
#> Setting initial values of the lower triangle to 0
#> w is not specified in initial values.
#> Setting initial value to 0
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> Latent Factor Multi-species Poisson N-Mixture model fit with 48 sites and 6 species.
#> 
#> Samples per Chain: 100 
#> Burn-in: 10 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 90 
#> 
#> Using 3 latent factors.
#> 
#> 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 4, 25.00%
#> 	Species	Parameter	Acceptance	Tuning
#> 	1	beta[1]		32.0		0.29406
#> 	1	alpha[1]	12.0		0.29406
#> 	2	beta[1]		48.0		0.30606
#> 	2	alpha[1]	72.0		0.30606
#> 	3	beta[1]		40.0		0.30000
#> 	3	alpha[1]	52.0		0.30000
#> 	4	beta[1]		36.0		0.29406
#> 	4	alpha[1]	52.0		0.30000
#> 	5	beta[1]		28.0		0.30000
#> 	5	alpha[1]	44.0		0.30606
#> 	6	beta[1]		64.0		0.30606
#> 	6	alpha[1]	48.0		0.30000
#> -------------------------------------------------
#> Batch: 2 of 4, 50.00%
#> 	Species	Parameter	Acceptance	Tuning
#> 	1	beta[1]		16.0		0.29113
#> 	1	alpha[1]	36.0		0.29113
#> 	2	beta[1]		44.0		0.30914
#> 	2	alpha[1]	76.0		0.30914
#> 	3	beta[1]		48.0		0.30302
#> 	3	alpha[1]	52.0		0.30302
#> 	4	beta[1]		40.0		0.29113
#> 	4	alpha[1]	32.0		0.29701
#> 	5	beta[1]		32.0		0.29701
#> 	5	alpha[1]	24.0		0.30302
#> 	6	beta[1]		68.0		0.30914
#> 	6	alpha[1]	68.0		0.30302
#> -------------------------------------------------
#> Batch: 3 of 4, 75.00%
#> 	Species	Parameter	Acceptance	Tuning
#> 	1	beta[1]		20.0		0.28824
#> 	1	alpha[1]	28.0		0.28824
#> 	2	beta[1]		28.0		0.30606
#> 	2	alpha[1]	72.0		0.31224
#> 	3	beta[1]		32.0		0.30000
#> 	3	alpha[1]	36.0		0.30000
#> 	4	beta[1]		24.0		0.28824
#> 	4	alpha[1]	32.0		0.29406
#> 	5	beta[1]		36.0		0.29406
#> 	5	alpha[1]	40.0		0.30000
#> 	6	beta[1]		68.0		0.31224
#> 	6	alpha[1]	64.0		0.30606
#> -------------------------------------------------
#> Batch: 4 of 4, 100.00%

summary(out, level = 'community')
#> 
#> Call:
#> lfMsNMix(abund.formula = ~abund.cov, det.formula = ~det.cov.1 + 
#>     det.cov.2, data = data.list, inits = inits.list, priors = prior.list, 
#>     tuning = tuning, n.factors = n.factors, n.batch = n.batch, 
#>     batch.length = batch.length, accept.rate = 0.43, family = "Poisson", 
#>     n.omp.threads = 1, verbose = TRUE, n.report = 1)
#> 
#> Samples per Chain: 100
#> Burn-in: 10
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 90
#> Run Time (min): 0.0029
#> 
#> ----------------------------------------
#> 	Community Level
#> ----------------------------------------
#> Abundance Means (log scale): 
#>                Mean     SD    2.5%     50%  97.5% Rhat ESS
#> (Intercept) -0.0142 0.3828 -0.6969 -0.0463 0.6221   NA  90
#> abund.cov    0.2797 0.3523 -0.7011  0.3447 0.8543   NA  90
#> 
#> Abundance Variances (log scale): 
#>               Mean     SD   2.5%    50%  97.5% Rhat ESS
#> (Intercept) 1.1445 0.7898 0.3160 0.8258 3.2644   NA  90
#> abund.cov   1.1538 4.9788 0.0766 0.4847 2.0539   NA  90
#> 
#> Detection Means (logit scale): 
#>                Mean     SD    2.5%     50%  97.5% Rhat ESS
#> (Intercept)  0.6193 0.2061  0.3099  0.6239 1.0120   NA  90
#> det.cov.1    0.2765 0.2507 -0.1387  0.2949 0.6849   NA  90
#> det.cov.2   -0.2658 0.5315 -1.2368 -0.3161 0.9059   NA  75
#> 
#> Detection Variances (logit scale): 
#>               Mean     SD   2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.2759 0.2349 0.0826 0.1709 0.8493   NA  90
#> det.cov.1   0.3557 0.3977 0.0717 0.2305 1.3313   NA  90
#> det.cov.2   1.5663 1.2003 0.3782 1.0704 4.7341   NA  14

# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0)
str(out.pred)
#> List of 3
#>  $ mu.0.samples: num [1:90, 1:6, 1:16] 3.263 1.849 3.996 0.134 4.197 ...
#>  $ N.0.samples : int [1:90, 1:6, 1:16] 6 4 6 0 5 10 2 18 8 2 ...
#>  $ call        : language predict.lfMsNMix(object = out, X.0 = X.0, coords.0 = coords.0)
#>  - attr(*, "class")= chr "predict.lfMsNMix"