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

The function predict collects posterior predictive samples for a set of new locations given an object of class `stMsPGOcc`. Prediction is possible for both the latent occupancy state as well as detection. Predictions are currently only possible for sampled primary time periods.

Usage

# S3 method for stMsPGOcc
predict(object, X.0, coords.0, t.cols, n.omp.threads = 1, 
                          verbose = TRUE, n.report = 100, 
                          ignore.RE = FALSE, type = 'occupancy', grid.index.0, ...)

Arguments

object: an object of class stMsPGOcc
X.0: the design matrix of covariates at the prediction locations. This should be a three-dimensional array, with dimensions corresponding to site, primary time period, and covariate, respectively. Note that the first covariate should consist of all 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/time periods should be included as an element of the three-dimensional array. The ordering of the levels should match the ordering used to fit the data in stMsPGOcc. The covariates should be organized in the same order as they were specified in the corresponding formula argument of stMsPGOcc. Names of the third dimension (covariates) of any random effects in X.0 must match the name of the random effects used to fit the model, if specified in the corresponding formula argument of stMsPGOcc. See example below.
coords.0: the spatial coordinates corresponding to X.0. Note that spOccupancy assumes coordinates are specified in a projected coordinate system.
t.cols: an indexing vector used to denote which primary time periods are contained in the design matrix of covariates at the prediction locations (X.0). The values should denote the specific primary time periods used to fit the model. The values should indicate the columns in data$y used to fit the model for which prediction is desired. See example below.
n.omp.threads: a positive integer indicating the number of threads to use for SMP parallel processing. The package must be compiled for OpenMP support. For most Intel-based machines, we recommend setting n.omp.threads up to the number of hyperthreaded cores. Note, n.omp.threads > 1 might not work on some systems.
verbose: if TRUE, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen.
ignore.RE: logical value that specifies whether or not to remove random unstructured occurrence (or detection if type = 'detection') effects from the subsequent predictions. If TRUE, random effects will be included. If FALSE, unstructured random effects will be set to 0 and predictions will only be generated from the fixed effects, the spatial random effects, and AR(1) random effects if the model was fit with ar1 = TRUE.
n.report: the interval to report sampling progress.
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.
grid.index.0: an indexing vector used to specify how each row in X.0 corresponds to the coordinates specified in coords.0. Only relevant if the spatial random effect was estimated at a higher spatial resolution (e.g., grid cells) than point locations.
...: currently no additional arguments

Note

When ignore.RE = FALSE, both sampled levels and non-sampled levels of unstructured 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.

Occurrence predictions at sites that are only sampled for a subset of the total number of primary time periods are obtained directly when fitting the model. See the psi.samples and z.samples portions of the output list from the model object of class stMsPGOcc.

Author

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

Value

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

psi.0.samples: a four-dimensional object of posterior predictive samples for the latent occupancy probability values with dimensions corresponding to posterior predictive sample, species, site, and primary time period.
z.0.samples: a three-dimensional object of posterior predictive samples for the latent occupancy values with dimensions corresponding to posterior predictive sample, species, site, and primary time period.
w.0.samples: a three-dimensional array of posterior predictive samples for the latent spatial factors with dimensions correpsonding to MCMC sample, latent factor, and site.

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

p.0.samples: a four-dimensional object of posterior predictive samples for the detection probability values with dimensions corresponding to posterior predictive sample, site, and primary time period.

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

Examples

# Simulate Data -----------------------------------------------------------
set.seed(500)
J.x <- 8
J.y <- 8
J <- J.x * J.y
# Years sampled
n.time <- sample(3:10, J, replace = TRUE)
# n.time <- rep(10, J)
n.time.max <- max(n.time)
# Replicates
n.rep <- matrix(NA, J, max(n.time))
for (j in 1:J) {
  n.rep[j, 1:n.time[j]] <- sample(2:4, n.time[j], replace = TRUE)
  # n.rep[j, 1:n.time[j]] <- rep(4, n.time[j])
}
N <- 7
# Community-level covariate effects
# Occurrence
beta.mean <- c(-3, -0.2, 0.5)
trend <- FALSE
sp.only <- 0
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 1.5, 1.4)
# Detection
alpha.mean <- c(0, 1.2, -1.5)
tau.sq.alpha <- c(1, 0.5, 2.3)
p.det <- length(alpha.mean)
# Random effects
psi.RE <- list()
p.RE <- list()
# 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]))
}
sp <- TRUE
svc.cols <- c(1)
p.svc <- length(svc.cols)
n.factors <- 3
phi <- runif(p.svc * n.factors, 3 / .9, 3 / .3)
factor.model <- TRUE
cov.model <- 'exponential'
ar1 <- TRUE
sigma.sq.t <- runif(N, 0.05, 1)
rho <- runif(N, 0.1, 1)

dat <- simTMsOcc(J.x = J.x, J.y = J.y, n.time = n.time, n.rep = n.rep, N = N,
     beta = beta, alpha = alpha, sp.only = sp.only, trend = trend,
     psi.RE = psi.RE, p.RE = p.RE, factor.model = factor.model,
                 svc.cols = svc.cols, n.factors = n.factors, phi = phi, sp = sp,
                 cov.model = cov.model, ar1 = ar1, sigma.sq.t = sigma.sq.t, rho = rho)

# Subset data for prediction
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[, -pred.indx, , , drop = FALSE]
# Occupancy covariates
X <- dat$X[-pred.indx, , , drop = FALSE]
# Prediction covariates
X.0 <- dat$X[pred.indx, , , drop = FALSE]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , , , drop = FALSE]
# Coordinates
coords <- dat$coords[-pred.indx, ]
coords.0 <- dat$coords[pred.indx, ]

occ.covs <- list(occ.cov.1 = X[, , 2],
     occ.cov.2 = X[, , 3])
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,
                  coords = coords)
# Priors
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),
       rho.unif = list(a = -1, b = 1),
       sigma.sq.t.ig = list(a = 0.1, b = 0.1),
                   phi.unif = list(a = 3 / .9, b = 3 / .1))
z.init <- apply(y, c(1, 2, 3), function(a) as.numeric(sum(a, na.rm = TRUE) > 0))
inits.list <- list(alpha.comm = 0, beta.comm = 0, beta = 0,
       alpha = 0, tau.sq.beta = 1, tau.sq.alpha = 1,
       rho = 0.5, sigma.sq.t = 0.5,
       phi = 3 / .5, z = z.init)
# Tuning
tuning.list <- list(phi = 1, rho = 0.5)

# Number of batches
n.batch <- 2
# Batch length
batch.length <- 25
n.burn <- 25
n.thin <- 1
n.samples <- n.batch * batch.length
# Note that this is just a test case and more iterations/chains may need to 
# be run to ensure convergence.
out <- stMsPGOcc(occ.formula = ~ occ.cov.1 + occ.cov.2,
                det.formula = ~ det.cov.1 + det.cov.2,
                data = data.list,
                inits = inits.list,
                n.batch = n.batch,
                batch.length = batch.length,
                accept.rate = 0.43,
                ar1 = TRUE,
                NNGP = TRUE,
                n.neighbors = 5,
                n.factors = n.factors,
                cov.model = 'exponential',
                priors = prior.list,
                tuning = tuning.list,
                n.omp.threads = 1,
                verbose = TRUE,
                n.report = 1,
                n.burn = n.burn,
                n.thin = n.thin,
                n.chains = 1)
#> ----------------------------------------
#> 	Preparing to run the model
#> ----------------------------------------
#> lambda is not specified in initial values.
#> Setting initial values of the lower triangle to 0
#> ----------------------------------------
#> 	Building the neighbor list
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbors of neighbors list
#> ----------------------------------------
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> Spatial Factor NNGP Multi-season Multi-species Occupancy Model with Polya-Gamma latent
#> variables with 48 sites, 7 species, and 10 primary time periods.
#> 
#> Samples per chain: 50 (2 batches of length 25)
#> Burn-in: 25 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 25 
#> 
#> Using the exponential spatial correlation model.
#> 
#> Using 3 latent spatial factors.
#> Using 5 nearest neighbors.
#> 
#> 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 2, 50.00%
#> 	Latent Factor	Parameter	Acceptance	Tuning
#> 	1		phi		64.0		1.02020
#> 	2		phi		56.0		1.02020
#> 	3		phi		88.0		1.02020
#> 	Species		Parameter	Acceptance	Tuning
#> 	1		rho		96.0		0.51010
#> 	2		rho		84.0		0.51010
#> 	3		rho		72.0		0.51010
#> 	4		rho		84.0		0.51010
#> 	5		rho		68.0		0.51010
#> 	6		rho		80.0		0.51010
#> 	7		rho		68.0		0.51010
#> -------------------------------------------------
#> Batch: 2 of 2, 100.00%

summary(out)
#> 
#> Call:
#> stMsPGOcc(occ.formula = ~occ.cov.1 + occ.cov.2, det.formula = ~det.cov.1 + 
#>     det.cov.2, data = data.list, inits = inits.list, priors = prior.list, 
#>     tuning = tuning.list, cov.model = "exponential", NNGP = TRUE, 
#>     n.neighbors = 5, n.factors = n.factors, n.batch = n.batch, 
#>     batch.length = batch.length, accept.rate = 0.43, n.omp.threads = 1, 
#>     verbose = TRUE, ar1 = TRUE, n.report = 1, n.burn = n.burn, 
#>     n.thin = n.thin, n.chains = 1)
#> 
#> Samples per Chain: 50
#> Burn-in: 25
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 25
#> Run Time (min): 0.0028
#> 
#> ----------------------------------------
#> 	Community Level
#> ----------------------------------------
#> Occurrence Means (logit scale): 
#>                Mean     SD    2.5%     50%   97.5% Rhat ESS
#> (Intercept) -3.1954 0.2919 -3.7299 -3.2130 -2.7291   NA  25
#> occ.cov.1    0.5636 0.1224  0.3740  0.5673  0.7532   NA  13
#> occ.cov.2    0.5272 0.5239 -0.3549  0.4481  1.4771   NA  25
#> 
#> Occurrence Variances (logit scale): 
#>               Mean     SD   2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.8643 0.5468 0.3426 0.7342 2.2173   NA   7
#> occ.cov.1   0.1655 0.1898 0.0399 0.1161 0.6132   NA  25
#> occ.cov.2   2.2613 1.7700 0.6033 1.6873 6.8030   NA  25
#> 
#> Detection Means (logit scale): 
#>                Mean     SD    2.5%     50%  97.5% Rhat ESS
#> (Intercept)  0.3483 0.3827 -0.4923  0.4204 0.9452   NA  25
#> det.cov.1    1.0121 0.2185  0.5755  0.9769 1.4039   NA   8
#> det.cov.2   -1.0229 0.7532 -2.2908 -1.0010 0.5570   NA  25
#> 
#> Detection Variances (logit scale): 
#>               Mean     SD   2.5%    50%   97.5% Rhat ESS
#> (Intercept) 0.7999 0.5360 0.2861 0.4979  2.0088   NA  25
#> det.cov.1   0.2021 0.1753 0.0454 0.1439  0.6170   NA  25
#> det.cov.2   4.2037 2.9878 0.9484 3.8357 10.6184   NA  25
#> 
#> ----------------------------------------
#> 	Species Level
#> ----------------------------------------
#> Occurrence (logit scale): 
#>                    Mean     SD    2.5%     50%   97.5% Rhat ESS
#> (Intercept)-sp1 -3.2678 0.2238 -3.6713 -3.2746 -2.8777   NA   5
#> (Intercept)-sp2 -3.3036 0.2637 -3.8166 -3.3394 -2.9198   NA   5
#> (Intercept)-sp3 -3.7154 0.1715 -3.9653 -3.7427 -3.4554   NA   6
#> (Intercept)-sp4 -3.9140 0.4204 -4.6944 -3.9665 -3.1738   NA   5
#> (Intercept)-sp5 -4.0496 0.4544 -5.0515 -3.9128 -3.5246   NA   2
#> (Intercept)-sp6 -1.5687 0.1534 -1.8541 -1.5242 -1.2857   NA  10
#> (Intercept)-sp7 -3.6643 0.1920 -3.9911 -3.6769 -3.3250   NA  18
#> occ.cov.1-sp1    0.2988 0.2143 -0.0450  0.2927  0.7274   NA   8
#> occ.cov.1-sp2    0.6899 0.1399  0.4790  0.6570  0.9067   NA   7
#> occ.cov.1-sp3    0.4741 0.2077  0.1325  0.4913  0.8821   NA   9
#> occ.cov.1-sp4    0.4144 0.2473 -0.1117  0.3948  0.7881   NA   6
#> occ.cov.1-sp5    0.7242 0.1538  0.4686  0.7483  1.0121   NA   9
#> occ.cov.1-sp6    0.2707 0.1579  0.0590  0.2451  0.6280   NA  25
#> occ.cov.1-sp7    1.0389 0.2315  0.6829  1.0442  1.3969   NA  10
#> occ.cov.2-sp1    1.4815 0.3057  0.9415  1.4683  1.9314   NA   7
#> occ.cov.2-sp2    1.9986 0.2007  1.6724  2.0005  2.2729   NA   8
#> occ.cov.2-sp3   -0.8551 0.2283 -1.3189 -0.7893 -0.5885   NA  12
#> occ.cov.2-sp4   -0.5746 0.2389 -0.9716 -0.5406 -0.1571   NA   6
#> occ.cov.2-sp5    0.2369 0.2722 -0.1545  0.2368  0.7573   NA   7
#> occ.cov.2-sp6    1.1040 0.2584  0.6742  1.0424  1.5418   NA   4
#> occ.cov.2-sp7    1.3127 0.1641  1.0320  1.2928  1.6200   NA  25
#> 
#> Detection (logit scale): 
#>                    Mean     SD    2.5%     50%   97.5% Rhat ESS
#> (Intercept)-sp1  1.1430 0.3167  0.7416  1.1106  1.7837   NA   7
#> (Intercept)-sp2 -0.6973 0.1835 -0.9866 -0.6973 -0.4225   NA  25
#> (Intercept)-sp3 -0.0727 0.6205 -1.1066  0.0468  0.9218   NA  10
#> (Intercept)-sp4  1.0372 0.2785  0.5775  1.0518  1.4554   NA  24
#> (Intercept)-sp5  0.1780 0.4290 -0.5290  0.1156  0.7938   NA   8
#> (Intercept)-sp6  0.7014 0.2098  0.3254  0.7455  1.0377   NA  13
#> (Intercept)-sp7 -0.1688 0.2062 -0.5102 -0.1566  0.2150   NA  25
#> det.cov.1-sp1    1.2992 0.2372  0.9180  1.2845  1.6283   NA  23
#> det.cov.1-sp2    0.7861 0.2222  0.4663  0.7384  1.2467   NA  12
#> det.cov.1-sp3    0.5501 0.3393  0.0222  0.5553  1.2552   NA   9
#> det.cov.1-sp4    0.9494 0.2538  0.3487  0.9751  1.2814   NA  25
#> det.cov.1-sp5    1.1180 0.2281  0.7610  1.0572  1.4752   NA  37
#> det.cov.1-sp6    0.8690 0.1400  0.6828  0.9231  1.1108   NA  25
#> det.cov.1-sp7    1.2592 0.2326  0.8154  1.2885  1.6719   NA  11
#> det.cov.2-sp1   -0.2317 0.3018 -0.8039 -0.1536  0.1451   NA   6
#> det.cov.2-sp2   -0.0249 0.1693 -0.2694 -0.0706  0.2792   NA  11
#> det.cov.2-sp3   -4.9103 1.0032 -6.6918 -4.7640 -3.6317   NA   2
#> det.cov.2-sp4   -1.2373 0.2156 -1.5843 -1.2734 -0.7239   NA  25
#> det.cov.2-sp5   -0.6104 0.3098 -1.2420 -0.6630 -0.1337   NA  23
#> det.cov.2-sp6   -2.2039 0.3036 -2.6720 -2.2527 -1.5771   NA  16
#> det.cov.2-sp7   -1.8536 0.3258 -2.4508 -1.7920 -1.4084   NA  10
#> 
#> ----------------------------------------
#> 	Spatio-temporal Covariance: 
#> ----------------------------------------
#>                   Mean     SD    2.5%     50%   97.5% Rhat ESS
#> phi-1          28.9223 1.8729 24.1267 29.7315 29.9908   NA   4
#> phi-2           5.7173 2.0652  3.7635  4.5142  9.6623   NA   6
#> phi-3          21.9339 4.5352 12.1110 22.1993 27.6110   NA  10
#> sigma.sq.t-sp1  0.2524 0.2172  0.0706  0.1963  0.8326   NA  25
#> sigma.sq.t-sp2  0.6711 0.4107  0.2043  0.6104  1.6934   NA   7
#> sigma.sq.t-sp3  0.7681 0.6142  0.2540  0.5694  2.3622   NA   9
#> sigma.sq.t-sp4  0.2899 0.1806  0.1179  0.2270  0.7190   NA  25
#> sigma.sq.t-sp5  0.2449 0.4243  0.0547  0.1025  1.4558   NA   9
#> sigma.sq.t-sp6  0.1156 0.1089  0.0170  0.0929  0.4073   NA   9
#> sigma.sq.t-sp7  2.4598 1.9571  0.6719  1.7630  6.7120   NA   6
#> rho-sp1         0.2603 0.1805 -0.0954  0.2812  0.5782   NA  25
#> rho-sp2         0.6910 0.1474  0.3673  0.6996  0.8655   NA   8
#> rho-sp3         0.5476 0.1113  0.3484  0.5630  0.7117   NA  10
#> rho-sp4         0.8175 0.0796  0.6044  0.8213  0.9069   NA   8
#> rho-sp5         0.7929 0.0738  0.6390  0.8051  0.8866   NA   4
#> rho-sp6         0.1137 0.2946 -0.4302  0.2335  0.5088   NA   4
#> rho-sp7        -0.4087 0.3052 -0.7247 -0.5123  0.1953   NA   4

# Predict at new sites across all n.max.years
# Take a look at array of covariates for prediction
str(X.0)
#>  num [1:16, 1:10, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
# Subset to only grab time periods 1, 2, and 5
t.cols <- c(1, 2, 5)
X.pred <- X.0[, t.cols, ]
out.pred <- predict(out, X.pred, coords.0, t.cols = t.cols, type = 'occupancy')
#> ----------------------------------------
#> 	Prediction description
#> ----------------------------------------
#> Spatial Factor NNGP Multi-season, Multi-species Occupancy model with Polya-Gamma latent
#> variable fit with 48 sites and 3 years.
#> 
#> Number of covariates 3 (including intercept if specified).
#> 
#> Number of spatially-varying covariates 1 (including intercept if specified).
#> 
#> Using the exponential spatial correlation model.
#> 
#> Using 5 nearest neighbors.
#> Using 3 latent spatial factors.
#> 
#> Number of MCMC samples 25.
#> 
#> Predicting at 16 non-sampled locations.
#> 
#> 
#> Source compiled with OpenMP support and model fit using 1 threads.
#> -------------------------------------------------
#> 		Predicting
#> -------------------------------------------------
#> Location: 16 of 16, 100.00%
#> Generating latent occupancy state
str(out.pred)
#> List of 6
#>  $ z.0.samples  : num [1:25, 1:7, 1:16, 1:3] 0 0 0 0 0 1 1 0 0 0 ...
#>  $ w.0.samples  : num [1:25, 1:3, 1:16] 1.008 -0.122 -1.478 0.992 -1.274 ...
#>  $ psi.0.samples: num [1:25, 1:7, 1:16, 1:3] 0.05567 0.00589 0.00324 0.03192 0.00356 ...
#>  $ run.time     : 'proc_time' Named num [1:5] 0 0.01 0.003 0 0
#>   ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
#>  $ call         : language predict.svcTMsPGOcc(object = object, X.0 = X.0, coords.0 = coords.0, t.cols = t.cols,      n.omp.threads = n.omp.| __truncated__ ...
#>  $ object.class : chr "stMsPGOcc"
#>  - attr(*, "class")= chr "predict.svcTMsPGOcc"