glmmfields 
The glmmfields R package implements Bayesian spatiotemporal models that allow for extreme spatial deviations through time. It uses a predictive process approach with random fields implemented through a multivariate-t distribution instead of a multivariate normal. The models are fit with Stan.
We published a paper describing the model and package in Ecology:
Anderson, S. C., Ward, E. J. 2019. Black swans in space: modelling spatiotemporal processes with extremes. 100(1):e02403. https://doi.org/10.1002/ecy.2403
You can install the CRAN version of the package with:
install.packages("glmmfields")If you have a C++ compiler installed, you can install the development version of the package with:
# install.packages("remotes")
remotes::install_github("seananderson/glmmfields", build_vignettes = TRUE)glmmfields can also fit spatial GLMs with Stan. See the vignette:
vignette("spatial-glms", package = "glmmfields")An example spatiotemporal model
library(glmmfields)
#> Loading required package: Rcpp
library(ggplot2)Simulate data:
set.seed(42)
s <- sim_glmmfields(
df = 2.8, n_draws = 12, n_knots = 12, gp_theta = 2.5,
gp_sigma = 0.2, sd_obs = 0.1
)
head(s$dat)
#> time pt y lon lat station_id
#> 1 1 1 0.02818963 9.148060 6.262453 1
#> 2 1 2 -0.21924739 9.370754 2.171577 2
#> 3 1 3 -0.34719485 2.861395 2.165673 3
#> 4 1 4 -0.15785483 8.304476 3.889450 4
#> 5 1 5 -0.04703617 6.417455 9.424557 5
#> 6 1 6 -0.23904924 5.190959 9.626080 6print(s$plot)
Fit the model:
options(mc.cores = parallel::detectCores()) # for parallel processing
m <- glmmfields(y ~ 0,
data = s$dat, time = "time",
lat = "lat", lon = "lon",
nknots = 12, estimate_df = TRUE, iter = 800, seed = 1
)print(m)
#> Inference for Stan model: glmmfields.
#> 4 chains, each with iter=800; warmup=400; thin=1;
#> post-warmup draws per chain=400, total post-warmup draws=1600.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> df[1] 3.72 0.04 1.47 2.08 2.67 3.37 4.28 7.48 1331 1
#> gp_sigma 0.30 0.00 0.04 0.22 0.27 0.30 0.32 0.39 525 1
#> gp_theta 2.58 0.00 0.07 2.46 2.54 2.58 2.63 2.71 1434 1
#> sigma[1] 0.10 0.00 0.00 0.09 0.10 0.10 0.10 0.10 2207 1
#> lp__ 2291.28 0.42 9.59 2270.34 2285.12 2291.59 2297.73 2308.74 521 1
#>
#> Samples were drawn using NUTS(diag_e) at Mon Feb 13 12:45:42 2023.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).Plot:
plot(m, type = "prediction") + scale_color_gradient2()
plot(m, type = "spatial-residual")
Predictions:
# link scale:
p <- predict(m)
head(p)
#> # A tibble: 6 × 3
#> estimate conf_low conf_high
#> <dbl> <dbl> <dbl>
#> 1 -0.0283 -0.0868 0.0273
#> 2 -0.291 -0.365 -0.220
#> 3 -0.397 -0.448 -0.346
#> 4 -0.196 -0.266 -0.123
#> 5 -0.0370 -0.110 0.0360
#> 6 -0.214 -0.294 -0.140
# posterior predictive intervals on new observations (include observation error):
p <- predictive_interval(m)
head(p)
#> # A tibble: 6 × 3
#> estimate conf_low conf_high
#> <dbl> <dbl> <dbl>
#> 1 -0.0283 -0.236 0.181
#> 2 -0.291 -0.507 -0.0904
#> 3 -0.397 -0.596 -0.206
#> 4 -0.196 -0.392 0.00154
#> 5 -0.0370 -0.239 0.172
#> 6 -0.214 -0.423 -0.00659Use the tidy method to extract parameter estimates as a data frame:
x <- tidy(m, conf.int = TRUE)
head(x)
#> # A tibble: 6 × 5
#> term estimate std.error conf.low conf.high
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 df[1] 3.37 1.47 2.08 7.48
#> 2 gp_sigma 0.295 0.0432 0.216 0.388
#> 3 gp_theta 2.58 0.0662 2.46 2.71
#> 4 sigma[1] 0.0979 0.00214 0.0939 0.102
#> 5 spatialEffectsKnots[1,1] -0.110 0.0341 -0.175 -0.0442
#> 6 spatialEffectsKnots[2,1] -0.230 0.0386 -0.305 -0.155Make predictions on a fine-scale spatial grid:
pred_grid <- expand.grid(
lat = seq(min(s$dat$lat), max(s$dat$lat), length.out = 25),
lon = seq(min(s$dat$lon), max(s$dat$lon), length.out = 25),
time = unique(s$dat$time)
)
pred_grid$prediction <- predict(m,
newdata = pred_grid, type = "response", iter = 100, estimate_method = "median"
)$estimate
ggplot(pred_grid, aes(lon, lat, fill = prediction)) +
facet_wrap(~time) +
geom_raster() +
scale_fill_gradient2()
References
Anderson, S. C., Ward, E. J. 2019. Black swans in space: modelling spatiotemporal processes with extremes. 100(1):e02403. https://doi.org/10.1002/ecy.2403
Latimer, A. M., S. Banerjee, H. Sang Jr, E. S. Mosher, and J. A. Silander Jr. 2009. Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern United States. Ecology Letters 12:144–154.
Shelton, A. O., J. T. Thorson, E. J. Ward, and B. E. Feist. 2014. Spatial semiparametric models improve estimates of species abundance and distribution. Canadian Journal of Fisheries and Aquatic Sciences 71:1655–1666.
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