:earth_americas: An R package for spatial and spatiotemporal GLMMs with TMB
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "50%",
cache = FALSE,
autodep = TRUE,
dpi = 72
)
sdmTMB can be installed from CRAN:
install.packages("sdmTMB", dependencies = TRUE)
Assuming you have a C++ compiler installed, the development version is recommended and can be installed:
# install.packages("pak")
pak::pkg_install("pbs-assess/sdmTMB", dependencies = TRUE)
There are some extra utilities in the sdmTMBextra package.
Importantly, it is recommended to use an optimized BLAS library, which will result in major speed improvements for TMB (and other) models in R (e.g., often 8-fold speed increases for sdmTMB models).
Suggested installation instructions for Mac users, Linux users, Windows users, and Windows users without admin privileges.
To check that you’ve successfully linked the optimized BLAS, start a new session and run:
m <- 1e4; n <- 1e3; k <- 3e2
X <- matrix(rnorm(m*k), nrow=m); Y <- matrix(rnorm(n*k), ncol=n)
system.time(X %*% Y)
The result (‘elapsed’) should take a fraction of a second (e.g., 0.03 s), not multiple seconds.
Analyzing geostatistical data (coordinate-referenced observations from some underlying spatial process) is becoming increasingly common in ecology.
sdmTMB implements geostatistical spatial and spatiotemporal GLMMs using TMB for model fitting and R-INLA to set up SPDE (stochastic partial differential equation) matrices.
One common application is for species distribution models (SDMs), hence the package name.
The goal of sdmTMB is to provide a fast, flexible, and user-friendly interface—similar to the popular R package glmmTMB—but with a focus on spatial and spatiotemporal models with an SPDE approach.
We extend the generalized linear mixed models (GLMMs) familiar to ecologists to include the following optional features:
s() notation from mgcvtweedie(), nbinom1(), nbinom2(), lognormal(), and student(), plus some truncated and censored familiesdelta_gamma(), delta_lognormal(), and delta_truncated_nbinom2()Estimation is performed in sdmTMB via maximum marginal likelihood with the objective function calculated in TMB and minimized in R via stats::nlminb() with the random effects integrated over via the Laplace approximation.
The sdmTMB package also allows for models to be passed to Stan via tmbstan, allowing for Bayesian model estimation.
See ?sdmTMB and ?predict.sdmTMB for the most complete examples. Also see the vignettes (‘Articles’) on the documentation site and the preprint and appendices linked to below.
For questions about how to use sdmTMB or interpret the models, please post on the discussion board. If you email a question, we are likely to respond on the discussion board with an anonymized version of your question (and without data) if we think it could be helpful to others. Please let us know if you don’t want us to do that.
For bugs or feature requests, please post in the issue tracker.
Slides and recordings from a workshop on sdmTMB.
To cite sdmTMB in publications use:
citation("sdmTMB")
Anderson, S.C., E.J. Ward, P.A. English, L.A.K. Barnett., J.T. Thorson.
2024. sdmTMB: an R package for fast, flexible, and
user-friendly generalized linear mixed effects models with
spatial and spatiotemporal random fields. bioRxiv
2022.03.24.485545; doi: https://doi.org/10.1101/2022.03.24.485545
A list of (known) publications that use sdmTMB can be found here. Please use the above citation so we can track publications.
sdmTMB is heavily inspired by the VAST R package:
Thorson, J.T. 2019. Guidance for decisions using the Vector Autoregressive Spatio-Temporal (VAST) package in stock, ecosystem, habitat and climate assessments. Fisheries Research 210: 143–161. https://doi.org/10.1016/j.fishres.2018.10.013.
and the glmmTMB R package:
Brooks, M.E., Kristensen, K., van Benthem, K.J., Magnusson, A., Berg, C.W., Nielsen, A., Skaug, H.J., Maechler, M., and Bolker, B.M. 2017. glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. The R Journal 9(2): 378–400. https://doi.org/10.32614/rj-2017-066.
INLA and inlabru can fit many of the same models as sdmTMB (and many more) in an approximate Bayesian inference framework.
mgcv can fit similar SPDE-based Gaussian random field models with code included in Miller et al. (2019).
A table in the sdmTMB preprint describes functionality and timing comparisons between sdmTMB, VAST, INLA/inlabru, and mgcv and the discussion makes suggestions about when you might choose one package over another.
An sdmTMB model requires a data frame that contains a response column, columns for any predictors, and columns for spatial coordinates.
It usually makes sense to convert the spatial coordinates to an equidistant projection such as UTMs such that distance remains constant throughout the study region [e.g., using sf::st_transform()].
Here, we illustrate a spatial model fit to Pacific cod (Gadus macrocephalus) trawl survey data from Queen Charlotte Sound, BC, Canada.
Our model contains a main effect of depth as a penalized smoother, a spatial random field, and Tweedie observation error.
Our data frame pcod (built into the package) has a column year for the year of the survey, density for density of Pacific cod in a given survey tow, present for whether density > 0, depth for depth in meters of that tow, and spatial coordinates X and Y, which are UTM coordinates in kilometres.
library(dplyr)
library(ggplot2)
library(sdmTMB)
head(pcod)
library(dplyr)
library(ggplot2)
library(sdmTMB)
theme_set(theme_light())
dplyr::select(pcod, year, density, present, depth, X, Y) %>%
head(n = 3)
We start by creating a mesh object that contains matrices to apply the SPDE approach.
mesh <- make_mesh(pcod, xy_cols = c("X", "Y"), cutoff = 10)
Here, cutoff defines the minimum allowed distance between points in the units of X and Y (km). Alternatively, we could have created any mesh via the fmesher or INLA packages and supplied it to make_mesh().
We can inspect our mesh object with the associated plotting method plot(mesh).
Fit a spatial model with a smoother for depth:
fit <- sdmTMB(
density ~ s(depth),
data = pcod,
mesh = mesh,
family = tweedie(link = "log"),
spatial = "on"
)
Print the model fit:
fit
The output indicates our model was fit by maximum (marginal) likelihood (ML). We also see the formula, mesh, fitted data, and family. Next we see any estimated main effects including the linear component of the smoother (sdepth), the standard deviation on the smoother weights (sds(depth)), the Tweedie dispersion and power parameters, the Matérn range distance (distance at which points are effectively independent), the marginal spatial field standard deviation, and the negative log likelihood at convergence.
We can extract parameters as a data frame:
tidy(fit, conf.int = TRUE)
tidy(fit, effects = "ran_pars", conf.int = TRUE)
Run some basic sanity checks on our model:
sanity(fit)
Use the ggeffects package to plot the smoother effect:
ggeffects::ggpredict(fit, "depth [50:400, by=2]") |> plot()
If the depth effect was parametric and not a penalized smoother, we could have alternatively used ggeffects::ggeffect() for a fast marginal effect plot.
Next, we can predict on new data.
We will use a data frame qcs_grid from the package, which contains all the locations (and covariates) at which we wish to predict.
Here, these newdata are a grid, or raster, covering our survey.
p <- predict(fit, newdata = qcs_grid)
head(p)
select(p, X, Y, depth, est, est_non_rf, est_rf, omega_s) %>%
head(n = 3)
ggplot(p, aes(X, Y, fill = exp(est))) + geom_raster() +
scale_fill_viridis_c(trans = "sqrt")
We could switch to a presence-absence model by changing the response column and family:
fit <- sdmTMB(
present ~ s(depth),
data = pcod,
mesh = mesh,
family = binomial(link = "logit")
)
Or a hurdle/delta model by changing the family:
fit <- sdmTMB(
density ~ s(depth),
data = pcod,
mesh = mesh,
family = delta_gamma(link1 = "logit", link2 = "log"),
)
We could instead fit a spatiotemporal model by specifying the time column and a spatiotemporal structure:
fit_spatiotemporal <- sdmTMB(
density ~ s(depth, k = 5),
data = pcod,
mesh = mesh,
time = "year",
family = tweedie(link = "log"),
spatial = "off",
spatiotemporal = "ar1"
)
If we wanted to create an area-weighted standardized population index, we could predict on a grid covering the entire survey (qcs_grid) with grid cell area 4 (2 x 2 km) and pass the predictions to get_index():
grid_yrs <- replicate_df(qcs_grid, "year", unique(pcod$year))
p_st <- predict(fit_spatiotemporal, newdata = grid_yrs,
return_tmb_object = TRUE)
index <- get_index(p_st, area = rep(4, nrow(grid_yrs)))
ggplot(index, aes(year, est)) +
geom_ribbon(aes(ymin = lwr, ymax = upr), fill = "grey90") +
geom_line(lwd = 1, colour = "grey30") +
labs(x = "Year", y = "Biomass (kg)")
Or the center of gravity:
cog <- get_cog(p_st, format = "wide")
ggplot(cog, aes(est_x, est_y, colour = year)) +
geom_pointrange(aes(xmin = lwr_x, xmax = upr_x)) +
geom_pointrange(aes(ymin = lwr_y, ymax = upr_y)) +
scale_colour_viridis_c()
For more on these basic features, see the vignettes Intro to modelling with sdmTMB and Index standardization with sdmTMB.
Time-varying intercept:
fit <- sdmTMB(
density ~ 0 + s(depth, k = 5),
time_varying = ~ 1,
data = pcod, mesh = mesh,
time = "year",
family = tweedie(link = "log"),
silent = FALSE # see progress
)
Time-varying (random walk) effect of depth:
fit <- sdmTMB(
density ~ 1,
time_varying = ~ 0 + depth_scaled + depth_scaled2,
data = pcod, mesh = mesh,
time = "year",
family = tweedie(link = "log"),
spatial = "off",
spatiotemporal = "ar1",
silent = FALSE
)
See the vignette Intro to modelling with sdmTMB for more details.
Spatially varying effect of time:
pcod$year_scaled <- as.numeric(scale(pcod$year))
fit <- sdmTMB(
density ~ s(depth, k = 5) + year_scaled,
spatial_varying = ~ year_scaled,
data = pcod, mesh = mesh,
time = "year",
family = tweedie(link = "log"),
spatiotemporal = "off"
)
See zeta_s in the output, which represents the coefficient varying in space. You’ll want to ensure you set up your model such that it ballpark has a mean of 0 (e.g., by including it in formula too).
grid_yrs <- replicate_df(qcs_grid, "year", unique(pcod$year))
grid_yrs$year_scaled <- (grid_yrs$year - mean(pcod$year)) / sd(pcod$year)
p <- predict(fit, newdata = grid_yrs) %>%
subset(year == 2011) # any year
ggplot(p, aes(X, Y, fill = zeta_s_year_scaled)) + geom_raster() +
scale_fill_gradient2()
See the vignette on Fitting spatial trend models with sdmTMB for more details.
We can use the same syntax (1 | group) as lme4 or glmmTMB to fit random intercepts:
pcod$year_factor <- as.factor(pcod$year)
fit <- sdmTMB(
density ~ s(depth, k = 5) + (1 | year_factor),
data = pcod, mesh = mesh,
time = "year",
family = tweedie(link = "log")
)
fit <- sdmTMB(
present ~ 1 + breakpt(depth_scaled),
data = pcod, mesh = mesh,
family = binomial(link = "logit")
)
fit <- sdmTMB(
present ~ 1 + logistic(depth_scaled),
data = pcod, mesh = mesh,
family = binomial(link = "logit")
)
See the vignette on Threshold modeling with sdmTMB for more details.
predictor_dat <- expand.grid(
X = seq(0, 1, length.out = 100), Y = seq(0, 1, length.out = 100)
)
mesh <- make_mesh(predictor_dat, xy_cols = c("X", "Y"), cutoff = 0.05)
sim_dat <- sdmTMB_simulate(
formula = ~ 1,
data = predictor_dat,
mesh = mesh,
family = poisson(link = "log"),
range = 0.3,
sigma_O = 0.4,
seed = 1,
B = 1 # B0 = intercept
)
head(sim_dat)
# sample 200 points for fitting:
set.seed(1)
sim_dat_obs <- sim_dat[sample(seq_len(nrow(sim_dat)), 200), ]
ggplot(sim_dat, aes(X, Y)) +
geom_raster(aes(fill = exp(eta))) + # mean without observation error
geom_point(aes(size = observed), data = sim_dat_obs, pch = 21) +
scale_fill_viridis_c() +
scale_size_area() +
coord_cartesian(expand = FALSE)
Fit to the simulated data:
mesh <- make_mesh(sim_dat_obs, xy_cols = c("X", "Y"), cutoff = 0.05)
fit <- sdmTMB(
observed ~ 1,
data = sim_dat_obs,
mesh = mesh,
family = poisson()
)
See ?sdmTMB_simulate for more details.
s <- simulate(fit, nsim = 500)
dim(s)
s[1:3,1:4]
s <- simulate(fit, nsim = 500)
dim(s)
#> [1] 969 500
s[1:3,1:4]
#> [,1] [,2] [,3] [,4]
#> [1,] 0 59.40310 83.20888 0.00000
#> [2,] 0 34.56408 0.00000 19.99839
#> [3,] 0 0.00000 0.00000 0.00000
See the vignette on Residual checking with sdmTMB, ?simulate.sdmTMB, and ?dharma_residuals for more details.
We can take samples from the implied parameter distribution assuming an MVN covariance matrix on the internal parameterization:
samps <- gather_sims(fit, nsim = 1000)
ggplot(samps, aes(.value)) + geom_histogram() +
facet_wrap(~.variable, scales = "free_x")
See ?gather_sims and ?get_index_sims for more details.
The fastest way to get point-wise prediction uncertainty is to use the MVN samples:
p <- predict(fit, newdata = predictor_dat, nsim = 500)
predictor_dat$se <- apply(p, 1, sd)
ggplot(predictor_dat, aes(X, Y, fill = se)) +
geom_raster() +
scale_fill_viridis_c(option = "A") +
coord_cartesian(expand = FALSE)
sdmTMB has built-in functionality for cross-validation. If we were to set a future::plan(), the folds would be fit in parallel:
mesh <- make_mesh(pcod, c("X", "Y"), cutoff = 10)
## Set parallel processing if desired:
# library(future)
# plan(multisession)
m_cv <- sdmTMB_cv(
density ~ s(depth, k = 5),
data = pcod, mesh = mesh,
family = tweedie(link = "log"), k_folds = 2
)
# Sum of log likelihoods of left-out data:
m_cv$sum_loglik
See ?sdmTMB_cv for more details.
Priors/penalties can be placed on most parameters. For example, here we place a PC (penalized complexity) prior on the Matérn random field parameters, a standard normal prior on the effect of depth, a Normal(0, 10^2) prior on the intercept, and a half-normal prior on the Tweedie dispersion parameter (phi):
mesh <- make_mesh(pcod, c("X", "Y"), cutoff = 10)
fit <- sdmTMB(
density ~ depth_scaled,
data = pcod, mesh = mesh,
family = tweedie(),
priors = sdmTMBpriors(
matern_s = pc_matern(range_gt = 10, sigma_lt = 5),
b = normal(c(0, 0), c(1, 10)),
phi = halfnormal(0, 15)
)
)
We can visualize the PC Matérn prior:
plot_pc_matern(range_gt = 10, sigma_lt = 5)
See ?sdmTMBpriors for more details.
The fitted model can be passed to the tmbstan package to sample from the posterior with Stan. See the Bayesian vignette.
We can turn off the random fields for model comparison:
fit_sdmTMB <- sdmTMB(
present ~ poly(depth_scaled, 2),
data = pcod, mesh = mesh,
spatial = "off",
family = binomial()
)
fit_glm <- glm(
present ~ poly(depth_scaled, 2),
data = pcod,
family = binomial()
)
tidy(fit_sdmTMB)
broom::tidy(fit_glm)
Defining a mesh directly with INLA:
bnd <- INLA::inla.nonconvex.hull(cbind(pcod$X, pcod$Y), convex = -0.1)
mesh_inla <- INLA::inla.mesh.2d(
boundary = bnd,
max.edge = c(25, 50)
)
mesh <- make_mesh(pcod, c("X", "Y"), mesh = mesh_inla)
plot(mesh)
fit <- sdmTMB(
density ~ s(depth, k = 5),
data = pcod, mesh = mesh,
family = tweedie(link = "log")
)
A barrier mesh limits correlation across barriers (e.g., land or water). See add_barrier_mesh() in sdmTMBextra.