sdmTMB: Fit a spatial or spatiotemporal GLMM with TMB

In sdmTMB: Spatial and Spatiotemporal SPDE-Based GLMMs with 'TMB'

Fit a spatial or spatiotemporal GLMM with TMB

Description

Fit a spatial or spatiotemporal generalized linear mixed effects model (GLMM) with TMB (Template Model Builder), by default through the RTMB package. Spatial and spatiotemporal Gaussian random fields are approximated with the SPDE (stochastic partial differential equation) approach, which represents them as Gaussian Markov random fields on a mesh. This allows for efficient modelling of data that are correlated in space and/or time. Areal spatial and spatiotemporal models (simultaneous or conditional autoregressive; SAR or CAR) are also available. See the model description vignette for details.

Usage

sdmTMB(
  formula,
  data,
  mesh,
  time = NULL,
  family = gaussian(link = "identity"),
  spatial = c("on", "off"),
  spatiotemporal = c("iid", "ar1", "rw", "off"),
  offset = NULL,
  weights = NULL,
  spatial_model = c("spde", "sar", "car"),
  share_range = TRUE,
  anisotropy = FALSE,
  extra_time = NULL,
  spatial_varying = NULL,
  time_varying = NULL,
  time_varying_type = c("rw", "rw0", "ar1"),
  dispformula = ~1,
  nonlocal_formula = NULL,
  nonlocal_data = NULL,
  knots = NULL,
  censored_upper = NULL,
  distribution_column = NULL,
  silent = TRUE,
  reml = FALSE,
  priors = sdmTMBpriors(),
  bayesian = FALSE,
  control = sdmTMBcontrol(),
  previous_fit = NULL,
  do_fit = TRUE,
  experimental = NULL,
  do_index = FALSE,
  predict_args = NULL,
  index_args = NULL
)

Arguments

formula	A model formula. Random intercepts and slopes use lme4 syntax, e.g., (1 | g), (0 + depth | g), or (1 + depth | g), where g is a character or factor column. As in lme4, intercepts and slopes within a term are correlated. Penalized smooths use mgcv syntax, e.g., s(depth), and threshold terms use breakpt() or logistic(). For delta models, optionally a list of two formulas. See Details.
data	A data frame. Rows with missing values in the response or any variable the model uses (including weights and offset) are omitted before fitting, as with na.action = na.omit in stats::glm(). The rows used are stored in the returned object as data.
mesh	An object from make_mesh() for spatial_model = "spde" or from make_areal_domain() for "sar" or "car".
time	An optional time column name (as character). Can be left as NULL for a model with only spatial random fields; however, if the data are actually spatiotemporal and you wish to calculate derived quantities downstream (e.g., get_index() or get_cog()), then supply the time argument.
family	A family object specifying the response distribution and link: gaussian(), Gamma(), binomial(), poisson(), or one of the additional families listed in Families (e.g., tweedie(), nbinom2(), delta_gamma()). See 'Binomial families', 'Censored families', and 'Delta/hurdle models' in Details. Experimental multi-family models take a named list of families; distribution_column then assigns each row to one of them. See the multi-family vignette for supported combinations.
spatial	Estimate spatial random fields? Options are 'on' / 'off' or equivalently TRUE / FALSE. Optionally, a list for delta models, e.g. list('on', 'off').
spatiotemporal	Estimate the spatiotemporal random fields as 'iid' (independent and identically distributed; default), stationary 'ar1' (first-order autoregressive), a random walk ('rw'), or fixed at 0 'off'. Will be set to 'off' if time = NULL. If a delta model, can be a list. E.g., list('off', 'ar1'). Guidance: Use 'iid' if spatiotemporal correlation is negligible or already accounted for in fixed effects; 'ar1' if correlation between consecutive time steps decays gradually; 'rw' if changes between time steps are cumulative (each step builds on the last). If the AR1 correlation coefficient (rho) is estimated close to 1 (say > 0.99), consider switching to 'rw'. See the model description vignette for mathematical details. Capitalization is ignored. TRUE gets converted to 'iid' and FALSE gets converted to 'off'.
offset	A numeric vector representing the model offset or a character value representing the column name of the offset. In delta/hurdle models, this applies only to the positive component except for Poisson-link delta models, where it also enters the occurrence-probability calculation. Usually a log transformed variable.
weights	An optional numeric vector (not a column name) of weights on each observation's contribution to the likelihood. As in glmmTMB, weights need not sum to one and are not rescaled. For binomial-type families with a proportion response, weights gives the number of trials instead; see 'Binomial families' in Details.
spatial_model	Spatial process model. "spde" uses the default continuous-space SPDE approximation. "sar" and "car" use areal spatial autoregressive models with an areal domain supplied to mesh. Capitalization is ignored.
share_range	Logical: estimate a single range parameter shared by the spatial and spatiotemporal fields (TRUE, default) or separate range parameters (FALSE)? For delta models, can be a list, e.g., list(TRUE, FALSE). Applies to SPDE models only.
anisotropy	Logical: allow for anisotropy (spatial correlation that is directionally dependent)? See plot_anisotropy(). Applies to SPDE models only and is shared by both components of a delta model.
extra_time	Optional extra time slices (e.g., years) to include for interpolation or forecasting with the predict function. See the Details section below.
spatial_varying	An optional one-sided formula of coefficients that should vary in space as random fields. Allows the effect of a covariate to differ spatially. You likely want to include the same variable as a fixed effect in formula to estimate the average effect—the spatial field then represents deviations from that average. For example, use formula = y ~ depth and spatial_varying = ~ 0 + depth to model an average depth effect plus spatially varying deviations. If a (scaled) time column is used, this creates a local-time-trend model. See \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/ecog.05176")} and the spatial trends vignette. Predictors should usually be centered to have mean zero and standard deviation approximately 1. The spatial intercept is controlled by the spatial argument; set spatial = 'on' or 'off' to include or exclude it. For a factor, ~ 0 + f gives every level its own field, which would duplicate the spatial intercept field, so set spatial = 'off' to match. Structure is shared in delta models.
time_varying	An optional one-sided formula of coefficients that vary through time following the process set by time_varying_type. Whether the same covariates should also appear in formula depends on that type. Shared by both components of a delta model.
time_varying_type	The process for time_varying coefficients: 'rw' (default): a random walk with the first value estimated freely. Do not also include these covariates in formula, or the model is not identifiable; e.g., with time_varying = ~ 1, use formula = y ~ 0 + .... 'rw0': a random walk whose first value has a mean-zero normal prior. 'ar1': a stationary first-order autoregressive process with mean zero. For 'rw0' and 'ar1', include the same covariates in formula; the time-varying process then describes deviations from that average effect. Shared by both components of a delta model.
dispformula	A one-sided formula for the dispersion parameter (e.g., phi). The default, ~ 1, estimates a single value. Ignored for families without a dispersion parameter (e.g., binomial or Poisson). In delta models, applies to the positive component. Not yet available for multi-family models or truncated negative binomial families.
nonlocal_formula	An optional one-sided formula of non-local covariate effects: diffusion() for an effect of conditions in the surrounding area, and time_lag() for an effect of conditions in previous time steps, e.g., ~ diffusion(x) + time_lag(x). Using both on the same covariate gives one combined effect that spreads over both space and time; different covariates give separate effects. See time_lag() for how the lag starts (start). If time is NULL, a spatial-only covariate is held constant across time slices. See the non-local covariates vignette, which also explains the reported diffusion scales (MSDK and RMSDK).
nonlocal_data	An optional data frame supplying the nonlocal_formula covariate(s) at a different resolution and/or coverage than data (e.g., a finer grid, or one spanning extra_time slices). Must contain the mesh xy_cols, the diffusion covariate columns, and the time column if nonlocal_formula is time-indexed (time_lag() terms, or diffusion() terms with time specified). In that case, it must cover every fitted (+ extra_time) time slice. Defaults to NULL, in which case data is used.
knots	Optional named list containing knot values to be used for basis construction of smoothing terms. See mgcv::gam() and mgcv::gamm(). E.g., ⁠s(x, bs = 'cc', k = 4), knots = list(x = c(1, 2, 3, 4))⁠
censored_upper	Upper bounds for the censored families (see Families): a numeric vector or the name of a column in data. Each response is a count between its observed value and this bound. A bound equal to the response is uncensored, a larger bound is interval-censored, and Inf is right-censored (capped at the number of trials for censored_binomial() and censored_betabinomial()). Non-integer bounds are rounded down. For left censoring (e.g., fewer than 5), use a response of 0 and a bound of 4.
distribution_column	For experimental multi-family models, the name of the column in data mapping each row to a family in the named family list. See the multi-family vignette for the supported family and method combinations.
silent	Silent or include optimization details? Helpful to set to FALSE for models that take a while to fit.
reml	Logical: use REML (restricted maximum likelihood) estimation rather than maximum likelihood? REML accounts for uncertainty in estimating fixed effects and can reduce bias in variance parameter estimates, but prevents likelihood-based model comparison (e.g., AIC) between models with different fixed effects. Use TRUE if your focus is on random effect variance parameters; use FALSE (default) if comparing models with different fixed effects or performing index standardization.
priors	Optional penalties/priors via sdmTMBpriors(). Must currently be shared across delta models.
bayesian	Logical indicating if the model will be passed to tmbstan. If TRUE, Jacobian adjustments are applied to account for parameter transformations when priors are applied.
control	Optimization control options via sdmTMBcontrol().
previous_fit	A previously fitted sdmTMB model to initialize the optimization with. Can greatly speed up fitting. Note that the model must be set up exactly the same way. However, the data and weights arguments can change, which can be useful for cross-validation.
do_fit	Fit the model (TRUE) or return the processed data without fitting (FALSE)?
experimental	A named list for esoteric or in-development options. Here be dragons.
do_index	Do index standardization calculations while fitting? Instead, fit the model and then pass the fitted model and newdata directly to get_index(), get_cog(), get_eao(), or get_weighted_average(). If TRUE, then predict_args must have a newdata element supplied and area can be supplied to index_args.
predict_args	A list of arguments to pass to predict.sdmTMB() if do_index = TRUE.
index_args	A list of arguments to pass to get_index() if do_index = TRUE. Currently, area and derived_link are supported.

Details

Model description

sdmTMB fits GLMMs with spatial and/or spatiotemporal random fields, which account for correlation in the data due to spatial proximity, or alternatively, latent spatial and spatiotemporal effects. Spatial fields represent consistent spatial patterns, while spatiotemporal fields represent spatial patterns that vary over time. See the model description vignette for mathematical details and the paper: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v115.i02")}

Binomial families

Following the structure of stats::glm() and glmmTMB, a binomial family can be specified in one of four ways: (1) the response may be a factor (success is interpreted as any level other than the first level), (2) the response may be binary (0/1), (3) the response can be a matrix of form cbind(success, failure), and (4) the response may be observed proportions, and the weights argument is used to specify the binomial size (N) parameter (⁠prob ~ ..., weights = N⁠).

Smooth terms

Smooth terms can be included following GAMs (generalized additive models) using + s(x), which implements a smooth from mgcv::s(). sdmTMB uses penalized smooths, constructed via mgcv::smooth2random(). This is a similar approach implemented in gamm4 and brms, among other packages. Within these smooths, the same syntax commonly used in mgcv::s() or mgcv::t2() can be applied, e.g. 2-dimensional smooths may be constructed with + s(x, y) or + t2(x, y); smooths can be specific to various factor levels, + s(x, by = group); the basis function dimensions may be specified, e.g. + s(x, k = 4); and various types of splines may be constructed such as cyclic splines to model seasonality (perhaps with the knots argument also supplied).

Threshold models

A linear break-point relationship for a covariate can be included via + breakpt(variable) in the formula, where variable is a single covariate corresponding to a column in data. In this case, the relationship is linear up to a point and then constant (hockey-stick shaped).

Similarly, a logistic-function threshold model can be included via + logistic(variable). This option models the relationship as a logistic function of the 50% and 95% values. This is similar to length- or size-based selectivity in fisheries, and is parameterized by the points at which f(x) = 0.5 or 0.95. See the threshold vignette.

Note that only a single threshold covariate can be included. For delta families, the threshold applies to both components, and threshold terms are not available if formula is a list.

Extra time: forecasting or interpolating

Extra time slices (e.g., years) can be included for interpolation or forecasting with the predict function via the extra_time argument. The predict function requires all time slices to be defined when fitting the model to ensure the various time indices are set up correctly. Be careful if including extra time slices that the model remains identifiable. For example, including + as.factor(year) in formula will render a model with no data to inform the expected value in a missing year. sdmTMB() makes no attempt to determine if the model makes sense for forecasting or interpolation. The options time_varying, spatiotemporal = "rw", spatiotemporal = "ar1", or a smoother on the time column provide mechanisms to predict over missing time slices; time_varying and spatiotemporal random-walk or AR(1) fields include process error.

extra_time can also be used to fill in missing time steps for the purposes of a random walk or AR(1) process if the gaps between time steps are uneven.

extra_time can include only extra time steps or all time steps including those found in the fitted data. This latter option may be simpler.

Regularization and priors

You can achieve regularization via penalties (priors) on the fixed effect parameters. See sdmTMBpriors(). You can fit the model once without penalties and look at the output of print(your_model) or tidy(your_model) or fit the model with do_fit = FALSE and inspect head(your_model$tmb_data$X_ij[[1]]) if you want to see how the formula is translated to the fixed effect model matrix. Also see the Bayesian vignette.

Delta/hurdle models

Delta models (also known as hurdle models) can be fit as two separate models or at the same time by using an appropriate delta family (see the list under family). Delta families with type = "poisson-link" use a Poisson-link parameterization instead of a classic hurdle model; see the Poisson-link vignette. If fit with a delta family, by default the formula, spatial, and spatiotemporal components are shared. Some elements can be specified independently for the two models using a list format. These include formula, spatial, spatiotemporal, and share_range. The first element of the list is for the binomial component and the second element is for the positive component (e.g., Gamma). Other elements must be shared for now (e.g., spatially varying coefficients, time-varying coefficients), and dispformula applies to the positive component only. Furthermore, there are currently limitations if specifying two formulas as a list: smoothers and random effect terms must be identical between the two formulas, and threshold effects must be specified through a single formula that is shared across the two models.

The main advantage of specifying such models using a delta family (compared to fitting two separate models) is (1) coding simplicity and (2) calculation of uncertainty on derived quantities such as an index of abundance with get_index() using the generalized delta method within TMB. Also, selected parameters can be shared across the models.

See the delta-model vignette.

Censored families

Censored families treat some observations as known only to lie within a range, e.g., catch counts on longlines where competition for hooks hides the true number caught. Supply the bounds with censored_upper. All but censored_poisson() need the RTMB backend (the default). See Families and the hook competition vignette.

Areal models

For data on areal units (e.g., grid cells or management areas) rather than point locations, build a domain with make_areal_domain(), pass it to mesh, and set spatial_model = "sar" or "car". share_range and anisotropy do not apply. See the areal model vignette.

Index standardization

For index standardization, you may wish to include 0 + as.factor(year) (or whatever the time column is called) in the formula. See a basic example of index standardization in the relevant package vignette. You will need to specify the time argument. See get_index().

Value

An object (list) of class sdmTMB. Useful elements include:

• model: output from stats::nlminb()

• sd_report: output from TMB::sdreport() or RTMB::sdreport()

• gradients: gradients of the marginal log likelihood with respect to each fixed effect

• data: the data used in fitting (rows with missing values removed)

• spde: the object supplied to mesh

• family: the family object, including the inverse link function family$linkinv()

• backend: "rtmb" or "tmb"; see sdmTMBcontrol()

• tmb_obj: the objective function object from TMB::MakeADFun() or RTMB::MakeADFun()

• tmb_data, tmb_params, tmb_map: the data, parameter, and map lists passed to MakeADFun()

References

Main reference introducing the package to cite when using sdmTMB:

Anderson, S.C., E.J. Ward, P.A. English, L.A.K. Barnett, J.T. Thorson. 2025. sdmTMB: an R package for fast, flexible, and user-friendly generalized linear mixed effects models with spatial and spatiotemporal random fields. Journal of Statistical Software. 115(2):1–46. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v115.i02")}.

Reference for local trends:

Barnett, L.A.K., E.J. Ward, S.C. Anderson. 2021. Improving estimates of species distribution change by incorporating local trends. Ecography. 44(3):427-439. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/ecog.05176")}.

Further explanation of the model and application to calculating climate velocities:

English, P., E.J. Ward, C.N. Rooper, R.E. Forrest, L.A. Rogers, K.L. Hunter, A.M. Edwards, B.M. Connors, S.C. Anderson. 2022. Contrasting climate velocity impacts in warm and cool locations show that effects of marine warming are worse in already warmer temperate waters. Fish and Fisheries. 23(1) 239-255. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/faf.12613")}.

Discussion of and illustration of some decision points when fitting these models:

Commander, C.J.C., L.A.K. Barnett, E.J. Ward, S.C. Anderson, T.E. Essington. 2022. The shadow model: how and why small choices in spatially explicit species distribution models affect predictions. PeerJ 10: e12783. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.7717/peerj.12783")}.

Application and description of threshold/break-point models:

Essington, T.E., S.C. Anderson, L.A.K. Barnett, H.M. Berger, S.A. Siedlecki, E.J. Ward. 2022. Advancing statistical models to reveal the effect of dissolved oxygen on the spatial distribution of marine taxa using thresholds and a physiologically based index. Ecography. 2022: e06249 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/ecog.06249")}.

Application to fish body condition:

Lindmark, M., S.C. Anderson, M. Gogina, M. Casini. 2023. Evaluating drivers of spatiotemporal variability in individual condition of a bottom-associated marine fish, Atlantic cod (Gadus morhua). ICES Journal of Marine Science. 80(5): 1539–1550.

Non-local covariates:

Lindmark, M., Anderson, S.C., and Thorson, J.T. 2026. Estimating scale-dependent covariate responses using two-dimensional diffusion derived from the stochastic partial differential equation method. Methods in Ecology and Evolution 17: 207–218. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.70177")}.

Thorson, J.T., Anderson, S.C., and Lindmark, M. 2026. Temperature carryover effect revealed for marine fishes using spatio-temporal distributed lag models. EcoEvoRxiv. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32942/X2W95P")}.

Several sections of the original TMB model code were adapted from 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. Fish. Res. 210:143–161. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.fishres.2018.10.013")}.

Code for the family R-to-TMB implementation, selected parameterizations of the observation likelihoods, general package structure inspiration, and the idea behind the TMB prediction approach were adapted from the glmmTMB R package:

Brooks, M.E., K. Kristensen, K.J. van Benthem, A. Magnusson, C.W. Berg, A. Nielsen, H.J. Skaug, M. Maechler, B.M. Bolker. 2017. glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling. The R Journal, 9(2):378-400. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/rj-2017-066")}.

Implementation of geometric anisotropy with the SPDE and use of random field GLMMs for index standardization:

Thorson, J.T., A.O. Shelton, E.J. Ward, H.J. Skaug. 2015. Geostatistical delta-generalized linear mixed models improve precision for estimated abundance indices for West Coast groundfishes. ICES J. Mar. Sci. 72(5): 1297–1310. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/icesjms/fsu243")}.

Examples

library(sdmTMB)

# Build a mesh to implement the SPDE approach:
mesh <- make_mesh(pcod_2011, c("X", "Y"), cutoff = 20)

# - this example uses a fairly coarse mesh so these examples run quickly
# - 'cutoff' is the minimum distance between mesh vertices in units of the
#   x and y coordinates
# - 'cutoff = 10' might make more sense in applied situations for this dataset
# - or build any mesh in 'fmesher' and pass it to the 'mesh' argument in make_mesh()
# - the mesh is not needed if you will be turning off all
#   spatial/spatiotemporal random fields

# Quick mesh plot:
plot(mesh)

# Fit a Tweedie spatial random field GLMM with a smoother for depth:
fit <- sdmTMB(
  density ~ s(depth),
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Extract coefficients:
tidy(fit, conf.int = TRUE)
tidy(fit, effects = "ran_par", conf.int = TRUE)

# Perform several 'sanity' checks:
sanity(fit)

# Predict on the fitted data; see ?predict.sdmTMB
p <- predict(fit)

# Predict on new data:
p <- predict(fit, newdata = qcs_grid)
head(p)


# Visualize the depth effect with ggeffects:
ggeffects::ggpredict(fit, "depth [all]") |> plot()

# Visualize depth effect with visreg: (see ?visreg_delta)
visreg::visreg(fit, xvar = "depth") # link space; randomized quantile residuals
visreg::visreg(fit, xvar = "depth", scale = "response")
visreg::visreg(fit, xvar = "depth", scale = "response", rug = FALSE)

# Add spatiotemporal random fields:
fit <- sdmTMB(
  density ~ 0 + as.factor(year),
  time = "year", #<
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Make the fields AR1:
fit <- sdmTMB(
  density ~ s(depth),
  time = "year",
  spatial = "off",
  spatiotemporal = "ar1", #<
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Make the fields a random walk:
fit <- sdmTMB(
  density ~ s(depth),
  time = "year",
  spatial = "off",
  spatiotemporal = "rw", #<
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Depth smoothers by year:
fit <- sdmTMB(
  density ~ s(depth, by = as.factor(year)), #<
  time = "year",
  spatial = "off",
  spatiotemporal = "rw",
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# 2D depth-year smoother:
fit <- sdmTMB(
  density ~ s(depth, year), #<
  spatial = "off",
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Turn off spatial random fields:
fit <- sdmTMB(
  present ~ poly(log(depth)),
  spatial = "off", #<
  data = pcod_2011, mesh = mesh,
  family = binomial()
)
fit

# Which matches glm():
fit_glm <- glm(
  present ~ poly(log(depth)),
  data = pcod_2011,
  family = binomial()
)
summary(fit_glm)
AIC(fit, fit_glm)

# Delta/hurdle binomial-Gamma model:
fit_dg <- sdmTMB(
  density ~ poly(log(depth), 2),
  data = pcod_2011, mesh = mesh,
  spatial = "off",
  family = delta_gamma() #<
)
fit_dg

# Delta model with different formulas and spatial structure:
fit_dg <- sdmTMB(
  list(density ~ depth_scaled, density ~ poly(depth_scaled, 2)), #<
  data = pcod_2011, mesh = mesh,
  spatial = list("off", "on"), #<
  family = delta_gamma()
)
fit_dg

# Delta/hurdle truncated NB2:
pcod_2011$count <- round(pcod_2011$density)
fit_nb2 <- sdmTMB(
  count ~ s(depth),
  data = pcod_2011, mesh = mesh,
  spatial = "off",
  family = delta_truncated_nbinom2() #<
)
fit_nb2

# Regular NB2:
fit_nb2 <- sdmTMB(
  count ~ s(depth),
  data = pcod_2011, mesh = mesh,
  spatial = "off",
  family = nbinom2() #<
)
fit_nb2

# IID random intercepts by year:
pcod_2011$fyear <- as.factor(pcod_2011$year)
fit <- sdmTMB(
  density ~ s(depth) + (1 | fyear), #<
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit

# Correlated random intercepts and slopes by year:
fit <- sdmTMB(
  density ~ (depth | fyear), #<
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)

# Spatially varying coefficient of year:
pcod_2011$year_scaled <- as.numeric(scale(pcod_2011$year))
fit <- sdmTMB(
  density ~ year_scaled,
  spatial_varying = ~ 0 + year_scaled, #<
  data = pcod_2011, mesh = mesh, family = tweedie(), time = "year"
)
fit

# Time-varying effects of depth and depth squared:
fit <- sdmTMB(
  density ~ 0 + as.factor(year),
  time_varying = ~ 0 + depth_scaled + depth_scaled2, #<
  data = pcod_2011, time = "year", mesh = mesh,
  family = tweedie()
)
print(fit)
# Extract values:
est <- as.list(fit$sd_report, "Estimate")
se <- as.list(fit$sd_report, "Std. Error")
est$b_rw_t[, , 1]
se$b_rw_t[, , 1]

# Linear break-point effect of depth:
fit <- sdmTMB(
  density ~ breakpt(depth_scaled), #<
  data = pcod_2011,
  mesh = mesh,
  family = tweedie()
)
fit

sdmTMB documentation built on Oct. 17, 2026, 1:07 a.m.