Non-local covariate terms

Wrappers that mark covariates in the nonlocal_formula argument of sdmTMB() and sdmTMB_simulate(). They are not called directly. diffusion(x) spreads covariate x across space via an SPDE diffusion operator with estimated scale kappaS_nl. time_lag(x) carries x forward in time via \(z_t = (x_t + \kappa_T z_{t-1}) / (1 + \kappa_T)\) with estimated kappaT_nl and first-order autocorrelation \(\rho_T = \kappa_T / (1 + \kappa_T)\). When both wrap the same covariate (~ diffusion(x) + time_lag(x)), they select one joint space-time operator with a single transformed predictor and coefficient.

Usage

diffusion(x)

time_lag(x, start = c("stationary", "zero"))

Arguments

x

A bare covariate name found in data or nonlocal_data.

start

The transformed state before the first time slice. "stationary" (default) assumes the covariate was held at its first time slice beforehand, so the state starts at the operator's fixed point: the first slice itself for a time lag, or its spatial diffusion for the joint operator. Results are then invariant to shifting the covariate by a constant. "zero" starts from zero as in Thorson et al. (2026), which shrinks early time slices toward zero (e.g., \(z_1 = (1 - \rho_T) x_1\) for a time lag alone) and makes results depend on how the covariate is centered: centering at a constant c is equivalent to assuming the covariate equaled c before the first time slice.

Value

These functions error if called outside nonlocal_formula.

See also

sdmTMB(), plot_nonlocal_covariate(), and the non-local covariates vignette.

Examples

# Pass as `nonlocal_formula` in sdmTMB(); see ?plot_nonlocal_covariate
nonlocal_formula <- ~ diffusion(x) + time_lag(x, start = "zero")
nonlocal_formula
#> ~diffusion(x) + time_lag(x, start = "zero")
#> <environment: 0x560cdb7be5d0>