Modeling without covariates

[joao-pompeu]

Hello sdmTMB team,

It might be a silly question, but is it possible to model spatiotemporal distribution considering only coordinates, like a variogram?

[ericward-noaa]

Yes—this is totally reasonable. For example, we might want to build an intercept only model, like the following. Here a spatial field is estimated (using coordinates) and the focus of inference would be on the spatial range, spatial variance, etc. You could also include spatiotemporal fields.

library(sdmTMB)
mesh <- make_mesh(pcod_2011, c("X", "Y"), cutoff = 20)
# Fit a Tweedie spatial random field GLMM with an intercept
fit <- sdmTMB(
  density ~ 1,
  data = pcod_2011, mesh = mesh,
  family = tweedie(link = "log")
)
fit
#> Spatial model fit by ML ['sdmTMB']
#> Formula: density ~ 1
#> Mesh: mesh (isotropic covariance)
#> Data: pcod_2011
#> Family: tweedie(link = 'log')
#>  
#>             coef.est coef.se
#> (Intercept)        3    0.43
#> 
#> Dispersion parameter: 15.52
#> Tweedie p: 1.59
#> Matérn range: 33.23
#> Spatial SD: 2.03
#> ML criterion at convergence: 3023.736
#> 
#> See ?tidy.sdmTMB to extract these values as a data frame.

^{Created on 2023-03-08 with reprex v2.0.2}