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INLAspacetime

CRAN Status check no-suggestions check pkgdown

This is a R package to implement certain spatial and spatio-temporal models, including some of the spatio-temporal models proposed here. It uses the cgeneric interface in the INLA package, to implement models by writing C code to build the precision matrix compiling it so that INLA can use it internally.

We have implemented

  1. some of the models presented in A diffusion-based spatio-temporal extension of Gaussian Matérn fields (2024). Finn Lindgren, Haakon Bakka, David Bolin, Elias Krainski and Håvard Rue. SORT 48 (1) January-June 2024, 3-66. (https://www.idescat.cat/sort/sort481/48.1.1.Lindgren-etal.pdf)

  2. the barrier (and transparent barriers) model proposed in https://doi.org/10.1016/j.spasta.2019.01.002

Vignettes

Please check here

Installation

The ‘INLA’ package is a suggested one, but you will need it for actually fitting a model. You can install it with

install.packages("INLA",repos=c(getOption("repos"),INLA="https://inla.r-inla-download.org/R/testing"), dep=TRUE)

You can install the current CRAN version of INLAspacetime:

install.packages("INLAspacetime")

You can install the latest version of INLAspacetime from GitHub with

## install.packages("remotes")
remotes::install_github("eliaskrainski/INLAspacetime",  build_vignettes=TRUE)

A spacetime example

Simulate some fake data.

set.seed(1)
n <- 5
dataf <- data.frame(
    s1   = runif(n, -1, 1),
    s2   = runif(n, -1, 1),
    time = runif(n, 1, 4),
    y    = rnorm(n, 0, 1))
str(dataf)
#> 'data.frame':    5 obs. of  4 variables:
#>  $ s1  : num  -0.469 -0.256 0.146 0.816 -0.597
#>  $ s2  : num  0.797 0.889 0.322 0.258 -0.876
#>  $ time: num  1.62 1.53 3.06 2.15 3.31
#>  $ y   : num  -0.00577 2.40465 0.76359 -0.79901 -1.14766

Loading packages:

library(fmesher)
library(INLA)
library(INLAspacetime)
#> see more on https://eliaskrainski.github.io/INLAspacetime

Define spatial and temporal discretization meshes

smesh <- fm_mesh_2d(
  loc = cbind(0,0), 
  max.edge = 5, 
  offset = 2)
tmesh <- fm_mesh_1d(
  loc = 0:5)

Define the spacetime model object to be used

stmodel <- stModel.define(
    smesh = smesh, ## spatial mesh
    tmesh = tmesh, ## temporal mesh
    model = '121', ## model, see the paper
    control.priors = list(
        prs = c(1, 0.1), ## P(spatial range < 1) = 0.1
        prt = c(5, 0), ## temporal range fixed to 5
        psigma = c(1, 0.1) ## P(sigma > 1) = 0.1
        )
    )
#> Warning in stModel.define(smesh = smesh, tmesh = tmesh, model = "121",
#> control.priors = list(prs = c(1, : Setting 'useINLAprecomp = FALSE' to use new
#> code.

Fit the model

Define a projector matrix from the spatial and temporal meshes to the data

Aproj <- inla.spde.make.A(
    mesh = smesh,
    loc = cbind(dataf$s1, dataf$s2),
    group = dataf$time,
    group.mesh = tmesh
)

Create a ‘fake’ column to be used as index. in the f() term

dataf$st <- NA

Setting the likelihood precision (as fixed)

ctrl.lik <- list(
  hyper = list(
    prec = list(
      initial = 10, 
      fixed = TRUE)    
  )
)

Combine a ‘fake’ index column with A.local

fmodel <- y ~ f(st, model = stmodel, A.local = Aproj)

Call the main INLA function:

fit <- inla(
    formula = fmodel,
    data = dataf,
    control.family = ctrl.lik)

Posterior marginal summaries for fixed effect and the model parameters that were not fixed.

fit$summary.fixed
#>                 mean      sd 0.025quant  0.5quant 0.975quant      mode
#> (Intercept) 0.693389 4.03265  -6.962331 0.5227188   9.417425 0.5550712
#>                      kld
#> (Intercept) 7.398472e-05
fit$summary.hyperpar
#>                   mean        sd 0.025quant 0.5quant 0.975quant     mode
#> Theta1 for st 1.199222 0.4918533  0.3653818 1.161539   2.277396 0.974993
#> Theta2 for st 1.435517 0.1710676  1.1031120 1.434032   1.776667 1.427752

Using the inlabru

library(inlabru)

Setting the observation (likelihood) model object

data_model <- bru_obs(
  formula = y ~ ., 
  family = "gaussian",
  control.family = ctrl.lik, 
  data = dataf)

Define the data model: the linear predictor terms

linpred <- ~ 1 +
    field(list(space = cbind(s1, s2), 
               time = time),
          model = stmodel)

Fitting

result <- bru(
  components = linpred,
  data_model)

Summary of the model parameters

result$summary.fixed
#>                mean       sd 0.025quant 0.5quant 0.975quant      mode
#> Intercept 0.6690302 3.970182  -6.887199 0.509471   9.214066 0.5379221
#>                    kld
#> Intercept 5.683968e-05
result$summary.hyperpar
#>                      mean        sd 0.025quant 0.5quant 0.975quant      mode
#> Theta1 for field 1.190438 0.4868951  0.3623876 1.153809   2.256071 0.9726162
#> Theta2 for field 1.435268 0.1709839  1.1033563 1.433674   1.776580 1.4269195

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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