Spatial and Spatio-Temporal Models using 'INLA'.

INLAspacetime

This is a R package to implement certain spatial and spatio-temporal models taking use to the cgeneric interface in the INLA package. This interface is a way to implement models by writing C code to build the precision matrix compiling it so that INLA can use it internally.

Installation

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)

We have implemented

1. some of the models presented in https://arxiv.org/abs/2006.04917

2. the barrier model proposed in https://doi.org/10.1016/j.spasta.2019.01.002

Example

This is a basic example which fit a spacetime model for some fake data. The model fitting using inlabru facilitates coding.

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 the packages:

library(INLA)
#> Loading required package: Matrix
#> Loading required package: foreach
#> Loading required package: parallel
#> Loading required package: sp
#> The legacy packages maptools, rgdal, and rgeos, underpinning this package
#> will retire shortly. Please refer to R-spatial evolution reports on
#> https://r-spatial.org/r/2023/05/15/evolution4.html for details.
#> This package is now running under evolution status 0
#> This is INLA_23.05.30-1 built 2023-05-30 11:52:19 UTC.
#>  - See www.r-inla.org/contact-us for how to get help.
#>  - To enable PARDISO sparse library; see inla.pardiso()
library(INLAspacetime)
library(inlabru)

Define spatial and temporal discretization meshes

smesh <- inla.mesh.2d(
  loc = cbind(0,0), 
  max.edge = 5, 
  offset = 2)
tmesh <- inla.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
        )
    )

Define the data model: the linear predictor terms

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

Setting the likelihood

ctrlf <- list(
  hyper = list(
    prec = list(
      initial = 10, 
      fixed = TRUE)    
  )
)
datalike <- like(
  formula = y ~ ., 
  family = "gaussian",
  control.family = ctrlf, 
  data=dataf)

Fitting

result <- 
  bru(
    components = linpred,
    datalike,
    options = list(
      control.inla = list(
        int.strategy = "eb"
        ),
      verbose = !TRUE)
    )
#> Warning in inla.model.properties.generic(inla.trim.family(model), mm[names(mm) == : Model 'cgeneric' in section 'latent' is marked as 'experimental'; changes may appear at any time.
#>   Use this model with extra care!!! Further warnings are disabled.

Summary of the model parameters

result$summary.fixed
#>                mean      sd 0.025quant  0.5quant 0.975quant      mode kld
#> Intercept 0.5211454 3.49482  -6.328575 0.5211454   7.370866 0.5211454   0
result$summary.hyperpar
#>                      mean        sd 0.025quant 0.5quant 0.975quant      mode
#> Theta1 for field 1.202935 0.5125858  0.3321324 1.162519   2.324768 0.9707531
#> Theta2 for field 1.435746 0.1706775  1.1044643 1.434143   1.776487 1.4273398

Vignettes

Please check it out at the Tutorials.