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

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)

We have implemented

1. some of the models presented in https://www.idescat.cat/sort/sort481/48.1.1.Lindgren-etal.pdf

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)
library(INLAspacetime)
#> Loading required package: fmesher
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)
    )

Summary of the model parameters

result$summary.fixed
#>                mean       sd 0.025quant  0.5quant 0.975quant      mode kld
#> Intercept 0.5264782 3.500849   -6.33506 0.5264782   7.388016 0.5264782   0
result$summary.hyperpar
#>                      mean        sd 0.025quant 0.5quant 0.975quant     mode
#> Theta1 for field 1.190361 0.4867876  0.3624381 1.153754   2.255724 0.972674
#> Theta2 for field 1.435282 0.1709783  1.1034628 1.433661   1.776664 1.426789

Vignettes

Please check it out at the Tutorials.