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.
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)some of the models presented in https://www.idescat.cat/sort/sort481/48.1.1.Lindgren-etal.pdf
the barrier model proposed in https://doi.org/10.1016/j.spasta.2019.01.002
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 -1.14766Loading packages:
library(fmesher)
library(INLA)
library(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
)
)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 <- NASetting 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$summary.fixed
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> (Intercept) 0.6933766 4.032586 -6.962245 0.5227216 9.417188 0.555068
#> kld
#> (Intercept) 7.411114e-05
fit$summary.hyperpar
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> Theta1 for st 1.199194 0.4918107 0.365412 1.161518 2.277266 0.9750084
#> Theta2 for st 1.435519 0.1710698 1.103120 1.434030 1.776684 1.4277357library(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$summary.fixed
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> Intercept 0.6690379 3.969851 -6.886589 0.5095207 9.213142 0.5379552
#> kld
#> Intercept 5.713904e-05
result$summary.hyperpar
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> Theta1 for field 1.190355 0.4867797 0.3624472 1.153749 2.255702 0.9726699
#> Theta2 for field 1.435283 0.1709777 1.1034676 1.433660 1.776667 1.4267841Please check it out at the Tutorials