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This supplementary material illustrate fitting the model discussed in Detecting Subnational Diffusion Processes of Lethal Terrorism: Global Study, 2010-2016 using a subset of the data discussed in that article. Please note that this material should be treated as an illustration of the method only. Due to the computational time required to fit the models discussed in the article the illustration here uses only a subset of the data and a coarser mesh to enable readers to run through an example and amend for their own data.

The package , available here, contains the data and the functionality to fit the model deailed herein.

## to install the lgcpSPDE package from github
devtools::install_github("cmjt/lgcpSPDE")

library(lgcpSPDE)
## only using a subset of the data for illustration
data <- terrorism_aggregate[terrorism_aggregate$iyear <= 2011, 
    ]

## x, y, z locations (latitude and longitude projected onto
## the unit sphere)
locs <- cbind(data$x.coord, data$y.coord, data$z.coord)
## create mesh of the world projected onto the unit sphere
bdry <- inla.sp2segment(world)
bdry$loc <- inla.mesh.map(bdry$loc, projection = "longlat", inverse = TRUE)
## course mesh for illustration
mesh <- inla.mesh.2d(boundary = bdry, loc = locs, max.edge = c(5, 
    50)/180, cutoff = 5/180)  ## plot(mesh) to vizualise
## Create a named data frame of covariates
covariates <- data.frame(population = data$pop, time.to.city = data$tt, 
    luminosity = data$lum)
## create temporal indecies
time <- data$iyear - min(data$iyear) + 1

To fit this crude model run the following code.

fit <- geo.fit(mesh = mesh, locs = locs, response = data$total, 
    covariates = covariates, control.time = list(model = "rw1", 
        param = list(theta = list(prior = "pc.prec", param = c(1, 
            0.01)))), temp = time, family = "poisson", sig0 = 0.2, 
    rho0 = 0.01, Prho = 0.9, control.compute = list(waic = TRUE, 
        config = TRUE, openmp.strategy = "huge"), control.inla = list(int.strategy = "eb", 
        strategy = "gaussian", diagonal = 100))

The function is a wrapper for 's (Finn Lindgren, Havard Rue (2015)) function and has the following main arguments:

  • mesh: a ``mesh'' object i.e. Delauney triangulation of the domain,
  • locs: a matrix of observation locations, where each row corresponds to the observation.
  • response: a vector of response variable, each corresponds to the spatial locations in .
  • temp: (optional) a numeric vector specifying a temporal index for each observation (starting at 1.....T).
  • covariates: (optional) a named data.frame of covariates.
  • family: a character vector specifying the assumed likelihood of the response, by default is "gaussian".
  • control.time: (optional) supplied if the argument is given to fit a spatio-temporal model. This argument controls the model and prior put on the hyperparameters of the model for the temporal component of the spatio-temporal model. By default this is which is a pc.prior put on the rho coefficient of a AR(1) model with P(rho>0)=0.9.
  • control.inla: a list which controls the fitting procedures INLA uses. By default this is for quick and dirty fitting. control.compute: a list of fit statistics the user wants INLA to return. By default this is .
  • non.linear: (optional) should be used if the user requires a non-linear covariate to be included in the model Must be supplied as a named list with elements a numeric vector of the random effect indices, and the random effect model the user wishes to use for

References

Finn Lindgren, Havard Rue. 2015. “Bayesian Spatial Modelling with R-INLA.” Nature Materials 19 (63). Journal of Statistical Software: 1–25. http://www.jstatsoft.org/v63/i19/.