inla.knmodels {INLA}R Documentation

Spacetime interaction models

Description

It implements the models in Knorr-Held, L. (2000) with three different constraint approaches: sum-to-zero, contrast or diagonal add.

Usage

inla.knmodels(
  formula,
  progress = FALSE,
  control.st = list(time, space, spacetime, graph, type = c(paste(1:4), paste0(2:4, "c"),
    paste0(2:4, "d")), diagonal = 1e-05, timeref = 1, spaceref = 1),
  ...,
  envir = parent.frame()
)

Arguments

formula

The formula specifying the other model components, without the spacetime interaction term. The spacetime interaction term will be added accordly to the specification in the control.st argument. See inla

progress

If it is to be shown the model fitting progress. Useful if more than one interaction type is being fitted.

control.st

Named list of arguments to control the spacetime interaction. It should contain:

time

to be used as the index set for the main temporal effect which will be considered for the constraints when it is the case.

space

to be used as the index set for the main spatial effect which will be considered for the constraints when it is the case.

spacetime

to be the index set for the spacetime interaction effect.

graph

to be the graph for the spatial neighbor structure to be used in a f() term for the main spatial random effect term or for building the spacetime interaction model.

type

to specify the spacetime interaction type. 1 to 4 corresponds to the four interaction types in Knorr-Held, L. (2000) with all the needed sum-to-zero constraints. ⁠2c⁠, ⁠3c⁠ and ⁠4c⁠ are the contrast version considering the first time or space constrained to be equal to zero. ⁠2d⁠, ⁠3d⁠ and ⁠4d⁠ are the corresponding versions when considering the diagonal add approach.

diagonal

to be the value to be added to the diagonal when using the diagonal add approach.

timeref

to specify the time point to be the reference time in the contrast parametrization.

spaceref

to specify the area to be the reference for the contrast parametrization.

...

where additional arguments can be passed to f() function. Specification of the hyperparameter, fixed or random, initial value, prior and its parameters for the spacetime interaction. See ?inla.models and look for generic0. By default we scale it and use the PC-prior to set the prior using the pc.prec prior with param = c(0.5, 0.5). See documentation with ?inla.doc("pc.prec").

...

Arguments to be passed to the inla() function.

envir

Environment in which to evaluate the ... arguments.

Value

inla.knmodels returns an object of class "inla". or a list of objects of this class if it is asked to compute more than one interaction type at once. Note: when the model type is 2c, 3c, 4c, 2d, 3d or 4d, it also includes linear combinations summary.

Author(s)

Elias T. Krainski

See Also

inla.knmodels.sample() to sample from

Examples



### define space domain as a grid
grid <- sp::SpatialGrid(sp::GridTopology(c(0,0), c(1, 1), c(4, 5)))
(n <- nrow(xy <- sp::coordinates(grid)))

### build a spatial neighborhood list
jj <- lapply(1:n, function(i)
    which(sqrt((xy[i,1]-xy[,1])^2 + (xy[i,2]-xy[,2])^2)==1))

### build the spatial adjacency matrix
graph <- sparseMatrix(rep(1:n, sapply(jj, length)),
                      unlist(jj), x=1, dims=c(n, n))

### some random data at 10 time point
dat <- inla.knmodels.sample(graph, m=10, tau.t=2, tau.s=2, tau.st=3)
str(dat)
sapply(dat$x, summary)

nd <- length(dat$x$eta)
dat$e <- runif(nd, 0.9, 1.1)*rgamma(n, 40, 2)
dat$y <- rpois(nd, dat$e*exp(dat$x$eta-3))
summary(dat$y)

### fit the type 4 considering three different approaches
tgraph <- sparseMatrix(i=c(2:10, 1:9), j=c(1:9, 2:10), x=1)
res <- inla.knmodels(y ~ f(time, model='bym2', graph=tgraph) +
     f(space, model='bym2', graph=graph),
     data=dat, family='poisson', E=dat$E, progress=TRUE,
     control.st=list(time=time, space=space,
        spacetime=spacetime, graph=graph, type=c(4, '4c')), 
     control.compute=list(dic=TRUE, waic=TRUE, cpo=TRUE))
sapply(res, function(x)
       c(dic=x$dic$dic, waic=x$waic$waic, cpo=-sum(log(x$cpo$cpo))))
[Package INLA version 25.10.19 Index]