knmodels: Spacetime interaction models

In INBO-BMK/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

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,
 data,
 progress=FALSE, 
 control.st=list(
   t=NULL, 
   s=NULL,
   st=NULL,
   graph=NULL,
   type=c(paste(1:4), paste0(2:4, 'c'), paste0(2:4, 'd')), 
   diagonal=1e-5, 
   ...) 
 )

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 contains: 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. \itemspaceref 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"). \item...Arguments to be passed to the inla function.

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 <- SpatialGrid(GridTopology(c(0,0), c(1, 1), c(4, 5)))
(n <- nrow(xy <- 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 points
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$E, progress=TRUE, 
     control.st=list(time=time, space=space, 
        spacetime=spacetime, graph=graph, type=c(4, '4c', '4d')), 
     control.compute=list(dic=TRUE, waic=TRUE, cpo=TRUE))
sapply(res, function(x)
       c(dic=x$dic$dic, waic=x$waic$waic, cpo=-sum(log(x$cpo$cpo))))

INBO-BMK/INLA documentation built on Dec. 4, 2019, 11:43 p.m.