R/scale.model.R

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

## Export: inla.scale.model

##! \name{scale.model}
##! \alias{inla.scale.model}
##! \alias{scale.model}
##!
##! \title{Scale an intrinsic GMRF model}
##!
##! \description{This function scales an intrinsic GMRF model so the geometric mean of the
##!              marginal variances is one}
##!
##! \usage{
##!     inla.scale.model(Q, constr = NULL, eps = sqrt(.Machine$double.eps))
##! }
##!
##! \arguments{
##!   \item{Q}{A SPD matrix,  either as a (dense) matrix or \code{sparseMatrix}}
##!   \item{constr}{Linear constraints spanning the null-space of \code{Q};
##!                 see \code{?INLA::f} and argument \code{extraconstr}} 
##!   \item{eps}{A small constant added to the diagonal of \code{Q} if \code{constr}}
##!  }
##! \value{
##!   \code{inla.scale.model} returns a \code{sparseMatrix} of type \code{dgTMatrix} 
##!   scaled so the geometric mean of the marginal variances (of the possible
##!   non-singular part of \code{Q}) is one,  for each connected component of the matrix.
##! }
##! \author{Havard Rue \email{hrue@r-inla.org}}
##!
##! \examples{
##! ## Q is singular
##! data(Germany)
##! g = system.file("demodata/germany.graph", package="INLA")
##! Q = -inla.graph2matrix(g)
##! diag(Q) = 0
##! diag(Q) = -rowSums(Q)
##! n = dim(Q)[1]
##! Q.scaled = inla.scale.model(Q, constr = list(A = matrix(1, 1, n), e=0))
##! print(diag(INLA:::inla.ginv(Q.scaled)))
##!
##! ## Q is singular with 3 connected components
##! g = inla.read.graph("6 1 2 2 3 2 2 1 3 3 2 1 2 4 1 5 5 1 4 6 0")
##! print(paste("Number of connected components", g$cc$n))
##! Q = -inla.graph2matrix(g)
##! diag(Q) = 0
##! diag(Q) = -rowSums(Q)
##! n = dim(Q)[1]
##! Q.scaled = inla.scale.model(Q, constr = list(A = matrix(1, 1, n), e=0))
##! print(diag(INLA:::inla.ginv(Q.scaled)))
##!
##! ## Q is non-singular with 3 connected components. no constraints needed
##! diag(Q) = diag(Q) + 1
##! Q.scaled = inla.scale.model(Q)
##! print(diag(INLA:::inla.ginv(Q.scaled)))
##! }

inla.scale.model.internal = function(Q, constr = NULL, eps = sqrt(.Machine$double.eps))
{
    ## return also the scaled marginal variances
    
    marg.var = rep(0, nrow(Q))
    Q = inla.as.sparse(Q)
    g = inla.read.graph(Q)
    for(k in seq_len(g$cc$n)) {
        i = g$cc$nodes[[k]]
        n = length(i)
        QQ = Q[i, i, drop=FALSE]
        if (n == 1) {
            QQ[1, 1] = 1
            marg.var[i] = 1
        } else {
            cconstr = constr
            if (!is.null(constr)) {
                ## the GMRFLib will automatically drop duplicated constraints; how convenient...
                cconstr$A = constr$A[, i, drop = FALSE]
                eeps = eps
            } else {
                eeps = 0
            }
            res = inla.qinv(QQ + Diagonal(n) * max(diag(QQ)) * eeps, constr = cconstr)
            fac = exp(mean(log(diag(res))))
            QQ = fac * QQ
            marg.var[i] = diag(res)/fac
        }
        Q[i, i] = QQ
    }
    return (list(Q=Q, var = marg.var))
}

inla.scale.model = function(Q, constr = NULL, eps = sqrt(.Machine$double.eps))
{
    res = inla.scale.model.internal(Q = Q, constr = constr, eps = eps)
    return (res$Q)
}