scale.model: Scale an intrinsic GMRF model

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

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

Q	A SPD matrix, either as a (dense) matrix or sparseMatrix
constr	Linear constraints spanning the null-space of Q; see ?INLA::f and argument extraconstr
eps	A small constant added to the diagonal of Q if constr

Value

inla.scale.model returns a sparseMatrix of type dgTMatrix scaled so the geometric mean of the marginal variances (of the possible non-singular part of Q) is one, for each connected component of the matrix.

Author(s)

Havard Rue [e-mail]

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)))
 

inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.