scale.model {INLA} | R Documentation

## 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.internal(Q, constr = NULL, eps = sqrt(.Machine$double.eps))

    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 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(MASS::ginv(as.matrix(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(MASS::ginv(as.matrix(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(MASS::ginv(as.matrix(Q.scaled))))

[Package INLA version 26.08.22 Index]