Scale an intrinsic GMRF model

This function scales an intrinsic GMRF model so the geometric mean of the marginal variances is one

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

Havard Rue hrue@r-inla.org

Examples

 ## Q is singular
 data(Germany)
 g = system.file("demodata/germany.graph", package="INLA")
 Q = -inla.graph2matrix(g)
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
 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))
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Error in system(paste(shQuote(inla.call.no.remote()), "-s -m qinv", "-r",     reordering, "-t", num.threads, "-S", smtp, qinv.file, constr.file,     out.file), intern = TRUE): error in running command
 print(diag(INLA:::inla.ginv(Q.scaled)))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'print': error in evaluating the argument 'x' in selecting a method for function 'diag': object 'Q.scaled' not found

 ## 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))
#> [1] "Number of connected components 3"
 Q = -inla.graph2matrix(g)
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
 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))
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Error in system(paste(shQuote(inla.call.no.remote()), "-s -m qinv", "-r",     reordering, "-t", num.threads, "-S", smtp, qinv.file, constr.file,     out.file), intern = TRUE): error in running command
 print(diag(INLA:::inla.ginv(Q.scaled)))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'print': error in evaluating the argument 'x' in selecting a method for function 'diag': object 'Q.scaled' not found

 ## Q is non-singular with 3 connected components. no constraints needed
 diag(Q) = diag(Q) + 1
 Q.scaled = inla.scale.model(Q)
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Warning: 'as(<dgCMatrix>, "dgTMatrix")' is deprecated.
#> Use 'as(., "TsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> Error in system(paste(shQuote(inla.call.no.remote()), "-s -m qinv", "-r",     reordering, "-t", num.threads, "-S", smtp, qinv.file, constr.file,     out.file), intern = TRUE): error in running command
 print(diag(INLA:::inla.ginv(Q.scaled)))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'print': error in evaluating the argument 'x' in selecting a method for function 'diag': object 'Q.scaled' not found