inla.cgeneric to implement a
model whose precision has a conditional
precision parameter. See details.
This uses the cgeneric interface that can be used as a
model in a INLA f() model component.Build an inla.cgeneric to implement a
model whose precision has a conditional
precision parameter. See details.
This uses the cgeneric interface that can be used as a
model in a INLA f() model component.
cgeneric_generic0(
R,
param,
constr = TRUE,
scale = TRUE,
debug = FALSE,
useINLAprecomp = TRUE,
libpath = NULL
)cgeneric_iid(
n,
param,
constr = FALSE,
scale = TRUE,
debug = FALSE,
useINLAprecomp = TRUE,
libpath = NULL
)
a inla.cgeneric, cgeneric() object.
the structure matrix for the model definition.
length two vector with the parameters
a and p for the PC-prior distribution defined from
$$P(\sigma > a) = p$$
where \(\sigma\) can be interpreted as marginal standard
deviation of the process if scale = TRUE. See details.
logical indicating if it is to add a sum-to-zero constraint. Default is TRUE.
logical indicating if it is to scale the mnodel. See detais.
integer, default is zero, indicating the verbose level. Will be used as logical by INLA.
logical, default is TRUE, indicating if it is to be used the shared object pre-compiled by INLA. This is not considered if 'libpath' is provided.
string, default is NULL, with the path to the shared object.
size of the model
cgeneric_iid(): The cgeneric_iid() uses the cgeneric_generic0
with the structure matrix as the identity.
The precision matrix is defined as $$Q = \tau R$$ where the structure matrix R is supplied by the user and \(\tau\) is the precision parameter. Following Sørbie and Rue (2014), if scale = TRUE the model is scaled so that $$Q = \tau s R$$ where \(s\) is the geometric mean of the diagonal elements of the generalized inverse of \(R\). $$s = \exp{\sum_i \log((R^{-})_{ii})/n}$$ If the model is scaled, the geometric mean of the marginal variances, the diagonal of \(Q^{-1}\), is one. Therefore, when the model is scaled, \(\tau\) is the marginal precision, otherwise \(\tau\) is the conditional precision.
Sigrunn Holbek Sørbye and Håvard Rue (2014). Scaling intrinsic Gaussian Markov random field priors in spatial modelling. Spatial Statistics, vol. 8, p. 39-51.