cgeneric object for a generic0 model.
See details.Build data needed to implement a model whose precision has a conditional precision parameter. This uses the C interface in the 'INLA' package, that can be used as a linear predictor model component with an 'f' term.
cgeneric_generic0(R, param, constr = TRUE, scale = TRUE, ...)cgeneric_iid(n, param, constr = FALSE, ...)
a cgeneric object, see cgeneric().
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 model. See detais.
arguments (debug,useINLAprecomp,shlib)
passed on to cgeneric().
integer required to specify the model size
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.
prior.cgeneric()