ed.inla: Empirical determinacy for INLA

In hunansona/ed4bhm: Empirical Determinacy for Bayesian Hierarchical Models

Empirical determinacy for INLA

Description

Calculates the total empirical determinacy (TED) and proportional empirical determinacy for location (pEDL) and for spread (pEDS) for INLA.

Usage

ed.inla(inla.object.base, distance = "H2ALL", dz = 0.75, diff.logdens = 15, delta = 0.01)

Arguments

inla.object.base	character string, the name of the INLA object fitted in R-INLA with the base model (non-weighted likelihood)
distance	character string, specifies the type of the empirical determinacy measure. It can have values "H2" for TED, "BCL" for EDL and "BCS" for EDS and "H2ALL" for all the five measures (TED, EDL, EDS, pEDL and pEDS). The default value is "H2ALL".
dz	Step length in the standardized scale used in the construction of the grid, default 0.75.
diff.logdens	The difference of the log.density for the hyperpameters to stop numerical integration using int.strategy='grid'. Default 15.
delta	numeric, numerical differentiation step, the weighting factor w = 1 \pm δ, the default value is 0.01.

Details

The first element in the final returned value does not depend on the value of distance. The argument distance = "H2ALL" provides a list, where the second element of the list is a matrix of five empirical determinacy measures.

Value

A list of length two. The first element of the list is a list containing the matrix of descriptive statistics (mean and standard deviation) for each parameter in the model and the value of δ. The second element of the list is a matrix of empirical determinacy measures for each parameter in the model. This matrix has columns c("TED", "EDL", "EDS", "pEDL", "pEDS") when distance = "H2ALL".

References

Hunanyan, S., Roos, M., Plummer, M., Rue, H. (2021). Quantification of empirical determinacy: the impact of likelihood weighting on posterior location and spread in Bayesian meta-analysis estimated with JAGS and INLA. Bayesian Analaysis (under review). https://arxiv.org/abs/2109.11870.

See Also

ed, package inla

Examples

data(eight_schools)
#prior settings
mean_mu<-0
prec_mu<-1/(4^2)
prec_tau<-1/(5^2)

library(INLA)
HN.prior = "expression:
  tau0 =  1/(5^2);
  sigma = exp(-theta/2);
  log_dens = log(2) - 0.5 * log(2 * pi) + 0.5 * log(tau0);
  log_dens = log_dens - 0.5 * tau0 * sigma^2;
  log_dens = log_dens - log(2) - theta / 2;
  return(log_dens);
"

formula.8schools.HN <- y ~ 1+f(schooln, model="iid", 
                                      hyper = list(prec = list(prior = HN.prior)))

# INLA uses the centered parametrization of the 8 schools model by default
fit.inla.8schools <- inla(formula.8schools.HN,
                                data = eight_schools,
                                family = "gaussian",
                                scale = eight_schools$prec,
                                control.family = list(hyper=list(prec=list(initial = log(1), fixed=TRUE))),
                                control.fixed = list(mean.intercept=mean_mu, prec.intercept=prec_mu),
                                control.compute=list(hyperpar=TRUE),
                                num.threads=1)
del <- 0.01
ed_inla_8schools <- ed.inla(inla.object.base = fit.inla.8schools, delta = del, dz = 0.75, 
                            diff.logdens = 15, distance = "H2ALL")

hunansona/ed4bhm documentation built on June 15, 2022, 6:42 p.m.