m_inf_sgc: Optimization function for the SGC(m) prior: Adjust the prior to a target
relative latent model complexity (RLMC)
Description
Computes the parameter value \(m=m_{inf}\) of the SGC(\(m\)) prior,
such that the relative latent model complexity (RLMC) with respect
to the reference threshold is approximately rlmc.
The reference threshold is chosen as the (1-alpha)-quantile of the
SGC(\(m_{inf}\)) prior.
Usage
m_inf_sgc(rlmc, alpha=0.5)
Value
Parameter value \(m=m_{inf}\) of the SGC(\(m\)) prior. Real number > 1.
Arguments
rlmc
target RLMC value. Real number in \((0,1)\).
alpha
determines the (1-alpha)-quantile of the SGC(\(m\)) prior,
which is used as reference threshold. Defaults to 0.5 (i.e. the median).
Details
See the Supplementary Material of Ott et al. (2021), Section 2.3.1,
for the formulas and explanations.
Note that the parameter value \(m_{inf}\) does not depend
on the data set considered.
References
Ott, M., Plummer, M., Roos, M. (2021). Supplementary Material:
How vague is vague? How informative is informative? Reference analysis for
Bayesian meta-analysis. Statistics in Medicine.
tools:::Rd_expr_doi("10.1002/sim.9076")
# extreme RLMC target value close to 0 used in Ott et al. (2021)m_inf_sgc(rlmc=0.0001)
# 25% quantile instead of the median as ref. thresholdm_inf_sgc(rlmc=0.0001, alpha=0.75)