M_j_sigc {ra4bayesmeta}

Optimization function for the SIGC(m) prior: Approximate Jeffreys reference posterior

Description

Numerically determines the parameter value M=M_J of the SIGC(M) prior, such that the Hellinger distance between the marginal posteriors for the heterogeneity standard deviation \tau induced by the SIGC(M_J) prior and Jeffreys (improper) reference prior is minimal.

Usage

M_j_sigc(df, upper=3, digits=2, mu.mean=0, mu.sd=4)

Arguments

df

data frame with one column "y" containing the (transformed) effect estimates for the individual studies and one column "sigma" containing the standard errors of these estimates.

upper

upper bound for parameter M. Real number in (1,\infty).

digits

specifies the desired precision of the parameter value M=M_J, i.e. to how many digits this value should be determined. Possible values are 1,2,3. Defaults to 2.

mu.mean

mean of the normal prior for the effect mu.

mu.sd

standard deviation of the normal prior for the effect mu.

Details

See the Supplementary Material of Ott et al. (2021, Section 2.6) for details.

Value

Parameter value M=M_J of the SIGC(M) prior. Real number > 1.

Warning

This function takes several minutes to run if the desired precision is digits=2 and even longer for higher precision.

For some data sets, the optimal parameter value M=M_J is very large (e.g. of order 9*10^5). If this function returns M_J=upper, then the optimal parameter value may be larger than upper.

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. doi:10.1002/sim.9076

See Also

m_j_sgc

Examples

# for aurigular acupuncture (AA) data set
data(aa)
# warning: it takes ca. 2 min. to run this function
M_j_sigc(df=aa, digits=1)