# m_j_sgc: Optimization function for the SGC(m) prior: Approximate... In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

 m_j_sgc R Documentation

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

### Description

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

### Usage

m_j_sgc(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 SGC(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.

### 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.9076")}

M_j_sigc

### Examples

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



ra4bayesmeta documentation built on Oct. 7, 2023, 1:07 a.m.