dsgc {ra4bayesmeta}

Density function of the square-root generalized conventional (SGC) benchmark prior

Description

Density function of the SGC distribution described in the Supplementary Material of Ott et al. (2021).

Usage

dsgc(x, m, C)

Arguments

x

vector of quantiles.

m

real number in (1,\infty).

C

non-negative real number.

Details

The density function with domain [0, \infty) is given by

\pi(x) = 2(m-1)Cx(1+Cx^2)^{-m}

for x >= 0. This is the transformation of the density function for variance components given in equation (2.15) in Berger & Deely (1988) to the standard deviation scale. See the Supplementary Material of Ott et al. (2021), Section 2.2, for more information.

For meta-analsis data sets, Ott et al. (2021) choose C=\sigma_{ref}^{-2}, where \sigma_{ref} is the reference standard deviation (see function sigma_ref) of the data set, which is defined as the geometric mean of the standard deviations of the individual studies.

Value

Value of the density function at locations x, where x >= 0. Vector of non-negative real numbers.

References

Berger, J. O., Deely, J. (1988). A Bayesian approach to ranking and selection of related means with alternatives to analysis-of-variance methodology. Journal of the American Statistical Association 83(402), 364–373.

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

dsigc

Examples

dsgc(x=c(0.1,0.5,1), m=1.2, C=10)