dsigc: Density function of the square-root inverse generalized...
In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

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

1	dsigc(x, M, C)

`x`	vector of quantiles.
`M`	real number in (1,∞).
`C`	non-negative real number.

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

π(x) = 4(M-1)Cx^{-5}(1+Cx^{-4})^{-M}

for x >= 0. This density is obtained if the density function for variance components given in equation (2.15) in Berger & Deely (1988) is assigned to the precision (i.e. the inverse of the variance) and then transformed 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=σ_{ref}^{-2}, where σ_{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 of the density function at locations x, where x >= 0. Vector of non-negative real numbers.

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. Supplementary Material: How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Revised for Statistics in Medicine. 2021.

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