post_mu_fe {ra4bayesmeta}

Normal posterior for the overall mean parameter in the fixed effects model

Description

This function computes the mean and the standard deviation of the normal posterior distribution for the overall mean parameter mu in the fixed effects model.

Usage

post_mu_fe(df, 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.

mu.mean

mean of the normal prior for the overall mean parameter mu. Defaults to 0.

mu.sd

standard deviation of the normal prior for the overall mean parameter mu. Defaults to 4.

Details

For the fixed effects model, the normal posterior for the overall mean parameter mu can be computed analytically (under the common assumption of a normal prior on mu) since this is a conjugate Bayesian normal-normal model. See for example Ott et al. (2021), Equation (2) for the formula (mu.mean corresponds to \nu and mu.sd corresponds to \gamma).

The default values for mu.mean and mu.sd are suitable for effects mu on the log odds (ratio) scale (Roever, 2020).

Value

A list with two elements: the first element "mean" and the second element "sd", which refer to the mean and the standard deviation of the normal posterior of mu.

References

Ott, M., Plummer, M., Roos, M. (2021). How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Statistics in Medicine 40, 4505–4521. doi:10.1002/sim.9076

Roever C. Bayesian random-effects meta-analysis using the bayesmeta R package (2020). Journal of Statistical Software 93(6), 1–51.

Examples

# load the aurigular acupuncture (AA) data set
data(aa)
# normal prior for log odds ratios suggested by Roever (2020)
post_mu_fe(df=aa, mu.mean=0, mu.sd=4)