metaBMA (version 0.6.1)

meta_random: Bayesian Random-Effects Meta-Analysis

Description

Bayesian meta-analysis assuming that the effect size \(d\) varies across studies with standard deviation \(\tau\) (i.e., a random-effects model).

Usage

meta_random(y, SE, labels, data, d = prior("norm", c(mean = 0, sd =
  0.3)), tau = prior("invgamma", c(shape = 1, scale = 0.15)),
  rscale_contin = 1/2, rscale_discrete = sqrt(2)/2, centering = TRUE,
  logml = "integrate", summarize = "stan", ci = 0.95,
  rel.tol = .Machine$double.eps^0.3, logml_iter = 5000,
  silent_stan = TRUE, ...)

Arguments

y

effect size per study. Can be provided as (1) a numeric vector, (2) the quoted or unquoted name of the variable in data, or (3) a formula to include discrete or continuous moderator variables.

SE

standard error of effect size for each study. Can be a numeric vector or the quoted or unquoted name of the variable in data

labels

optional: character values with study labels. Can be a character vector or the quoted or unquoted name of the variable in data

data

data frame containing the variables for effect size y, standard error SE, labels, and moderators per study.

d

prior distribution on the average effect size \(d\). The prior probability density function is defined via prior.

tau

prior distribution on the between-study heterogeneity \(\tau\) (i.e., the standard deviation of the study effect sizes dstudy in a random-effects meta-analysis. A (nonnegative) prior probability density function is defined via prior.

rscale_contin

scale parameter of the JZS prior for the continuous covariates.

rscale_discrete

scale parameter of the JZS prior for discrete moderators.

centering

whether continuous moderators are centered.

logml

how to estimate the log-marginal likelihood: either by numerical integration ("integrate") or by bridge sampling using MCMC/Stan samples ("stan"). To obtain high precision with logml="stan", many MCMC samples are required (e.g., iter=10000, warmup=1000).

summarize

how to estimate parameter summaries (mean, median, SD, etc.): Either by numerical integration (summarize = "integrate") or based on MCMC/Stan samples (summarize = "stan").

ci

probability for the credibility/highest-density intervals.

rel.tol

relative tolerance used for numerical integration using integrate. Use rel.tol=.Machine$double.eps for maximal precision (however, this might be slow).

logml_iter

number of iterations from the posterior of d and tau for computing the marginal likelihood for the random-effects model with bridge sampling. Note that the argument iter=2000 controls the number of iterations for parameter estimation of the random effects.

silent_stan

whether to suppress the Stan progress bar.

...

further arguments passed to rstan::sampling (see stanmodel-method-sampling). For instance: warmup=500, chains=4, control=list(adapt_delta=.95)).

Examples

# NOT RUN {
### Bayesian Random-Effects Meta-Analysis
# Note: The following code optimizes speed (for CRAN checks).
#       The settings are not suitable for actual data analysis!

data(towels)
set.seed(123)
mr <- meta_random(logOR, SE, study, data = towels,
                  d = prior("norm", c(mean=0, sd=.3), lower = 0),
                  tau = prior("invgamma", c(shape = 1, scale = 0.15)),
                  rel.tol=.Machine$double.eps^.15, iter=1000)
mr
plot_posterior(mr)
# }