meta_bma  R Documentation 
Fits random and fixedeffects metaanalyses and performs Bayesian model averaging for H1 (d != 0) vs. H0 (d = 0).
meta_bma(
y,
SE,
labels,
data,
d = prior("cauchy", c(location = 0, scale = 0.707)),
tau = prior("invgamma", c(shape = 1, scale = 0.15)),
rscale_contin = 0.5,
rscale_discrete = 0.707,
centering = TRUE,
prior = c(1, 1, 1, 1),
logml = "integrate",
summarize = "stan",
ci = 0.95,
rel.tol = .Machine$double.eps^0.3,
logml_iter = 5000,
silent_stan = TRUE,
...
)
y 
effect size per study. Can be provided as (1) a numeric vector, (2)
the quoted or unquoted name of the variable in 
SE 
standard error of effect size for each study. Can be a numeric
vector or the quoted or unquoted name of the variable in 
labels 
optional: character values with study labels. Can be a
character vector or the quoted or unquoted name of the variable in

data 
data frame containing the variables for effect size 
d 

tau 

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. 
prior 
prior probabilities over models (possibly unnormalized) in the
order 
logml 
how to estimate the logmarginal likelihood: either by numerical
integration ( 
summarize 
how to estimate parameter summaries (mean, median, SD,
etc.): Either by numerical integration ( 
ci 
probability for the credibility/highestdensity intervals. 
rel.tol 
relative tolerance used for numerical integration using

logml_iter 
number of iterations (per chain) from the posterior
distribution of 
silent_stan 
whether to suppress the Stan progress bar. 
... 
further arguments passed to 
Bayesian model averaging for four metaanalysis models: Fixed vs.
randomeffects and H0 (d=0
) vs. H1 (e.g., d>0
).
For a primer on Bayesian modelaveraged metaanalysis,
see Gronau, Heck, Berkhout, Haaf, and Wagenmakers (2020).
By default, the logmarginal likelihood is computed by numerical integration
(logml="integrate"
). This is relatively fast and gives precise,
reproducible results. However, for extreme priors or data (e.g., very small
standard errors), numerical integration is not robust and might provide
incorrect results. As an alternative, the logmarginal likelihood can be
estimated using MCMC/Stan samples and bridge sampling (logml="stan"
).
To obtain posterior summary statistics for the average effect size d
and the heterogeneity parameter tau
, one can also choose between
numerical integration (summarize="integrate"
) or MCMC sampling in Stan
(summarize="stan"
). If any moderators are included in a model, both
the marginal likelihood and posterior summary statistics can only be computed
using Stan.
Gronau, Q. F., Erp, S. V., Heck, D. W., Cesario, J., Jonas, K. J., & Wagenmakers, E.J. (2017). A Bayesian modelaveraged metaanalysis of the power pose effect with informed and default priors: the case of felt power. Comprehensive Results in Social Psychology, 2(1), 123138. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/23743603.2017.1326760")}
Gronau, Q. F., Heck, D. W., Berkhout, S. W., Haaf, J. M., & Wagenmakers, E.J. (2021). A primer on Bayesian modelaveraged metaanalysis. Advances in Methods and Practices in Psychological Science, 4(3), 1–19. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/25152459211031256")}
Berkhout, S. W., Haaf, J. M., Gronau, Q. F., Heck, D. W., & Wagenmakers, E.J. (2023). A tutorial on Bayesian modelaveraged metaanalysis in JASP. Behavior Research Methods.
meta_fixed, meta_random
### Bayesian ModelAveraged MetaAnalysis (H1: d>0)
data(towels)
set.seed(123)
mb < meta_bma(logOR, SE, study, towels,
d = prior("norm", c(mean = 0, sd = .3), lower = 0),
tau = prior("invgamma", c(shape = 1, scale = 0.15))
)
mb
plot_posterior(mb, "d")
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