`RoBMA`

is used to estimate a Robust Bayesian
Meta-Analysis. The interface allows a complete customization of
the ensemble with different prior (or list of prior) distributions
for each component.

```
RoBMA(
d = NULL,
r = NULL,
logOR = NULL,
z = NULL,
y = NULL,
se = NULL,
v = NULL,
n = NULL,
lCI = NULL,
uCI = NULL,
t = NULL,
study_names = NULL,
study_ids = NULL,
data = NULL,
transformation = if (is.null(y)) "fishers_z" else "none",
prior_scale = if (is.null(y)) "cohens_d" else "none",
effect_direction = "positive",
model_type = NULL,
priors_effect = prior(distribution = "normal", parameters = list(mean = 0, sd = 1)),
priors_heterogeneity = prior(distribution = "invgamma", parameters = list(shape = 1,
scale = 0.15)),
priors_bias = list(prior_weightfunction(distribution = "two.sided", parameters =
list(alpha = c(1, 1), steps = c(0.05)), prior_weights = 1/12),
prior_weightfunction(distribution = "two.sided", parameters = list(alpha = c(1, 1,
1), steps = c(0.05, 0.1)), prior_weights = 1/12), prior_weightfunction(distribution =
"one.sided", parameters = list(alpha = c(1, 1), steps = c(0.05)), prior_weights =
1/12), prior_weightfunction(distribution = "one.sided", parameters = list(alpha =
c(1, 1, 1), steps = c(0.025, 0.05)), prior_weights = 1/12),
prior_weightfunction(distribution = "one.sided", parameters = list(alpha = c(1, 1,
1), steps = c(0.05, 0.5)), prior_weights = 1/12), prior_weightfunction(distribution =
"one.sided", parameters = list(alpha = c(1, 1, 1, 1), steps = c(0.025, 0.05, 0.5)),
prior_weights = 1/12), prior_PET(distribution = "Cauchy", parameters = list(0, 1),
truncation = list(0, Inf), prior_weights = 1/4), prior_PEESE(distribution = "Cauchy",
parameters = list(0, 5), truncation = list(0, Inf), prior_weights = 1/4)),
priors_effect_null = prior(distribution = "point", parameters = list(location = 0)),
priors_heterogeneity_null = prior(distribution = "point", parameters = list(location
= 0)),
priors_bias_null = prior_none(),
priors_rho = prior("beta", parameters = list(alpha = 1, beta = 1)),
priors_rho_null = NULL,
chains = 3,
sample = 5000,
burnin = 2000,
adapt = 500,
thin = 1,
parallel = FALSE,
autofit = TRUE,
autofit_control = set_autofit_control(),
convergence_checks = set_convergence_checks(),
save = "all",
seed = NULL,
silent = TRUE,
...
)
```

- d
a vector of effect sizes measured as Cohen's d

- r
a vector of effect sizes measured as correlations

- logOR
a vector of effect sizes measured as log odds ratios

- z
a vector of effect sizes measured as Fisher's z

- y
a vector of unspecified effect sizes (note that effect size transformations are unavailable with this type of input)

- se
a vector of standard errors of the effect sizes

- v
a vector of variances of the effect sizes

- n
a vector of overall sample sizes

- lCI
a vector of lower bounds of confidence intervals

- uCI
a vector of upper bounds of confidence intervals

- t
a vector of t/z-statistics

- study_names
an optional argument with the names of the studies

- study_ids
an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to

`NULL`

for studies being independent.- data
a data object created by the

`combine_data`

function. This is an alternative input entry to specifying the`d`

,`r`

,`y`

, etc... directly. I.e., you cannot pass the a data.frame and reference to the columns.- transformation
transformation to be applied to the supplied effect sizes before fitting the individual models. Defaults to

`"fishers_z"`

. We highly recommend using`"fishers_z"`

transformation since it is the only variance stabilizing measure and does not bias PET and PEESE style models. The other options are`"cohens_d"`

, correlation coefficient`"r"`

and`"logOR"`

. Supplying`"none"`

will treat the effect sizes as unstandardized and refrain from any transformations.- prior_scale
a scale used to define priors. Defaults to

`"cohens_d"`

. Other options are`"fishers_z"`

, correlation coefficient`"r"`

, and`"logOR"`

. The prior scale does not need to match the effect sizes measure - the samples from prior distributions are internally transformed to match the`transformation`

of the data. The`prior_scale`

corresponds to the scale of default output, but can be changed within the summary function.- effect_direction
the expected direction of the effect. The one-sided selection sets the weights omega to 1 to significant results in the expected direction. Defaults to

`"positive"`

(another option is`"negative"`

).- model_type
string specifying the RoBMA ensemble. Defaults to

`NULL`

. The other options are`"PSMA"`

,`"PP"`

, and`"2w"`

which override settings passed to the`priors_effect`

,`priors_heterogeneity`

,`priors_effect`

,`priors_effect_null`

,`priors_heterogeneity_null`

,`priors_bias_null`

, and`priors_effect`

. See details for more information about the different model types.- priors_effect
list of prior distributions for the effect size (

`mu`

) parameter that will be treated as belonging to the alternative hypothesis. Defaults to a standard normal distribution`prior(distribution = "normal", parameters = list(mean = 0, sd = 1))`

.- priors_heterogeneity
list of prior distributions for the heterogeneity

`tau`

parameter that will be treated as belonging to the alternative hypothesis. Defaults to`prior(distribution = "invgamma", parameters = list(shape = 1, scale = .15))`

that is based on heterogeneities estimates from psychology (van Erp et al. 2017) .- priors_bias
list of prior distributions for the publication bias adjustment component that will be treated as belonging to the alternative hypothesis. Defaults to

`list( prior_weightfunction(distribution = "two.sided", parameters = list(alpha = c(1, 1), steps = c(0.05)), prior_weights = 1/12), prior_weightfunction(distribution = "two.sided", parameters = list(alpha = c(1, 1, 1), steps = c(0.05, 0.10)), prior_weights = 1/12), prior_weightfunction(distribution = "one.sided", parameters = list(alpha = c(1, 1), steps = c(0.05)), prior_weights = 1/12), prior_weightfunction(distribution = "one.sided", parameters = list(alpha = c(1, 1, 1), steps = c(0.025, 0.05)), prior_weights = 1/12), prior_weightfunction(distribution = "one.sided", parameters = list(alpha = c(1, 1, 1), steps = c(0.05, 0.5)), prior_weights = 1/12), prior_weightfunction(distribution = "one.sided", parameters = list(alpha = c(1, 1, 1, 1), steps = c(0.025, 0.05, 0.5)), prior_weights = 1/12), prior_PET(distribution = "Cauchy", parameters = list(0,1), truncation = list(0, Inf), prior_weights = 1/4), prior_PEESE(distribution = "Cauchy", parameters = list(0,5), truncation = list(0, Inf), prior_weights = 1/4) )`

, corresponding to the RoBMA-PSMA model introduce by Bartoš et al. (2021) .- priors_effect_null
list of prior distributions for the effect size (

`mu`

) parameter that will be treated as belonging to the null hypothesis. Defaults to a point null hypotheses at zero,`prior(distribution = "point", parameters = list(location = 0))`

.- priors_heterogeneity_null
list of prior distributions for the heterogeneity

`tau`

parameter that will be treated as belonging to the null hypothesis. Defaults to a point null hypotheses at zero (a fixed effect meta-analytic models),`prior(distribution = "point", parameters = list(location = 0))`

.- priors_bias_null
list of prior weight functions for the

`omega`

parameter that will be treated as belonging to the null hypothesis. Defaults no publication bias adjustment,`prior_none()`

.- priors_rho
list of prior distributions for the variance allocation (

`rho`

) parameter that will be treated as belonging to the alternative hypothesis. This setting allows users to fit a three-level meta-analysis when`study_ids`

are supplied. Note that this is an experimental feature and see News for more details. Defaults to a beta distribution`prior(distribution = "beta", parameters = list(alpha = 1, beta = 1))`

.- priors_rho_null
list of prior distributions for the variance allocation (

`rho`

) parameter that will be treated as belonging to the null hypothesis. Defaults to`NULL`

.- chains
a number of chains of the MCMC algorithm.

- sample
a number of sampling iterations of the MCMC algorithm. Defaults to

`5000`

.- burnin
a number of burnin iterations of the MCMC algorithm. Defaults to

`2000`

.- adapt
a number of adaptation iterations of the MCMC algorithm. Defaults to

`500`

.- thin
a thinning of the chains of the MCMC algorithm. Defaults to

`1`

.- parallel
whether the individual models should be fitted in parallel. Defaults to

`FALSE`

. The implementation is not completely stable and might cause a connection error.- autofit
whether the model should be fitted until the convergence criteria (specified in

`autofit_control`

) are satisfied. Defaults to`TRUE`

.- autofit_control
allows to pass autofit control settings with the

`set_autofit_control()`

function. See`?set_autofit_control`

for options and default settings.- convergence_checks
automatic convergence checks to assess the fitted models, passed with

`set_convergence_checks()`

function. See`?set_convergence_checks`

for options and default settings.- save
whether all models posterior distributions should be kept after obtaining a model-averaged result. Defaults to

`"all"`

which does not remove anything. Set to`"min"`

to significantly reduce the size of final object, however, some model diagnostics and further manipulation with the object will not be possible.- seed
a seed to be set before model fitting, marginal likelihood computation, and posterior mixing for reproducibility of results. Defaults to

`NULL`

- no seed is set.- silent
whether all print messages regarding the fitting process should be suppressed. Defaults to

`TRUE`

. Note that`parallel = TRUE`

also suppresses all messages.- ...
additional arguments.

`RoBMA`

returns an object of class 'RoBMA'.

The default settings of the RoBMA 2.0 package corresponds to the RoBMA-PSMA
ensemble proposed by Bartoš et al. (2021)
. The previous versions
of the package (i.e., RoBMA < 2.0) used specifications proposed by
Maier et al. (in press)
(this specification can be easily
obtained by setting `model_type = "2w"`

. The RoBMA-PP specification from
Bartoš et al. (2021)
can be obtained by setting
`model_type = "PP"`

.

The `vignette("CustomEnsembles", package = "RoBMA")`

and `vignette("ReproducingBMA", package = "RoBMA")`

vignettes describe how to use `RoBMA()`

to fit custom meta-analytic ensembles (see `prior()`

,
`prior_weightfunction()`

, `prior_PET()`

, and `prior_PEESE()`

for more information about prior
distributions).

The RoBMA function first generates models from a combination of the provided priors for each of the model parameters. Then, the individual models are fitted using autorun.jags function. A marginal likelihood is computed using bridge_sampler function. The individual models are then combined into an ensemble using the posterior model probabilities using BayesTools package.

Generic `summary.RoBMA()`

, `print.RoBMA()`

, and `plot.RoBMA()`

functions are
provided to facilitate manipulation with the ensemble. A visual check of the
individual model diagnostics can be obtained using the `diagnostics()`

function.
The fitted model can be further updated or modified by `update.RoBMA()`

function.

Bartoš F, Maier M, Wagenmakers E, Doucouliagos H, Stanley TD (2021).
“Robust Bayesian meta-analysis: Model-averaging across complementary publication bias adjustment methods.”
doi:10.31234/osf.io/kvsp7
, preprint at https://doi.org/10.31234/osf.io/kvsp7.

Maier M, Bartoš F, Wagenmakers E (in press).
“Robust Bayesian Meta-Analysis: Addressing Publication Bias with Model-Averaging.”
*Psychological Methods*.
doi:10.31234/osf.io/u4cns
.

van Erp S, Verhagen J, Grasman RP, Wagenmakers E (2017).
“Estimates of between-study heterogeneity for 705 meta-analyses reported in Psychological Bulletin from 1990--2013.”
*Journal of Open Psychology Data*, **5**(1).
doi:10.5334/jopd.33
.

```
if (FALSE) {
# using the example data from Bem 2011 and fitting the default (RoBMA-PSMA) model
fit <- RoBMA(d = Bem2011$d, se = Bem2011$se, study_names = Bem2011$study)
# in order to speed up the process, we can turn the parallelization on
fit <- RoBMA(d = Bem2011$d, se = Bem2011$se, study_names = Bem2011$study, parallel = TRUE)
# we can get a quick overview of the model coefficients just by printing the model
fit
# a more detailed overview using the summary function (see '?summary.RoBMA' for all options)
summary(fit)
# the model-averaged effect size estimate can be visualized using the plot function
# (see ?plot.RoBMA for all options)
plot(fit, parameter = "mu")
# forest plot can be obtained with the forest function (see ?forest for all options)
forest(fit)
# plot of the individual model estimates can be obtained with the plot_models function
# (see ?plot_models for all options)
plot_models(fit)
# diagnostics for the individual parameters in individual models can be obtained using diagnostics
# function (see 'diagnostics' for all options)
diagnostics(fit, parameter = "mu", type = "chains")
# the RoBMA-PP can be fitted with addition of the 'model_type' argument
fit_PP <- RoBMA(d = Bem2011$d, se = Bem2011$se, study_names = Bem2011$study, model_type = "PP")
# as well as the original version of RoBMA (with two weightfunctions)
fit_original <- RoBMA(d = Bem2011$d, se = Bem2011$se, study_names = Bem2011$study,
model_type = "2w")
# or different prior distribution for the effect size (e.g., a half-normal distribution)
# (see 'vignette("CustomEnsembles")' for a detailed guide on specifying a custom model ensemble)
fit <- RoBMA(d = Bem2011$d, se = Bem2011$se, study_names = Bem2011$study,
priors_effect = prior("normal", parameters = list(0, 1),
truncation = list(0, Inf)))
}
```