RoBMA (version 3.5.1)

RoBMA: Estimate a Robust Bayesian Meta-Analysis

Description

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.

Usage

RoBMA(
  d = NULL,
  r = NULL,
  logOR = NULL,
  OR = 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,
  weight = 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,
  rescale_priors = 1,
  priors_effect = set_default_priors("effect", rescale = rescale_priors),
  priors_heterogeneity = set_default_priors("heterogeneity", rescale = rescale_priors),
  priors_bias = set_default_priors("bias", rescale = rescale_priors),
  priors_effect_null = set_default_priors("effect", null = TRUE),
  priors_heterogeneity_null = set_default_priors("heterogeneity", null = TRUE),
  priors_bias_null = set_default_priors("bias", null = TRUE),
  priors_hierarchical = set_default_priors("hierarchical"),
  priors_hierarchical_null = set_default_priors("hierarchical", null = TRUE),
  algorithm = "bridge",
  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,
  ...
)

Value

RoBMA returns an object of class 'RoBMA'.

Arguments

d

a vector of effect sizes measured as Cohen's d / Hedges' g (standardized mean differences)

r

a vector of effect sizes measured as correlations

logOR

a vector of effect sizes measured as log odds ratios

OR

a vector of effect sizes measured as 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., RoBMA function does not allow passing a data.frame and referencing to the columns.

weight

specifies likelihood weights of the individual estimates. Notes that this is an untested experimental feature.

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

an effect size 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 effect size scale of default output, but can be changed within the summary function.

effect_direction

the expected direction of the effect. Correctly specifying the expected direction of the effect is crucial for one-sided selection models, as they specify cut-offs using one-sided p-values. 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.

rescale_priors

a re-scaling factor for the prior distributions. The re-scaling factor allows to adjust the width of all default priors simultaneously. Defaults to 1.

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 erp2017estimatesRoBMA.

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 bartos2021no;textualRoBMA.

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_hierarchical

list of prior distributions for the correlation of random effects (rho) parameter that will be treated as belonging to the alternative hypothesis. This setting allows users to fit a hierarchical (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_hierarchical_null

list of prior distributions for the correlation of random effects (rho) parameter that will be treated as belonging to the null hypothesis. Defaults to NULL.

algorithm

a string specifying the algorithm used for the model averaging. Defaults to "bridge" which results in estimating individual models using JAGS and computing the marginal likelihood using bridge sampling. An alternative is "ss" which uses spike and slab like parameterization to approximate the Bayesian model averaging with a single model. Note that significantly more sample, burnin, and adapt iterations are needed for the "ss" algorithm.

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.

Details

The default settings of the RoBMA 2.0 package corresponds to the RoBMA-PSMA ensemble proposed by bartos2021no;textualRoBMA. The previous versions of the package (i.e., RoBMA < 2.0) used specifications proposed by maier2020robust;textualRoBMA (this specification can be easily obtained by setting model_type = "2w". The RoBMA-PP specification from bartos2021no;textualRoBMA can be obtained by setting model_type = "PP". The complete list of default prior distributions is described at set_default_priors(). Note that inclusion of the PET and PEESE style publication bias adjustments models might pick up on small-study effects. To remove true heterogeneity due to study design, sub-populations, treatments etc. potentially causing small-study effects, use meta-regression via the RoBMA.reg() function, or remove the PET and PEESE style models from the publication bias adjustment component of the ensemble.

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.

References

See Also

summary.RoBMA(), update.RoBMA(), check_setup()

Examples

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)))
}