Estimate a Robust Bayesian Meta-Analysis Meta-Regression

RoBMA is used to estimate a robust Bayesian meta-regression. The interface allows a complete customization of the ensemble with different prior (or list of prior) distributions for each component.

Usage

RoBMA.reg(
  formula,
  data,
  test_predictors = TRUE,
  study_names = NULL,
  study_ids = NULL,
  transformation = if (any(colnames(data) != "y")) "fishers_z" else "none",
  prior_scale = if (any(colnames(data) != "y")) "cohens_d" else "none",
  standardize_predictors = TRUE,
  effect_direction = "positive",
  priors = NULL,
  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),
  prior_covariates = set_default_priors("covariates", rescale = rescale_priors),
  prior_covariates_null = set_default_priors("covariates", null = TRUE),
  prior_factors = set_default_priors("factors", rescale = rescale_priors),
  prior_factors_null = set_default_priors("factors", null = TRUE),
  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,
  ...
)

Arguments

formula: a formula for the meta-regression model
data: a data.frame containing the data for the meta-regression. Note that the column names have to correspond to the effect sizes (d, logOR, OR, r, z), a measure of sampling variability (se, v, n, lCI, uCI, t), and the predictors. See combine_data() for a complete list of reserved names and additional information about specifying input data.
test_predictors: vector of predictor names to test for the presence of moderation (i.e., assigned both the null and alternative prior distributions). Defaults to TRUE, all predictors are tested using the default prior distributions (i.e., prior_covariates, prior_covariates_null, prior_factors, and prior_factors_null). To only estimate and adjust for the effect of predictors use FALSE. If priors is specified, any settings in test_predictors is overridden.
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.
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.
standardize_predictors: whether continuous predictors should be standardized prior to estimating the model. Defaults to TRUE.
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").
priors: named list of prior distributions for each predictor (with names corresponding to the predictors). It allows users to specify both the null and alternative hypothesis prior distributions for each predictor by assigning the corresponding element of the named list with another named list (with "null" and "alt"). If only one prior is specified for a given parameter, it is assumed to correspond to the alternative hypotheses and the default null hypothesis is specified (i.e., prior_covariates_null or prior_factors_null). If a named list with only one named prior distribution is provided (either "null" or "alt"), only this prior distribution is used and no default distribution is filled in. Parameters without specified prior distributions are assumed to be only adjusted for using the default alternative hypothesis prior distributions (i.e., prior_covariates or prior_factors). If priors is specified, test_predictors is ignored.
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.
prior_covariates: a prior distributions for the regression parameter of continuous covariates on the effect size under the alternative hypothesis (unless set explicitly in priors). Defaults to a relatively wide normal distribution prior(distribution = "normal", parameters = list(mean = 0, sd = 0.25)).
prior_covariates_null: a prior distributions for the regression parameter of continuous covariates on the effect size under the null hypothesis (unless set explicitly in priors). Defaults to a no effect prior("spike", parameters = list(location = 0)).
prior_factors: a prior distributions for the regression parameter of categorical covariates on the effect size under the alternative hypothesis (unless set explicitly in priors). Defaults to a relatively wide multivariate normal distribution specifying differences from the mean contrasts prior_factor("mnormal", parameters = list(mean = 0, sd = 0.25), contrast = "meandif").
prior_factors_null: a prior distributions for the regression parameter of categorical covariates on the effect size under the null hypothesis (unless set explicitly in priors). Defaults to a no effect prior("spike", parameters = list(location = 0)).
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.

Value

RoBMA.reg returns an object of class 'RoBMA.reg'.

Details

The vignette("/MetaRegression", package = "RoBMA") vignette describes how to use RoBMA.reg() function to fit Bayesian meta-regression ensembles. See bartos2023robust;textualRoBMA for more details about the methodology and RoBMA() for more details about the function options.

The RoBMA.reg 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. Estimated marginal means can be computed by marginal_summary() function and visualized by the marginal_plot() function.

References

Examples

if (FALSE) { # \dontrun{
# using the example data from Andrews et al. (2021) and reproducing the example from
# Bartos et al. (2024) with measure and age covariate.

 # note the the Andrews2021 data.frame columns identify the effect size "r" and
 # the standard error "se" of the effect size that are used to estimate the model
 fit_RoBMA <- RoBMA.reg(~ measure + age, data = Andrews2021, parallel = TRUE, seed = 1)

 # summarize the results
 summary(fit_RoBMA, output_scale = "r")

 # compute effect size estimates for each group
 marginal_summary(fit_RoBMA, output_scale = "r")

 # visualize the effect size estimates for each group
 marginal_plot(fit_RoBMA, parameter = "measure", output_scale = "r", lwd = 2)
} # }