a vector with the number of successes in the first group

a vector with the number of successes in the second group

a vector with the number of observations in the first group

a vector with the number of observations in the second group

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

list of prior distributions for the effect size (mu) parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "student", parameters = list(location = 0, scale = 0.58, df = 4)), based on logOR meta-analytic estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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 = 1.77, scale = 0.55)) that is based on heterogeneities of logOR estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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)).

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)).

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)).

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 distributions for the alternative hypothesis about intercepts (pi) of each study. Defaults to NULL.

prior distributions for the null hypothesis about intercepts (pi) for each study. Defaults to an independent uniform prior distribution for each intercept prior("beta", parameters = list(alpha = 1, beta = 1), contrast = "independent").

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

a formula for the meta-regression model

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.

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.

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

whether continuous predictors should be standardized prior to estimating the model. Defaults to TRUE. Continuous predictor standardization is important for applying the default prior distributions for continuous predictors. Note that the resulting output corresponds to standardized meta-regression coefficients.

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.

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.

list of prior distributions for the effect size (mu) parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "student", parameters = list(location = 0, scale = 0.58, df = 4)), based on logOR meta-analytic estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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 = 1.77, scale = 0.55)) that is based on heterogeneities of logOR estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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)).

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)).

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)).

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)).

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").

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)).

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)).

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 distributions for the alternative hypothesis about intercepts (pi) of each study. Defaults to NULL.

prior distributions for the null hypothesis about intercepts (pi) for each study. Defaults to an independent uniform prior distribution for each intercept prior("beta", parameters = list(alpha = 1, beta = 1), contrast = "independent").

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.

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

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

a vector of effect sizes measured as correlations

a vector of effect sizes measured as log odds ratios

a vector of effect sizes measured as odds ratios

a vector of effect sizes measured as Fisher's z

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

a vector of standard errors of the effect sizes

a vector of variances of the effect sizes

a vector of overall sample sizes

a vector of lower bounds of confidence intervals

a vector of upper bounds of confidence intervals

a vector of t/z-statistics

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

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

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.

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.

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.

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.

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)).

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).

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)).

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)).

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)).

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.

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.

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

a formula for the meta-regression model

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.

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.

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

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.

whether continuous predictors should be standardized prior to estimating the model. Defaults to TRUE. Continuous predictor standardization is important for applying the default prior distributions for continuous predictors. Note that the resulting output corresponds to standardized meta-regression coefficients.

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.

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.

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.

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)).

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).

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)).

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)).

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)).

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.

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)).

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)).

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").

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)).

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.

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

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

a vector of effect sizes measured as correlations

a vector of effect sizes measured as log odds ratios

a vector of effect sizes measured as odds ratios

a vector of effect sizes measured as Fisher's z

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

a vector of standard errors of the effect sizes

a vector of variances of the effect sizes

a vector of overall sample sizes

a vector of lower bounds of confidence intervals

a vector of upper bounds of confidence intervals

a vector of t/z-statistics

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

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

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.

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.

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").

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.

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.

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)).

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).

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. (2023).

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)).

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)).

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().

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)).

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.

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.

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

a formula for the meta-regression model

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.

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.

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

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.

whether continuous predictors should be standardized prior to estimating the model. Defaults to TRUE. Continuous predictor standardization is important for applying the default prior distributions for continuous predictors. Note that the resulting output corresponds to standardized meta-regression coefficients.

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").

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.

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.

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.

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)).

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).

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. (2023).

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)).

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)).

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().

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)).

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.

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)).

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)).

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").

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)).

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.

a number of chains of the MCMC algorithm.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

maximum value of the R-hat diagnostic. Defaults to 1.05.

minimum estimated sample size. Defaults to 500.

maximum value of the MCMC error. Defaults to NULL. Be aware that PEESE publication bias adjustment can have estimates on different scale than the rest of the output, resulting in relatively large max MCMC error.

maximum value of the proportion of MCMC error of the estimated SD of the parameter. Defaults to NULL.

list with the time and unit specifying the maximum autofitting process per model. Passed to difftime function (possible units are "secs", "mins", "hours", "days", "weeks", "years"). Defaults to list(time = 60, unit = "mins").

number of samples to extend the fitting process if the criteria are not satisfied. Defaults to 1000.

number of times new initial values should be generated in case a model fails to initialize. Defaults to 10.

number of times after which the automatic fitting function is stopped.

whether models not satisfying the convergence checks should be removed from the inference. Defaults to FALSE - only a warning is raised.

whether prior model probability should be balanced across the combinations of models with the same H0/H1 for effect / heterogeneity / bias in the case of non-convergence. Defaults to TRUE.

named option(s) to change - for a list of available options, see details below.

the name of the option to get the current value of - for a list of available options, see details below.

a fitted RoBMA object

show the conditional estimates (assuming that the alternative is true). Defaults to FALSE. Only available for type == "ensemble".

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

quantiles of the posterior samples to be displayed. Defaults to c(.025, .975)

additional arguments

a fitted RoBMA object.

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.

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)).

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).

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. (2023).

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)).

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)).

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().

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)).

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.

should the models' details be printed.

do not print the results.

list of prior distributions for the effect size (mu) parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "student", parameters = list(location = 0, scale = 0.58, df = 4)), based on logOR meta-analytic estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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 = 1.77, scale = 0.55)) that is based on heterogeneities of logOR estimates from the Cochrane Database of Systematic Reviews (Bartoš et al. 2023).

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)).

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)).

prior distributions for the alternative hypothesis about intercepts (pi) of each study. Defaults to NULL.

prior distributions for the null hypothesis about intercepts (pi) for each study. Defaults to an independent uniform prior distribution for each intercept prior("beta", parameters = list(alpha = 1, beta = 1), contrast = "independent").

should the models' details be printed.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

a formula for the meta-regression model

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.

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.

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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.

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.

whether continuous predictors should be standardized prior to estimating the model. Defaults to TRUE. Continuous predictor standardization is important for applying the default prior distributions for continuous predictors. Note that the resulting output corresponds to standardized meta-regression coefficients.

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").

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.

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.

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)).

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).

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. (2023).

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)).

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)).

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().

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)).

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.

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)).

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)).

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").

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)).

should the models' details be printed.

do not print the results.

additional arguments.

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

a vector of effect sizes measured as correlations

a vector of effect sizes measured as Fisher's z

a vector of effect sizes measured as log odds ratios

a vector of effect sizes measured as odds ratios

a vector of t/z-statistics

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

a vector of standard errors of the effect sizes

a vector of variances of the effect sizes

a vector of overall sample sizes

a vector of lower bounds of confidence intervals

a vector of upper bounds of confidence intervals

an optional argument with the names of the studies

an optional argument specifying dependency between the studies (for using a multilevel model). Defaults to NULL for studies being independent.

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

a data frame with column names corresponding to the variable names used to supply data individually

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.

whether data frame containing all filled values should be returned. Defaults to FALSE

additional arguments.

a vector of levels for a factor, or the number of levels

logical indicating whether contrasts should be computed

a fitted RoBMA object

a parameter to be plotted. Either "mu", "tau", "omega", "PET", or "PEESE".

type of MCMC diagnostic to be plotted. Options are "chains" for the chains' trace plots, "autocorrelation" for autocorrelation of the chains, and "densities" for the overlaying densities of the individual chains. Can be abbreviated to first letters.

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

MCMC diagnostics of which models should be plotted. Defaults to NULL which plots MCMC diagnostics for a specified parameter for every model that is part of the ensemble.

number of lags to be shown for type = "autocorrelation". Defaults to 30.

whether the model number should be displayed in title. Defaults to TRUE when more than one model is selected.

additional arguments to be passed to par if plot_type = "base".

Cohen's d.

correlation coefficient.

Fisher's z.

log(odds ratios).

offs ratios.

a fitted RoBMA object

whether conditional estimates should be plotted. Defaults to FALSE which plots the model-averaged estimates. Note that both "weightfunction" and "PET-PEESE" are always ignoring the other type of publication bias adjustment.

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

transform the effect sizes and the meta-analytic effect size estimate to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

order of the studies. Defaults to NULL - ordering as supplied to the fitting function. Studies can be ordered either "increasing" or "decreasing" by effect size, or by labels "alphabetical".

list of additional graphical arguments to be passed to the plotting function. Supported arguments are lwd, lty, col, col.fill, xlab, ylab, main, xlim, ylim to adjust the line thickness, line type, line color, fill color, x-label, y-label, title, x-axis range, and y-axis range respectively.

a fitted RoBMA object

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

an object to test

a fitted RoBMA regression object

regression parameter to be plotted

whether conditional marginal estimates should be plotted. Defaults to FALSE which plots the model-averaged estimates.

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

whether prior distribution should be added to figure. Defaults to FALSE.

transform the effect sizes and the meta-analytic effect size estimate to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

list of additional graphical arguments to be passed to the plotting function of the prior distribution. Supported arguments are lwd, lty, col, and col.fill, to adjust the line thickness, line type, line color, and fill color of the prior distribution respectively.

list of additional graphical arguments to be passed to the plotting function. Supported arguments are lwd, lty, col, col.fill, xlab, ylab, main, xlim, ylim to adjust the line thickness, line type, line color, fill color, x-label, y-label, title, x-axis range, and y-axis range respectively.

a fitted RoBMA regression object

show the conditional estimates (assuming that the alternative is true).

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

quantiles of the posterior samples to be displayed. Defaults to c(.025, .975)

show log of Bayes factors. Defaults to FALSE.

show Bayes factors in support of the null hypotheses. Defaults to FALSE.

a fitted RoBMA object

a parameter to be plotted. Defaults to "mu" (for the effect size). The additional options are "tau" (for the heterogeneity), "weightfunction" (for the estimated weightfunction), or "PET-PEESE" (for the PET-PEESE regression).

whether conditional estimates should be plotted. Defaults to FALSE which plots the model-averaged estimates. Note that both "weightfunction" and "PET-PEESE" are always ignoring the other type of publication bias adjustment.

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

whether prior distribution should be added to figure. Defaults to FALSE.

transform the effect sizes and the meta-analytic effect size estimate to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

whether the x-axis of the "weightfunction" should be re-scaled to make the x-ticks equally spaced. Defaults to FALSE.

whether the study estimates and standard errors should be show in the "PET-PEESE" plot. Defaults to TRUE.

list of additional graphical arguments to be passed to the plotting function of the prior distribution. Supported arguments are lwd, lty, col, and col.fill, to adjust the line thickness, line type, line color, and fill color of the prior distribution respectively.

list of additional graphical arguments to be passed to the plotting function. Supported arguments are lwd, lty, col, col.fill, xlab, ylab, main, xlim, ylim to adjust the line thickness, line type, line color, fill color, x-label, y-label, title, x-axis range, and y-axis range respectively.

a fitted RoBMA object

a parameter to be plotted. Defaults to "mu" (for the effect size). The additional option is "tau" (for the heterogeneity).

whether conditional estimates should be plotted. Defaults to FALSE which plots the model-averaged estimates. Note that both "weightfunction" and "PET-PEESE" are always ignoring the other type of publication bias adjustment.

transform the effect sizes and the meta-analytic effect size estimate to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

how the models should be ordered. Defaults to "decreasing" which orders them in decreasing order in accordance to order_by argument. The alternative is "increasing".

what feature should be use to order the models. Defaults to "model" which orders the models according to their number. The alternatives are "estimate" (for the effect size estimates), "probability" (for the posterior model probability), and "BF" (for the inclusion Bayes factor).

list of additional graphical arguments to be passed to the plotting function. Supported arguments are lwd, lty, col, col.fill, xlab, ylab, main, xlim, ylim to adjust the line thickness, line type, line color, fill color, x-label, y-label, title, x-axis range, and y-axis range respectively.

a fitted RoBMA object

show the conditional estimates (assuming that the alternative is true). Defaults to FALSE. Only available for type == "ensemble".

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

quantiles of the posterior samples to be displayed. Defaults to c(.025, .975)

additional arguments

a fitted RoBMA object.

additional arguments.

a summary of a RoBMA object

additional arguments

a summary of a RoBMA object

additional arguments

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The later is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses a 1/gamma distribution with a shape and rate parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

list of appropriate parameters for a given distribution.

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The later is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses a 1/gamma distribution with a shape and rate parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

list of appropriate parameters for a given distribution.

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The later is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses a 1/gamma distribution with a shape and rate parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

list of appropriate parameters for a given distribution.

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The later is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses a 1/gamma distribution with a shape and rate parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

list of appropriate parameters for a given distribution.

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

type of contrast for the prior distribution. The possible options are

"meandif"

for contrast centered around the grand mean with equal marginal distributions, making the prior distribution exchangeable across factor levels. In contrast to "orthonormal", the marginal distributions are identical regardless of the number of factor levels and the specified prior distribution corresponds to the difference from grand mean for each factor level. Only supports distribution = "mnormal" and distribution = "mt" which generates the corresponding multivariate normal/t distributions.

"orthonormal"

for contrast centered around the grand mean with equal marginal distributions, making the prior distribution exchangeable across factor levels. Only supports distribution = "mnormal" and distribution = "mt" which generates the corresponding multivariate normal/t distributions.

"treatment"

for contrasts using the first level as a comparison group and setting equal prior distribution on differences between the individual factor levels and the comparison level.

"independent"

for contrasts specifying dependent prior distribution for each factor level (note that this leads to an overparameterized model if the intercept is included).

name of the prior distribution. There are many options based on prior psychological or medical research. For psychology, the possible options are

"van Erp"

for an informed prior distribution for the heterogeneity parameter tau of meta-analytic effect size estimates based on standardized mean differences (van Erp et al. 2017),

"Oosterwijk"

for an informed prior distribution for the effect sizes expected in social psychology based on prior elicitation with dr. Oosterwijk (Gronau et al. 2017).

For medicine, the possible options are based on Bartoš et al. (2021) and Bartoš et al. (2023) who developed empirical prior distributions for the effect size and heterogeneity parameters of the continuous outcomes (standardized mean differences), dichotomous outcomes (logOR, logRR, and risk differences), and time to event outcomes (logHR) based on the Cochrane database of systematic reviews. Use "Cochrane" for a prior distribution based on the whole database or call print(prior_informed_medicine_names) to inspect the names of all 46 subfields and set the appropriate parameter and type.

parameter name describing what prior distribution is supposed to be produced in cases where the name corresponds to multiple prior distributions. Relevant only for the empirical medical prior distributions.

prior type describing what prior distribution is supposed to be produced in cases where the name and parameter correspond to multiple prior distributions. Relevant only for the empirical medical prior distributions with the following options

"smd"

for standardized mean differences

"logOR"

for log odds ratios

"logRR"

for log risk ratios

"RD"

for risk differences

"logHR"

for hazard ratios

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

name of the prior distribution. The possible options are

"two.sided"

for a two-sided weight function characterized by a vector steps and vector alpha parameters. The alpha parameter determines an alpha parameter of Dirichlet distribution which cumulative sum is used for the weights omega.

"one.sided"

for a one-sided weight function characterized by either a vector steps and vector alpha parameter, leading to a monotonic one-sided function, or by a vector steps, vector alpha1, and vector alpha2 parameters leading non-monotonic one-sided weight function. The alpha / alpha1 and alpha2 parameters determine an alpha parameter of Dirichlet distribution which cumulative sum is used for the weights omega.

list of appropriate parameters for a given distribution.

prior odds associated with a given distribution. The model fitting function usually creates models corresponding to all combinations of prior distributions for each of the model parameters, and sets the model priors odds to the product of its prior distributions.

Cohen's d

sample size of the corresponding effect size

standard error of the corresponding effect size

correlation coefficient

a character string specifying the parameter for which the prior distribution should be set. Available options are "effect", "heterogeneity", "baseline", "covariates", "factors".

a logical indicating whether the prior distribution should be set for the null hypothesis. Defaults to FALSE.

a numeric value specifying the re-scaling factor for the default prior distributions. Defaults to 1. Allows convenient re-scaling of prior distributions simultaneously.

a character string specifying the parameter for which the prior distribution should be set. Available options are "effect", "heterogeneity", "bias", "hierarchical", "covariates", "factors".

a logical indicating whether the prior distribution should be set for the null hypothesis. Defaults to FALSE.

a numeric value specifying the re-scaling factor for the default prior distributions. Defaults to 1. Allows convenient re-scaling of prior distributions simultaneously.

standard error of Cohen's d

log(odds ratios)

Cohen's d

standard error of correlation coefficient

correlation coefficient

standard error of log(odds ratios)

standard error of Fisher's z

Fisher's z

a fitted RoBMA object

whether to show the overall RoBMA results ("ensemble"), an overview of the individual models ("models"), an overview of the individual models MCMC diagnostics ("diagnostics"), or a detailed summary of the individual models ("individual"). Can be abbreviated to first letters.

show the conditional estimates (assuming that the alternative is true). Defaults to FALSE. Only available for type == "ensemble".

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

quantiles of the posterior samples to be displayed. Defaults to c(.025, .975)

show log of Bayes factors. Defaults to FALSE.

show Bayes factors in support of the null hypotheses. Defaults to FALSE.

whether priors names should be shortened to the first (couple) of letters. Defaults to FALSE.

whether spike prior distributions with location at zero should be omitted from the summary. Defaults to FALSE.

additional arguments

a fitted RoBMA object

whether to show the overall RoBMA results ("ensemble") or a detailed summary of the individual models ("individual"). Can be abbreviated to first letters.

show the conditional estimates (assuming that the alternative is true). Defaults to FALSE. Only available for type == "ensemble".

transform the meta-analytic estimates to a different scale. Defaults to NULL which returns the same scale as the model was estimated on.

quantiles of the posterior samples to be displayed. Defaults to c(.025, .975)

whether priors names should be shortened to the first (couple) of letters. Defaults to FALSE.

whether spike prior distributions with location at zero should be omitted from the summary. Defaults to FALSE.

a fitted BiBMA object

whether failed models should be refitted. Relevant only if new priors or prior_weights are not supplied. Defaults to TRUE.

extend sampling in all fitted models based on "sample_extend" argument in set_autofit_control() function. Defaults to FALSE.

prior distribution for the effect size (mu) parameter that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

prior distribution for the heterogeneity tau parameter that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

prior distribution for the intercepts (pi) of each study that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

either a single value specifying prior model weight of a newly specified model using priors argument, or a vector of the same length as already fitted models to update their prior weights.

prior distribution for the effect size (mu) parameter that will be treated as belonging to the null hypothesis. Defaults to NULL.

prior distribution for the heterogeneity tau parameter that will be treated as belonging to the null hypothesis. Defaults to NULL.

prior distribution for the intercepts (pi) of each study that will be treated as belonging to the null hypothesis. Defaults to NULL.

an optional argument with the names of the studies

a number of chains of the MCMC algorithm.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

a fitted RoBMA object

whether failed models should be refitted. Relevant only if new priors or prior_weights are not supplied. Defaults to TRUE.

extend sampling in all fitted models based on "sample_extend" argument in set_autofit_control() function. Defaults to FALSE.

prior distribution for the effect size (mu) parameter that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

prior distribution for the heterogeneity tau parameter that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

prior distribution for the publication bias adjustment component that will be treated as belonging to the alternative hypothesis. Defaults to NULL.

prior distribution 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)).

either a single value specifying prior model weight of a newly specified model using priors argument, or a vector of the same length as already fitted models to update their prior weights.

prior distribution for the effect size (mu) parameter that will be treated as belonging to the null hypothesis. Defaults to NULL.

prior distribution for the heterogeneity tau parameter that will be treated as belonging to the null hypothesis. Defaults to NULL.

prior distribution for the publication bias adjustment component that will be treated as belonging to the null hypothesis. Defaults to NULL.

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

an optional argument with the names of the studies

a number of chains of the MCMC algorithm.

a number of adaptation iterations of the MCMC algorithm. Defaults to 500.

a number of burnin iterations of the MCMC algorithm. Defaults to 2000.

a number of sampling iterations of the MCMC algorithm. Defaults to 5000.

a thinning of the chains of the MCMC algorithm. Defaults to 1.

whether the model should be fitted until the convergence criteria (specified in autofit_control) are satisfied. Defaults to TRUE.

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

allows to pass autofit control settings with the set_autofit_control() function. See ?set_autofit_control for options and default settings.

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

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.

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.

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

additional arguments.

quantiles.

vector of probabilities.

mean

covariance matrix.

vector of critical values defining steps.

vector of weights defining the probability of observing a t-statistics between each of the two steps.

type of weight function (defaults to "two.sided").

logical; if TRUE, probabilities p are given as log(p).

vector of quantiles.

mean

standard deviation.

vector of steps for the weight function.

vector of weights defining the probability of observing a t-statistics between each of the two steps.

vector of critical values defining steps (if steps are not supplied).

type of weight function (defaults to "two.sided").

logical; if TRUE, probabilities p are given as log(p).

logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X \ge x].

vector of probabilities.

number of observations. If length(n) > 1, the length is taken to be the number required.