meta_default: Defaults for Model Averaging in Meta-Analysis

Description

Wrapper with default prior for Bayesian meta-analysis. Since version 0.6.6, the default priors for Cohen's d have been changed from a normal distribution with scale=0.3 to a Cauchy distribution with scale=0.707. Moreover, scale adjustments were implemented when using Fisher's z or log odds-ratios.

Usage

meta_default(y, SE, labels, data, field = "psychology", effect = "d", ...)

Arguments

y: effect size per study. Can be provided as (1) a numeric vector, (2) the quoted or unquoted name of the variable in data, or (3) a formula to include discrete or continuous moderator variables.
SE: standard error of effect size for each study. Can be a numeric vector or the quoted or unquoted name of the variable in data
labels: optional: character values with study labels. Can be a character vector or the quoted or unquoted name of the variable in data
data: data frame containing the variables for effect size y, standard error SE, labels, and moderators per study.
field: either"psychology" or "medicine"
effect: the type of effect size used in the meta-analysis: either Cohen's d ("d"), Fisher's z-transformed correlation ("z"), or log odds ratios ("logOR").
...: further arguments passed to meta_bma

Details

The prior distribution depends on the scale of the effect size that is used in the meta-analysis (Cohen's d, Fisher's z, or log odds ratio). To ensure that the results are comparable when transforming between different effect sizes (e.g., using the function transform_es), it is necessary to adjust the prior distributions. The present adjustments merely use a linear re-scaling of the priors to achieve approximately invariant results when using different types of effect sizes.

The distribution of Fisher's z is approximately half as wide as the distribution of Cohen's d and hence the prior scale parameter is divided by two.
The distribution of the log odds ratio is approximately pi / sqrt(3) = 1.81 times as wide as the distribution of Cohen's d. Hence, the prior scale parameter is doubled by this factor.

For field = "psychology", this results in the following defaults:

effect = "d" (Cohen's d): Cauchy distribution with scale=0.707 on the overall effect size (parameter d) and inverse gamma distribution with shape=1 and scale=0.15 on the standard deviation of effect sizes across studies (parameter tau).
effect = "z" (Fisher's z): Cauchy distribution with scale=0.354 on d and inverse gamma with shape=1 and scale=0.075 on tau.
effect = "logOR" (log odds ratio): Cauchy distribution with scale=1.283 on d and inverse gamma with shape=1 and scale=0.272 on tau.

Currently, the same priors are used when specifying field = "medicine".

Default prior distributions can be plotted using plot_default.

References

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Converting among effect sizes. In Introduction to Meta-Analysis (pp. 45–49). John Wiley & Sons, Ltd. tools:::Rd_expr_doi("10.1002/9780470743386.ch7")

Gronau, Q. F., Erp, S. V., Heck, D. W., Cesario, J., Jonas, K. J., & Wagenmakers, E.-J. (2017). A Bayesian model-averaged meta-analysis of the power pose effect with informed and default priors: the case of felt power. Comprehensive Results in Social Psychology, 2(1), 123-138. tools:::Rd_expr_doi("10.1080/23743603.2017.1326760")

Examples

Run this code

# \donttest{
data(towels)
set.seed(123)
md <- meta_default(logOR, SE, study, towels,
  field = "psychology", effect = "logOR"
)
md
plot_forest(md)
# }