meta_default {metaBMA}

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. 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. doi:10.1080/23743603.2017.1326760

See Also

meta_bma, plot_default, transform_es

Examples

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