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.
effect size per study. Can be provided as (1) a numeric vector, (2)
the quoted or unquoted name of the variable in
standard error of effect size for each study. Can be a numeric
vector or the quoted or unquoted name of the variable in
optional: character values with study labels. Can be a
character vector or the quoted or unquoted name of the variable in
data frame containing the variables for effect size
the type of effect size used in the meta-analysis: either
Cohen's d (
further arguments passed to
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.
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
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
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