brma  R Documentation 
This function conducts Bayesian regularized metaregression (Van Lissa & Van
Erp, 2021). It uses the stan
function
rstan::sampling to fit the model. A lasso or horseshoe prior is used to
shrink the regression coefficients of irrelevant moderators towards zero.
See Details.
brma(x, ...)
## S3 method for class 'formula'
brma(
formula,
data,
vi = "vi",
study = NULL,
method = "hs",
standardize = TRUE,
prior = switch(method, lasso = c(df = 1, scale = 1), hs = c(df = 1, df_global = 1,
df_slab = 4, scale_global = 1, scale_slab = 2, relevant_pars = NULL)),
mute_stan = TRUE,
...
)
## Default S3 method:
brma(
x,
y,
vi,
study = NULL,
method = "hs",
standardize,
prior,
mute_stan = TRUE,
intercept,
...
)
x 
An k x m numeric matrix, where k is the number of effect sizes and m is the number of moderators. 
... 
Additional arguments passed on to 
formula 
An object of class 
data 
Either a 
vi 
Character. Name of the column in the 
study 
Character. Name of the column in the

method 
Character, indicating the type of regularizing prior to use.
Supports one of 
standardize 
Either a logical argument or a list. If 
prior 
Numeric vector, specifying the prior to use. Note that the
different 
mute_stan 
Logical, indicating whether mute all 'Stan' output or not. 
y 
A numeric vector of k effect sizes. 
intercept 
Logical, indicating whether or not an intercept should be included in the model. 
The Bayesian regularized metaanalysis algorithm (Van Lissa & Van Erp, 2021) penalizes metaregression coefficients either via the lasso prior (Park & Casella, 2008) or the regularized horseshoe prior (Piironen & Vehtari, 2017).
The Bayesian equivalent of the lasso penalty is obtained when
placing independent Laplace (i.e., double exponential) priors on the
regression coefficients centered around zero. The scale of the Laplace
priors is determined by a global scale parameter scale
, which
defaults to 1 and an inversetuning parameter \frac{1}{\lambda}
which is given a chisquare prior governed by a degrees of freedom
parameter df
(defaults to 1). If standardize = TRUE
,
shrinkage will
affect all coefficients equally and it is not necessary to adapt the
scale
parameter. Increasing the df
parameter will allow
larger values for the inversetuning parameter, leading to less shrinkage.
One issue with the lasso prior is that it has relatively light
tails. As a result, not only does the lasso have the desirable behavior of
pulling small coefficients to zero, it also results in too much shrinkage
of large coefficients. An alternative prior that improves upon this
shrinkage pattern is the horseshoe prior (Carvalho, Polson & Scott, 2010).
The horseshoe prior has an infinitely large spike at zero, thereby pulling
small coefficients toward zero but in addition has fat tails, which allow
substantial coefficients to escape the shrinkage. The regularized horseshoe
is an extension of the horseshoe prior that allows the inclusion of prior
information regarding the number of relevant predictors and can
be more numerically stable in certain cases (Piironen & Vehtari, 2017).
The regularized horseshoe has a global shrinkage parameter that influences
all coefficients similarly and local shrinkage parameters that enable
flexible shrinkage patterns for each coefficient separately. The local
shrinkage parameters are given a Student's t prior with a default df
parameter of 1. Larger values for df
result in lighter tails and
a prior that is no longer strictly a horseshoe prior. However, increasing
df
slightly might be necessary to avoid divergent transitions in
Stan (see also https://mcstan.org/misc/warnings.html). Similarly,
the degrees of freedom for the Student's t prior on the global shrinkage
parameter df_global
can be increased from the default of 1 to, for
example, 3 if divergent transitions occur although the resulting
prior is then strictly no longer a horseshoe. The scale for the Student's t
prior on the global shrinkage parameter scale_global
defaults to 1
and can be decreased to achieve more shrinkage. Moreover, if prior
information regarding the number of relevant moderators is available, it is
recommended to include this information via the relevant_pars
argument by setting it to the expected number of relevant moderators. When
relevant_pars
is specified, scale_global
is ignored and
instead based on the available prior information. Contrary to the horseshoe
prior, the regularized horseshoe applies additional regularization on large
coefficients which is governed by a Student's t prior with a
scale_slab
defaulting to 2 and df_slab
defaulting to 4.
This additional regularization ensures at least some shrinkage of large
coefficients to avoid any sampling problems.
A list
object of class brma
, with the following structure:
list( fit # An object of class stanfit, for compatibility with rstan coefficients # A numeric matrix with parameter estimates; these are # interpreted as regression coefficients, except tau2 and tau, # which are interpreted as the residual variance and standard # deviation, respectively. formula # The formula used to estimate the model terms # The predictor terms in the formula X # Numeric matrix of moderator variables Y # Numeric vector with effect sizes vi # Numeric vector with effect size variances tau2 # Numeric, estimated tau2 R2 # Numeric, estimated heterogeneity explained by the moderators k # Numeric, number of effect sizes study # Numeric vector with study id numbers )
Van Lissa, C. J., van Erp, S., & Clapper, E. B. (2023). Selecting relevant moderators with Bayesian regularized metaregression. Research Synthesis Methods. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.31234/osf.io/6phs5")}
Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103(482), 681–686. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214508000000337")}
Carvalho, C. M., Polson, N. G., & Scott, J. G. (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2), 465–480. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asq017")}
Piironen, J., & Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics, 11(2). https://projecteuclid.org/journals/electronicjournalofstatistics/volume11/issue2/Sparsityinformationandregularizationinthehorseshoeandothershrinkage/10.1214/17EJS1337SI.pdf
data("curry")
df < curry[c(1:5, 50:55), c("d", "vi", "sex", "age", "donorcode")]
suppressWarnings({res < brma(d~., data = df, iter = 10)})
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.