weighted_multivariate_normal

Density function for the weighted multivariate normal
distribution with <code>mean</code>, covariance matrix <code>sigma</code>,
critical values <code>crit_x</code>, and weights <code>omega</code>.

A framework for estimating ensembles of meta-analytic, meta-regression, and
multilevel models (assuming either presence or absence of the effect, heterogeneity,
publication bias, and moderators). The RoBMA framework uses Bayesian model-averaging to
combine the competing meta-analytic models into a model ensemble, weights
the posterior parameter distributions based on posterior model probabilities
and uses Bayes factors to test for the presence or absence of the
individual components (e.g., effect vs. no effect; Bartoš et al., 2022,
<doi:10.1002/jrsm.1594>; Maier, Bartoš & Wagenmakers, 2022,
<doi:10.1037/met0000405>; Bartoš et al., 2025, <doi:10.1037/met0000737>).
Users can define a wide range of prior distributions for the effect size, heterogeneity,
publication bias (including selection models and PET-PEESE), and moderator components.
The package provides convenient functions for summary, visualizations, and fit diagnostics.

Franti<c5><a1>ek Barto<c5><a1>

RoBMA

Robust Bayesian Meta-Analyses

František Bartoš

Maximilian Maier

Eric-Jan Wagenmakers

Joris Goosen

Matthew Denwood

Martyn Plummer

weighted_multivariate_normal function

<dl><dt>x</dt>
<dd>quantiles.</dd>
<dt>p</dt>
<dd>vector of probabilities.</dd>
<dt>mean</dt>
<dd>mean</dd>
<dt>sigma</dt>
<dd>covariance matrix.</dd>
<dt>crit_x</dt>
<dd>vector of critical values defining steps.</dd>
<dt>omega</dt>
<dd>vector of weights defining the probability
of observing a t-statistics between each of the two steps.</dd>
<dt>type</dt>
<dd>type of weight function (defaults to <code>"two.sided"</code>).</dd>
<dt>log, log.p</dt>
<dd>logical; if <code>TRUE</code>, probabilities
<code>p</code> are given as <code>log(p)</code>.</dd></dl>

Arguments

Weighted multivariate normal distribution — weighted_multivariate_normal

<dl>

<dt>x</dt>
<dd>quantiles.</dd>


<dt>p</dt>
<dd>vector of probabilities.</dd>


<dt>mean</dt>
<dd>mean</dd>


<dt>sigma</dt>
<dd>covariance matrix.</dd>


<dt>crit_x</dt>
<dd>vector of critical values defining steps.</dd>


<dt>omega</dt>
<dd>vector of weights defining the probability
of observing a t-statistics between each of the two steps.</dd>


<dt>type</dt>
<dd>type of weight function (defaults to <code>"two.sided"</code>).</dd>


<dt>log, log.p</dt>
<dd>logical; if <code>TRUE</code>, probabilities
<code>p</code> are given as <code>log(p)</code>.</dd>

</dl>

weighted_multivariate_normal: Weighted multivariate normal distribution

Description

Value

Arguments

See Also