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Christian Roever
bayesmeta
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b923109b
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b923109b
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4 years ago
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Christian Roever
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extended documentation
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man/bayesmeta-package.Rd
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man/bmr.Rd
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errors) and prior information (effect and heterogeneity priors), and
returns an object containing functions that allow to derive posterior
quantities like joint or marginal densities, quantiles, etc.
The \code{\link{bmr}()} function extends the approach to meta-regression.
}
\author{
Christian Roever <christian.roever@med.uni-goettingen.de>
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(\sQuote{zero/one} variables) simply identifying subgroups of studies.
See also the examples shown below.
\subsection{Connection to the simple random-effects model}{
\subsection{Connection to the simple random-effects model}{
The meta-regression model is a generalisation of the \sQuote{simple}
random-effects model that is implemented in the
\code{\link{bayesmeta}()} function. Meta-regression reduces to the
estimation of a single \dQuote{intercept} term when the regressor
matrix (\eqn{X})
has
a single column
(\eqn{d=1}) and consists only
of
matrix (\eqn{X})
consists of
a single column of
ones (which is also the default setting in case the \sQuote{\code{X}}
argument is left unspecified). The single regression coefficient
\eqn{\beta_1}{beta[1]} then is equivalent to the \eqn{\mu} parameter
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section below).
}
\subsection{Prior specification}{
\subsection{Specification of the regressor matrix}{ The actual
regression model is specified through the regressor matrix \eqn{X},
which is supplied via the \sQuote{\code{X}} argument, and which
often may be specified in different ways. There usually is no unique
solution, and what serves the present purpose best then depends on
the context; see also the examples below. Sensible column names
should be specified for \code{X}, as these will subsequently
determine the labels for the associated parameters later on. Model
specification via the regressor matrix has the advantage of being
very explicit and transparent; if one prefers a
code{\link[stats]{formula}} interface instead, a regressor matrix may
be generated via the \sQuote{\code{\link[stats]{model.matrix}()}}
function.
}
\subsection{Prior specification}{
Priors for \eqn{\beta} and \eqn{\tau} are assumed to factor into
into independent marginals \eqn{p(\beta,\tau)=p(\beta)\times
p(\tau)}{p(beta, tau) = p(beta) * p(tau)} and either (improper)
uniform or a normal priors may be specified for the regression coefficients
\eqn{\beta}. Accuracy of the eventual computations is determined by the
\code{delta} (maximum divergence \eqn{\delta}) and \code{epsilon}
(tail probability \eqn{\epsilon}) parameters (Roever and Friede,
2017).
\eqn{\beta}.
For sensible prior choices for the heterogeneity parameter \eqn{\tau},
see also Roever (2020), Roever \emph{et al.} (2021) and the
\sQuote{\code{\link{bayesmeta}()}} function's help.
}
\subsection{Computation}{
\subsection{Computation}{
The \code{bmr()} function utilizes the same computational method
as the \code{\link{bayesmeta}()} function to derive the posterior
distribution, namely, the \acronym{DIRECT} algorithm. Numerical
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