Description Usage Arguments Details Value Warning References See Also Examples
Computes a table of Hellinger distance estimates between the actual heterogeneity prior(s) specified and four benchmark heterogeneity priors proposed in the Supplementary Material of Ott et al. (2021).
1 2 3 4 
df 
data frame with one column "y" containing the (transformed) effect estimates for the individual studies and one column "sigma" containing the standard errors of these estimates. 
tau.prior 
list of prior specifications, which are either functions returning the probability densities of the actual priors of interest for the heterogeneity parameter tau or character strings specifying priors implemented in the 
m_J 
parameter value m=m_J of the SGC(m) prior,
which induces a marignal posterior for the heterogeneity standard deviation tau close to Jeffreys reference posterior (wrt the Hellinger distance).
If set to 
M_J 
parameter value M=M_J of the SIGC(M) prior,
which induces a marignal posterior for the heterogeneity standard deviation tau close to Jeffreys reference posterior (wrt the Hellinger distance).
If set to 
upper.J 
upper bound for the parameters 
digits.J 
specifies the desired precision of the parameter values M_J and m_J, i.e. to how many digits these two values
should be determined. Possible values are 1,2,3. Defaults to 2.
Is required only if 
m_inf 
parameter value m=m_{inf} of the SGC(m) prior,
such that the median relative latent model complexity (RLMC) is close to 0.
If set to 
M_inf 
parameter value M=M_{inf} of the SIGC(M) prior,
such that the median relative latent model complexity (RLMC) is close to 1.
If set to 
rlmc0 
RLMC target value for the SGC(m_{inf}) benchmark prior (typically close to 0).
Is required only if 
rlmc1 
RLMC target value for the SIGC(M_{inf}) benchmark prior (typically close to 1).
Is required only if 
mu.mean 
mean of the normal prior for the effect mu. 
mu.sd 
standard deviation of the normal prior for the effect mu. 
The methodology for a prior reference analysis and the four proper heterogeneity benchmark priors used are introduced in the Supplementary Material of Ott et al. (2021, Sections 2.5 and 2.6). There, these four benchmark priors are denoted by SGC(m_J), SIGC(M_J), SGC(m_{inf}) and SIGC(M_{inf}).
A list with two elements:
The first element named "table" is a matrix containing the Hellinger distance estimates and the
second element called "par" is a named vector giving the parameter values
of the benchmark priors.
The vector "par" has the following five components:
m_inf
, M_J
, m_J
, M_inf
and C
.
The matrix "table" contains the Hellinger distance estimates between actual and benchmark
heterogeneity priors
and has 4 columns and n rows,
where n is the number of actual heterogeneity priors specified,
i.e. the length of the list tau.prior
.
The columns of the matrix give the following Hellinger distance estimates between two heterogeneity priors (from left to right):
H(SGC(m_inf), pri_act) 
benchmark prior SGC(m_inf) and actual prior 
H(SIGC(M_J), pri_act) 
benchmark prior SIGC(M_J) and actual prior 
H(SGC(m_J), pri_act) 
benchmark prior SGC(m_J) and actual prior 
H(SIGC(M_inf), pri_act) 
benchmark prior SIGC(M_inf) and actual prior 
Each row corresponds to one actual heterogeneity prior
specified in the list tau.prior
, in the same order
as in that list. Thus, the row names are:
pri_act_1 
first actual prior in 
pri_act_2 
second actual prior in 
... 

pri_act_n 
nth (last) actual prior in 
This function may take several minutes to run if the parameter m_J
and/or M_J
is not specified,
especially if the desired precision is digits.J=2
or even digits.J=3
.
Ott, M., Plummer, M., Roos, M. Supplementary Material: How vague is vague? How informative is informative? Reference analysis for Bayesian metaanalysis. Revised for Statistics in Medicine. 2021.
1 2 3 4 5 6 7 8 9 10 11  # for aurigular acupuncture (AA) data set with one
# actual halfnormal and the "DuMouchel" heterogeneity prior
data(aa)
# warning: it takes ca. 7 min. to run this function
pri_RA_5bm(df=aa, tau.prior=list(function(t)dhalfnormal(t, scale=1),
"DuMouchel"))
# computation is much faster if m_J and M_J are specified
pri_RA_5bm(df=aa, tau.prior=list(function(t)dhalfnormal(t, scale=1),
"DuMouchel"),
m_J = 1.35, M_J = 1.3)

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