Description Usage Arguments Details Value Warning References See Also Examples
Computes a table of Hellinger distances between marginal posterior distributions
for different parameters in the NNHM
between the actual model fits in fits.actual
and
the benchmark fits in fits.bm
.
All fits should be based on the same data set.
1 2  post_RA_fits(fits.actual, fits.bm,
H.dist.method = "integral")

fits.actual 
a list of model fits of class bayesmeta, computed with
the 
fits.bm 
a list of model fits of class bayesmeta, computed with
the 
H.dist.method 
method for computation of Hellinger distances between marginal posterior densities. Either 
Two alternative suggestions for posterior benchmarks are provided
in Ott et al. (2021, Section 3.4) and its Supplementary Material (Section 2.5) and they
can be computed using the functions fit_models_RA
and fit_models_RA_5bm
,
respectively.
If integralbased computation (H.dist.method = "integral"
) of Hellinger distances is selected (the default), numerical integration is applied to obtain the Hellinger distance between the two marginal posterior densities (by using the function H
).
If momentbased computation (H.dist.method = "moment"
) is selected, the marginal densities are first approximated by normal densities with the same means and standard deviations and then the Hellinger distance between these normal densities can be obtained by an analytical formula (implemented in the function H_normal
).
A matrix of Hellinger distance estimates between marginal posteriors
with n.bm columns and n.act*(k+3) rows,
where n.bm=length(fits.bm
) is the number of benchmark fits specified,
n.act=length(fits.actual
) the number of actual fits specified
and
k the number of studies in the metaanalysis data set
(so that there are k+3 parameters Ψ \in \{ μ, τ, θ_1, ..., θ_k, θ_{new} \} of potential interest in the NNHM).
The columns of the matrix give the following Hellinger distance estimates between two marginal posteriors (for the parameter of interest Ψ varying with rows) induced by the following two heterogeneity priors (from left to right):
H(po_bm_1, po_act) 
first benchmark prior bm_1 inducing the fit 
H(po_bm_2, po_act) 
second benchmark prior bm_2 inducing the fit 
... 
... 
H(po_bm_n.bm, po_act) 
last benchmark prior bm_n.bm inducing the fit 
The actual heterogenity prior and the parameter of interest Ψ vary with the rows in the following order:
mu, pri_act_1 
Ψ=μ and first actual prior in 
mu, pri_act_2 
Ψ=μ and second actual prior in 
... 
... 
mu, pri_act_n 
Ψ=μ and nth actual prior in 
tau, pri_act_1 
Ψ=τ and first actual prior in 
... 
... 
tau, pri_act_n 
Ψ=τ and nth actual prior 
theta_1, pri_act_1 
Ψ=θ_1 and first actual prior 
... 
... 
theta_k, pri_act_n 
Ψ=θ_k and nth actual prior 
theta_new, pri_act_1 
Ψ=θ_{new} and first actual prior 
... 
... 
theta_new, pri_act_n 
Ψ=θ_{new} and nth actual prior 
If the integralbased method is used to compute Hellinger distances (H.dist.method = "integral"
),
numerical problems may occur in some cases, which may lead to implausible outputs.
Therefore, we generally recommend to doublecheck the results of the integralbased method using the momentbased method (H.dist.method = "moment"
)  especially if the former results are implausibe. If large differences between the two methods are observed, we recommend to rely on the momentbased method unless a normal approximation of the involved densities is inappropriate.
Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is informative? Reference analysis for Bayesian metaanalysis. Manuscript revised for Statistics in Medicine. 2021.
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.
bayesmeta
in the package bayesmeta,
fit_models_RA
,
post_RA
,
pri_RA_fits
1 2 3 4 5 6 7 8 9 10 11  # for aurigular acupuncture (AA) data set
data(aa)
# compute the model fits % this example takes > 5 sec. to run
# actual standard halfnormal and halfCauchy heterogeneity priors
fits < fit_models_RA(df=aa, tau.prior=
list(function(t)dhalfnormal(t, scale=1),
function(t)dhalfcauchy(t, scale=1)))
# benchmark fits under HN0 and J (Jeffreys) priors
fits.bm.post < fits[c(1,2)]
fits.actual < fits[c(3,4)]
post_RA_fits(fits.actual=fits.actual, fits.bm=fits.bm.post)

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