pri_RA_5bm: Prior reference analysis based on a data frame using 5...
In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

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).

pri_RA_5bm(df, tau.prior=list(function(x) dhalfnormal(x, scale=1)),
           m_J=NA, M_J=NA, upper.J=3, digits.J=2,
           m_inf=NA, M_inf=NA, rlmc0=0.0001, rlmc1=0.9999,
           mu.mean=0, mu.sd=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 `bayesmeta` function. See the documentation of the argument `tau.prior` of the `bayesmeta` function for details.

`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 `NA` (the default), this parameter is computed using the function `m_j_sgc` and some other parameters.
`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 `NA` (the default), this parameter is computed using the function `M_j_sigc` and some other parameters.
`upper.J`	upper bound for the parameters `M_J` and `m_J`. Real number in (1,∞). Is required only if `M_J=NA` or `m_J=NA`.
`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_J=NA` or `m_J=NA`.
`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 `NA` (the default), this parameter is computed using the function `m_inf_sgc`, such that the median RLMC is approximately equal to `rlmc0`.
`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 `NA` (the default), this parameter is computed using the function `M_inf_sigc`, such that the median RLMC is approximately equal to `rlmc1`.
`rlmc0`	RLMC target value for the SGC(m_{inf}) benchmark prior (typically close to 0). Is required only if `m_inf=NA`.
`rlmc1`	RLMC target value for the SIGC(M_{inf}) benchmark prior (typically close to 1). Is required only if `M_inf=NA`.
`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 `tau.prior`
`pri_act_2`	second actual prior in `tau.prior`
`...`
`pri_act_n`	nth (last) actual prior in `tau.prior`

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 meta-analysis. Revised for Statistics in Medicine. 2021.

post_RA_3bm, pri_RA_fits

# for aurigular acupuncture (AA) data set with one
# actual half-normal 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)