Description Usage Arguments Details Value References Examples

By default (if `output="shift"`

), this function returns
the mean of a unit-variance normal distribution,
such that the Hellinger distance between this distribution and
the standard normal distribution equals the given value.
Offers the option to return the area of overlap (if `output="ao"`

) between these two unit-variance
normal distributions instead.
Gives an intuitive interpretation of Hellinger distance values.

1 | ```
cal_h_dist(h, output="shift")
``` |

`h` |
vector of Hellinger distances, consisting of real numbers in [0,1] |

`output` |
either |

For a given Hellinger distance h, there is a mean *μ(h)*, such that

*H(N(μ(h), 1), N(0, 1))=h,*

where H denotes the Hellinger distance. See Roos et al. (2015), Sect. 2.2 for details.

If `output="shift"`

, the function returns the shift *μ(h)* between
the two unit-variance normal distributions.
If `output="ao"`

, the function returns
the area of overlap between the *N(μ(h), 1)* and *N(0, 1)* distributions.
This area of overlap is given by

*AO(μ(h)) = Φ(μ(h)/2 ;μ(h), 1) + 1 - Φ(μ(h)/2 ;0, 1),*

where *Φ(. ;μ, σ^2)* denotes the cumulative distribution function of
the normal distribution with mean *μ* and variance *σ^2*.
See Ott et al. (2021, Section 3.5) for more information on this area of overlap calibration.

A vector of means (if `output="shift"`

) or areas of overlap (if `output="ao"`

), respectively.

Roos, M., Martins, T., Held, L., Rue, H. (2015). Sensitivity analysis for Bayesian hierarchical models.
*Bayesian Analysis* **10(2)**, 321–349.
https://projecteuclid.org/euclid.ba/1422884977

Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is
informative? Reference analysis for
Bayesian meta-analysis. Manuscript revised for *Statistics in Medicine*. 2021.

1 2 3 4 | ```
# calibration in terms of shifts
cal_h_dist(h=c(0.1, 0.5, 0.9))
# calibration in terms of areas of overlap
cal_h_dist(h=c(0.1, 0.5, 0.9), output="ao")
``` |

ra4bayesmeta documentation built on April 23, 2021, 9:06 a.m.

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