Reparameterize (mu, phi) into beta shape parameters

Converts a mean–dispersion pair \((\mu, \phi)\) to the shape parameters \((a, b)\) of the beta distribution under one of three reparameterization schemes.

Usage

brs_repar(mu, phi, repar = 2L)

Arguments

mu

Numeric vector of mean values in \((0, 1)\).

phi

Numeric vector (or scalar) of dispersion values.

repar

Integer (0, 1, or 2) selecting the scheme.

Value

A data.frame with columns shape1 and shape2.

Details

The three schemes are:

repar = 0

Direct: \(a = \mu,\; b = \phi\).

repar = 1

Ferrari–Cribari-Neto: \(a = \mu\phi,\; b = (1 - \mu)\phi\), where \(\phi\) acts as a precision parameter.

repar = 2

Mean–variance: \(a = \mu(1-\phi)/\phi,\; b = (1-\mu)(1-\phi)/\phi\), where \(\phi \in (0,1)\) is analogous to a coefficient of variation.

References

Hawker, G. A., Mian, S., Kendzerska, T., and French, M. (2011). Measures of adult pain: Visual Analog Scale for Pain (VAS Pain), Numeric Rating Scale for Pain (NRS Pain), McGill Pain Questionnaire (MPQ), Short-Form McGill Pain Questionnaire (SF-MPQ), Chronic Pain Grade Scale (CPGS), Short Form-36 Bodily Pain Scale (SF-36 BPS), and Measure of Intermittent and Constant Osteoarthritis Pain (ICOAP). Arthritis Care and Research, 63(S11), S240-S252. doi:10.1002/acr.20543.

Hjermstad, M. J., Fayers, P. M., Haugen, D. F., et al. (2011). Studies comparing Numerical Rating Scales, Verbal Rating Scales, and Visual Analogue Scales for assessment of pain intensity in adults: a systematic literature review. Journal of Pain and Symptom Management, 41(6), 1073-1093. doi:10.1016/j.jpainsymman.2010.08.016.

Examples

brs_repar(mu = 0.5, phi = 0.2, repar = 2)
#>   shape1 shape2
#> 1      2      2