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

Lopes, J. E. (2023). Modelos de regressao beta para dados de escala. Master's dissertation, Universidade Federal do Parana, Curitiba. URI: https://hdl.handle.net/1884/86624.

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