betar_family function

Family Objects for (Extended-Support) Beta Regression

Family objects for distributional regression with the (extended-support) beta distribution via bamlss or gamlss2.

betar_family(link = "logit", link.phi = "log", ...)

xbetax_family(link = "logit", link.phi = "log", link.nu = "log",
  quad = 20, tol = .Machine$double.eps^0.7, ...)

Arguments

• link: character specification of the link function in the mean model (mu). Currently, "logit", "probit", "cloglog", "cauchit", "log", "loglog" are supported.
• link.phi: character specification of the link function in the precision model (phi). Currently, "log", "identity", "sqrt" are supported.
• link.nu: character specification of the link function in the exceedence model (nu). Currently, "log", "identity", "sqrt" are supported.
• quad: numeric. The number of quadrature points for numeric integration of the continuous mixture in dxbetax. Alternatively, a matrix with nodes and weights for the quadrature points can be specified.
• tol: numeric. Accuracy (convergence tolerance) for numerically determining quantiles based on uniroot and pxbetax.
• ...: Arguments passed to functions that are called within the family object.

Details

Family objects for bamlss (Umlauf et al. 2019, 2021) and gamlss2

(Umlauf et al. 2024) are essentially lists of functions providing a standardized interface to the d/p/q/r functions of distributions. Hence, betar_family

interfaces the classical beta distribution in regression specification, see dbetar. Analogously, xbetax_family interfaces the extended-support beta mixture specification (Kosmidis and Zeileis 2024), see dxbetax.

Returns

A list of class family.bamlss.

See Also

dbetar, dxbetax, family.bamlss

References

Kosmidis I, Zeileis A (2024). Extended-Support Beta Regression for [0, 1] Responses. 2409.07233, arXiv.org E-Print Archive. tools:::Rd_expr_doi("10.48550/arXiv.2409.07233")

Umlauf N, Klein N, Zeileis A (2019). BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond). Journal of Computational and Graphical Statistics, 27 (3), 612--627. tools:::Rd_expr_doi("10.1080/10618600.2017.1407325")

Umlauf N, Klein N, Simon T, Zeileis A (2021). bamlss: A Lego Toolbox for Flexible Bayesian Regression (and Beyond). Journal of Statistical Software, 100 (4), 1--53. tools:::Rd_expr_doi("10.18637/jss.v100.i04")

Umlauf N, Stasinopoulos M, Rigby R, Stauffer R (2024). gamlss2: Infrastructure for Flexible Distributional Regression. R package version 0.1-0. https://gamlss-dev.github.io/gamlss2/

Examples

## package and data
library("betareg")
library("bamlss")
data("ReadingSkills", package = "betareg")

## classical beta regression via ML
rs1 <- betareg(accuracy ~ dyslexia * iq | dyslexia + iq, data = ReadingSkills)

## IGNORE_RDIFF_BEGIN
## Bayesian additive model (with low number of iterations to speed up the example)
set.seed(0)
rs2 <- bamlss(accuracy ~ s(iq, by = dyslexia) | dyslexia + iq, data = ReadingSkills,
  family = betar_family(), eps = 1e-7, n.iter = 400, burnin = 100)

## Bayesian model shrinks the effects compared to ML
plot(accuracy ~ iq, data = ReadingSkills, pch = 19, col = dyslexia)
nd <- data.frame(
  iq = rep(-19:20/10, 2),
  dyslexia = factor(rep(c("no", "yes"), each = 40), levels = c("no", "yes"))
)
nd$betareg <- predict(rs1, newdata = nd, type = "response")
nd$bamlss  <- predict(rs2, newdata = nd, type = "parameter", model = "mu")
lines(betareg ~ iq, data = nd, subset = dyslexia == "no",  col = 1, lwd = 2, lty = 1)
lines(betareg ~ iq, data = nd, subset = dyslexia == "yes", col = 2, lwd = 2, lty = 1)
lines(bamlss  ~ iq, data = nd, subset = dyslexia == "no",  col = 1, lwd = 2, lty = 2)
lines(bamlss  ~ iq, data = nd, subset = dyslexia == "yes", col = 2, lwd = 2, lty = 2)
legend("topleft", c("Dyslexia: no", "Dyslexia: yes", "betareg", "bamlss"),
  lty = c(0, 0, 1, 2), pch = c(19, 19, NA, NA), col = c(1, 2, 1, 1), bty = "n")
## IGNORE_RDIFF_END

## xbetax_family(): requires more time due to Gaussian quadrature
## for gamlss2: install.packages("gamlss2", repos = "https://gamlss-dev.R-universe.dev")