betareg (version 3.2-2)

betar_family: Family Objects for (Extended-Support) Beta Regression

Description

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

Usage

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, ...)

Value

A list of class family.bamlss.

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.

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/

See Also

dbetar, dxbetax, family.bamlss

Examples

 if(!requireNamespace("bamlss")) {
  if(interactive() || is.na(Sys.getenv("_R_CHECK_PACKAGE_NAME_", NA))) {
    stop("not all packages required for the example are installed")
  } else q() }

## 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")