betaregscale fits regression models for scores on a bounded rating scale (pain NRS-11 or NRS-101, Likert items, quality ratings). Each score is the coarsened reading of a latent beta variable on , written in mean–dispersion form: mean , dispersion with the beta precision, and . Both can depend on covariates through link functions. The latent scale is cut at cutpoints anchored on the score labels, so each score is an interval-censored observation and the likelihood is a probability mass function over the scores . The scale borders need no ad hoc squeezing: score 0 is left-censored and score right-censored. Fixed-effects models are fitted with brs() and mixed models with Gaussian random effects with brsmm(); the log-likelihood and its derivatives are compiled C++.
Installation
# Released version from CRAN
install.packages("betaregscale")
# Development version from GitHub
# install.packages("remotes")
remotes::install_github("evandeilton/betaregscale")Example
Simulated NRS-11 scores (0 to 10) for 200 patients, with a continuous covariate and a treatment indicator:
library(betaregscale)
set.seed(1)
d <- data.frame(x1 = rnorm(200), trt = rbinom(200, 1, 0.5))
nrs <- brs_sim(~ x1 + trt, data = d, beta = c(-0.4, 0.5, -0.6),
phi = qlogis(0.15), ncuts = 10)
# Mean with logit link, constant dispersion with logit link
fit <- brs(y ~ x1 + trt, data = nrs)
summary(fit)
# The fitted model is a pmf over the scores 0..10
round(head(brs_predict_scoreprob(fit), 3), 3)
# Expected score by arm at x1 = 0, and the difference between arms,
# with delta-method standard errors
nd <- data.frame(x1 = 0, trt = c(0, 1))
brs_marginal(fit, nd, type = "expected_score")
brs_marginal(fit, nd, type = "expected_score", contrast = c(2, 1))
# Diagnostic plots of randomized quantile residuals
plot(fit)Features
-
Interval maps
interval = "mid","right"or"left", and estimable boundary cutpoints (cutpoints = "boundary") for scores that pile up at the ends of the scale, with a likelihood-ratio test against the fixed map. -
Variable dispersion with a two-part formula
y ~ x | z, and three parameterizations of the beta law (repar). -
Mixed models (
brsmm()) with random intercepts and slopes, fitted by Laplace approximation, adaptive Gauss–Hermite quadrature or quasi-Monte Carlo, with chi-bar-square likelihood-ratio tests for variance components. -
Score-scale predictions: score probabilities (
brs_predict_scoreprob()), and score probabilities, expected scores, exceedance probabilities and contrasts with standard errors (brs_marginal()), population-averaged for mixed models. -
Diagnostics and validation: randomized quantile and cell deviance residuals, parametric bootstrap, k-fold and group-level cross-validation, and simulation (
brs_sim(),brsmm_sim(),simulate()).
Documentation
- Introduction: the model, interval maps, the likelihood and a first fit.
-
Mixed models:
brsmm(), integration methods, random effects and marginal predictions. - Analyst tools: predictions, contrasts, residuals, bootstrap, cross-validation, tables and plots.
- Advanced workflows: variable dispersion, boundary cutpoints and model comparison.
Function reference and changelog: https://evandeilton.github.io/betaregscale/. Bug reports and questions: https://github.com/evandeilton/betaregscale/issues.
Citation
citation("betaregscale") gives the reference for the package. The model is described in
- Lopes, J. E. (2023). Modelos de regressão beta para dados de escala. Master’s dissertation, Universidade Federal do Paraná, Curitiba. https://acervodigital.ufpr.br/xmlui/handle/1884/86624
Other references:
- Bayer, F. M. (2011). Modelagem e inferência em regressão beta. PhD thesis, Universidade Federal de Pernambuco.
- Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. https://doi.org/10.1080/0266476042000214501