betaregscale
betaregscale fits regression models for scores on a bounded rating scale
$0, 1, \ldots, K$ (pain NRS-11 or NRS-101, Likert items, quality ratings). Each
score is the coarsened reading of a latent beta variable on $(0, 1)$, written in
mean–dispersion form: mean $\mu$, dispersion $\sigma = 1/(1 + \phi) \in (0, 1)$
with $\phi$ the beta precision, and $\mathrm{Var}(Y) = \mu(1 - \mu)\sigma$. 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
$0, \ldots, K$. The scale borders need no ad hoc squeezing: score 0 is
left-censored and score $K$ 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
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
License
MIT © José Evandeilton Lopes and Wagner Hugo Bonat
