Type:	Package
Title:	Beta Regression for Interval-Censored Scale-Derived Outcomes
Version:	2.6.9
Maintainer:	José Evandeilton Lopes <evandeilton@gmail.com>
Description:	Maximum-likelihood estimation of beta regression models for responses derived from bounded rating scales. Observations are treated as interval-censored on (0, 1) after a scale-to-unit transformation, and the likelihood is built from the difference of the beta CDF at the interval endpoints. The complete likelihood supports mixed censoring types: uncensored, left-censored, right-censored, and interval-censored observations. Both fixed- and variable-dispersion submodels are supported, with flexible link functions for the mean and precision components. A compiled C++ backend (via 'Rcpp' and 'RcppArmadillo') provides numerically stable, high-performance log-likelihood evaluation. Standard S3 methods (print(), summary(), coef(), fitted(), residuals(), predict(), plot(), confint(), vcov(), logLik(), AIC(), BIC()) are available for fitted objects.
License:	MIT + file LICENSE
URL:	https://evandeilton.github.io/betaregscale/
BugReports:	https://github.com/evandeilton/betaregscale/issues
Depends:	R (≥ 4.1.0)
Imports:	Formula, ggplot2, numDeriv, Rcpp (≥ 1.0.12), rlang, stats
Suggests:	betareg, gridExtra, knitr, MASS, rmarkdown, testthat (≥ 3.0.0)
LinkingTo:	Rcpp, RcppArmadillo, RcppEigen
VignetteBuilder:	knitr
Encoding:	UTF-8
NeedsCompilation:	yes
RoxygenNote:	7.3.3
Config/testthat/edition:	3
Packaged:	2026-02-21 22:00:48 UTC; jlopes
Author:	José Evandeilton Lopes [aut, cre], Wagner Hugo Bonat [aut]
Repository:	CRAN
Date/Publication:	2026-02-25 19:30:02 UTC

Register S3 methods for ggplot2::autoplot

Description

Maximum-likelihood estimation of beta regression models for responses derived from bounded rating scales. Observations are treated as interval-censored on (0, 1) after a scale-to-unit transformation, and the likelihood is built from the difference of the beta CDF at the interval endpoints. The complete likelihood supports mixed censoring types: uncensored, left-censored, right-censored, and interval-censored observations. Both fixed- and variable-dispersion submodels are supported, with flexible link functions for the mean and precision components. A compiled C++ backend (via 'Rcpp' and 'RcppArmadillo') provides numerically stable, high-performance log-likelihood evaluation. Standard S3 methods (print(), summary(), coef(), fitted(), residuals(), predict(), plot(), confint(), vcov(), logLik(), AIC(), BIC()) are available for fitted objects.

Maximum-likelihood estimation of beta regression models for responses derived from bounded rating scales. Observations are treated as interval-censored on (0, 1) after a scale-to-unit transformation. The complete likelihood supports mixed censoring types: uncensored (exact), left-censored, right-censored, and interval-censored observations. Both fixed- and variable-dispersion submodels are supported, with flexible link functions for the mean and precision components. A compiled C++ backend (via Rcpp and RcppArmadillo) provides numerically stable, high-performance log-likelihood evaluation. Standard S3 methods (print(), summary(), coef(), fitted(), residuals(), predict(), plot(), confint(), vcov(), logLik(), AIC(), BIC()) are available for fitted objects.

Main functions

brs

Unified fitting interface for both fixed- and variable-dispersion models.

brs_fit_fixed

Fit a fixed-dispersion model.

brs_fit_var

Fit a variable-dispersion model.

brsmm

Fit a mixed-effects beta interval model with Gaussian random intercepts.

brs_sim

Simulate interval-censored data from fixed or variable-dispersion beta models.

brs_bootstrap

Parametric bootstrap confidence intervals for brs model parameters.

brs_cens

Visual and tabular summary of censoring structure.

brs_prep

Pre-process analyst data (validate, classify censoring, and rescale) before model fitting.

S3 methods

Objects of class "brs" support: print(), summary(), coef(), vcov(), logLik(), AIC(), BIC(), nobs(), formula(), model.matrix(), fitted(), residuals(), predict(), confint(), and plot().

The coef() and vcov() methods accept a model = c("full", "mean", "precision") argument following the betareg package convention.

Censoring types

The complete likelihood supports four censoring types, classified automatically by brs_check:

\delta = 0 (exact)

Continuous observations in (0, 1).

\delta = 1 (left-censored)

Observations at the scale minimum (y = 0).

\delta = 2 (right-censored)

Observations at the scale maximum (y = ncuts).

\delta = 3 (interval-censored)

Standard scale observations between the boundaries.

Author(s)

Maintainer: José Evandeilton Lopes evandeilton@gmail.com (ORCID)

Authors:

• Wagner Hugo Bonat (ORCID)

José Evandeilton Lopes evandeilton@gmail.com

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

See Also

Useful links:

• https://evandeilton.github.io/betaregscale/

• Report bugs at https://github.com/evandeilton/betaregscale/issues

Useful links: Package source https://github.com/evandeilton/betaregscale; report bugs at https://github.com/evandeilton/betaregscale/issues.

Internal ANOVA table builder for brs/brsmm

Description

Internal ANOVA table builder for brs/brsmm

Usage

.anova_brs_family(models, test = c("Chisq", "none"))

Arguments

C++ gradient for fixed-dispersion log-likelihood

Description

Returns the gradient vector of the log-likelihood with respect to all parameters (beta coefficients + scalar phi), using a central-difference numerical approximation (step = 1e-6).

Usage

.brs_grad_fixed_cpp(
  param,
  X,
  y_left,
  y_right,
  yt,
  delta,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Numeric gradient vector of length ncol(X) + 1.

C++ gradient for variable-dispersion log-likelihood

Description

Central-difference gradient for the variable-dispersion model.

Usage

.brs_grad_variable_cpp(
  param,
  X,
  Z,
  y_left,
  y_right,
  yt,
  delta,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Numeric gradient vector.

C++ log-likelihood for fixed-dispersion beta interval regression with mixed censoring

Description

Computes the total log-likelihood for a beta regression model with interval-censored responses and a single (scalar) dispersion parameter, supporting all four censoring types.

Usage

.brs_loglik_fixed_cpp(
  param,
  X,
  y_left,
  y_right,
  yt,
  delta,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Scalar log-likelihood value.

C++ log-likelihood for variable-dispersion beta interval regression with mixed censoring

Description

Computes the total log-likelihood for a beta regression model with interval-censored responses and observation-specific dispersion, supporting all four censoring types.

Usage

.brs_loglik_variable_cpp(
  param,
  X,
  Z,
  y_left,
  y_right,
  yt,
  delta,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Scalar log-likelihood value.

Group-level modes for random intercept (Laplace)

Description

Computes the posterior mode and local SD for each group random intercept under the current parameter vector.

Usage

.brsmm_group_modes_cpp(
  param,
  X,
  Z,
  y_left,
  y_right,
  yt,
  delta,
  group,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Numeric matrix with columns mode_b and sd_b.

C++ log-likelihood for mixed beta interval regression (Laplace)

Description

Computes the marginal log-likelihood for a random-intercept beta interval model using a Laplace approximation of group-specific integrals over Gaussian random effects.

Usage

.brsmm_loglik_laplace_cpp(
  param,
  X,
  Z,
  y_left,
  y_right,
  yt,
  delta,
  group,
  link_mu_code,
  link_phi_code,
  repar
)

Arguments

Value

Scalar marginal log-likelihood.

Validate a betaregscale object

Description

Validate a betaregscale object

Usage

.check_class(x, call. = FALSE)

Arguments

Validate a brsmm object

Description

Validate a brsmm object

Usage

.check_class_mm(x, call. = FALSE)

Arguments

Valid link names for the mean submodel

Description

Valid link names for the mean submodel

Usage

.mu_links

Format

An object of class character of length 4.

Valid link names for the dispersion submodel

Description

Valid link names for the dispersion submodel

Usage

.phi_links

Format

An object of class character of length 9.

Akaike information criterion

Description

Akaike information criterion

Usage

## S3 method for class 'brs'
AIC(object, ..., k = 2)

Arguments

Value

Scalar AIC value.

See Also

brs, logLik.brs, BIC.brs, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
AIC(fit)

AIC for brsmm models

Description

AIC for brsmm models

Usage

## S3 method for class 'brsmm'
AIC(object, ..., k = 2)

Arguments

Value

Numeric scalar.

See Also

brsmm, logLik.brsmm, BIC.brsmm, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
AIC(fit)

Bayesian information criterion

Description

Bayesian information criterion

Usage

## S3 method for class 'brs'
BIC(object, ...)

Arguments

Value

Scalar BIC value.

See Also

brs, logLik.brs, AIC.brs, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
BIC(fit)

BIC for brsmm models

Description

BIC for brsmm models

Usage

## S3 method for class 'brsmm'
BIC(object, ...)

Arguments

Value

Numeric scalar.

See Also

brsmm, logLik.brsmm, AIC.brsmm, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
BIC(fit)

Model comparison by analysis of deviance (LR test) for 'brs'

Description

Model comparison by analysis of deviance (LR test) for 'brs'

Usage

## S3 method for class 'brs'
anova(object, ..., test = c("Chisq", "none"))

Arguments

Value

An object of class "anova" and "data.frame" with model-wise log-likelihood, information criteria, and (optionally) LR test columns.

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

See Also

brs, logLik.brs, AIC.brs, BIC.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
m1 <- brs(y ~ 1, data = prep)
m2 <- brs(y ~ x1, data = prep)
m3 <- brs(y ~ x1 + x2, data = prep)
anova(m1, m2, m3)

Model comparison by analysis of deviance (LR test) for 'brsmm'

Description

Model comparison by analysis of deviance (LR test) for 'brsmm'

Usage

## S3 method for class 'brsmm'
anova(object, ..., test = c("Chisq", "none"))

Arguments

Value

An object of class "anova" and "data.frame" with model-wise log-likelihood, information criteria, and (optionally) LR test columns.

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

See Also

brsmm, logLik.brsmm, AIC.brsmm, BIC.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
m1 <- brs(y ~ 1, data = prep)
m2 <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
anova(m1, m2)

Apply the inverse-link function to a linear predictor

Description

Evaluates the inverse of a standard link function for a given linear-predictor vector or scalar. This is a convenience wrapper around make.link.

Usage

apply_inv_link(eta, link)

Arguments

Value

Numeric vector (or scalar) of the same length as eta, containing g^{-1}(\eta).

ggplot2 autoplot for brs models

Description

Produces ggplot2 diagnostics tailored to interval-censored scale models.

Usage

## S3 method for class 'brs'
autoplot(
  object,
  type = c("calibration", "score_dist", "cdf", "residuals_by_delta"),
  bins = 10L,
  scores = NULL,
  newdata = NULL,
  n_grid = 200L,
  max_curves = 6L,
  residual_type = "rqr",
  ...
)

Arguments

Details

type = "calibration" bins predictions and compares mean observed vs mean predicted response in each bin.

type = "score_dist" compares observed score frequencies against expected frequencies implied by the fitted beta interval model.

Value

A ggplot2 object.

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

See Also

brs, plot.brs, autoplot.brs_bootstrap

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1 + x2, data = prep)
ggplot2::autoplot(fit, type = "calibration")
ggplot2::autoplot(fit, type = "score_dist")

ggplot2 autoplot for bootstrap results

Description

Produces visual summaries for objects returned by brs_bootstrap.

Usage

## S3 method for class 'brs_bootstrap'
autoplot(
  object,
  type = c("ci_forest", "dist", "qq", "stability"),
  parameter = NULL,
  title = NULL,
  caption = NULL,
  max_parameters = 12L,
  ci_level = NULL,
  theme = NULL,
  ...
)

Arguments

Details

For type = "dist", "qq", and "stability", bootstrap draws must be present in attr(object, "boot_draws"), obtained by fitting with brs_bootstrap(..., keep_draws = TRUE).

Value

A ggplot2 object.

See Also

brs_bootstrap, brs, autoplot.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
boot <- brs_bootstrap(fit, R = 50)
ggplot2::autoplot(boot, type = "ci_forest")

ggplot2 autoplot for marginal effects

Description

Produces visual summaries for objects returned by brs_marginaleffects.

Usage

## S3 method for class 'brs_marginaleffects'
autoplot(
  object,
  type = c("forest", "magnitude", "dist"),
  variable = NULL,
  top_n = 12L,
  title = NULL,
  caption = NULL,
  theme = NULL,
  ...
)

Arguments

Details

type = "dist" requires AME simulation draws stored in attr(object, "ame_draws"), which are available when marginal effects are computed with keep_draws = TRUE and interval = TRUE.

Value

A ggplot2 object.

See Also

brs_marginaleffects, brs, autoplot.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
ame <- brs_marginaleffects(fit)
ggplot2::autoplot(ame, type = "forest")

ggplot2 autoplot for brsmm models

Description

Produces ggplot2 diagnostics tailored to mixed beta interval models.

Usage

## S3 method for class 'brsmm'
autoplot(
  object,
  type = c("calibration", "score_dist", "ranef_qq", "residuals_by_group",
    "ranef_caterpillar", "ranef_density", "ranef_pairs"),
  bins = 10L,
  scores = NULL,
  residual_type = c("response", "pearson"),
  max_groups = 25L,
  ...
)

Arguments

Value

A ggplot2 object.

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit_mm <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
ggplot2::autoplot(fit_mm, type = "calibration", bins = 4)
ggplot2::autoplot(fit_mm, type = "score_dist")
ggplot2::autoplot(fit_mm, type = "ranef_qq")
ggplot2::autoplot(fit_mm, type = "ranef_caterpillar")
ggplot2::autoplot(fit_mm, type = "ranef_density")

Fit a beta interval regression model

Description

Unified interface that dispatches to brs_fit_fixed (fixed dispersion) or brs_fit_var (variable dispersion) based on the formula structure.

Usage

brs(
  formula,
  data,
  link = "logit",
  link_phi = "logit",
  ncuts = 100L,
  lim = 0.5,
  repar = 2L,
  method = c("BFGS", "L-BFGS-B"),
  hessian_method = c("numDeriv", "optim")
)

Arguments

Details

If the formula contains a | separator (e.g., y ~ x1 + x2 | z1), the variable-dispersion model is fitted; otherwise, a fixed-dispersion model is used.

Value

An object of class "brs".

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
# Fixed dispersion
fit1 <- brs(y ~ x1, data = prep)
print(fit1)
# Variable dispersion
fit2 <- brs(y ~ x1 | x2, data = prep)
print(fit2)

Parametric bootstrap confidence intervals for brs models

Description

Computes bootstrap-based confidence intervals for the parameters of a fitted "brs" model by repeatedly simulating data from the fitted model and re-estimating parameters. Only "brs" (fixed or variable-dispersion) objects are supported; "brsmm" is not supported.

Usage

brs_bootstrap(
  object,
  R = 199L,
  level = 0.95,
  ci_type = c("percentile", "basic", "normal", "bca"),
  max_tries = NULL,
  keep_draws = FALSE
)

## S3 method for class 'brs_bootstrap'
print(x, ...)

Arguments

Details

For each replicate, data are simulated via brs_sim using the estimated coefficients (on the link scale) and the original design. The model is then re-fitted with brs. Replicates that fail to converge are discarded; if the number of successful replicates is too low, a warning is issued. Intervals are the empirical quantiles of the bootstrap distribution of each parameter.

Value

A data frame with columns parameter, estimate (original point estimate), se_boot (bootstrap standard error), ci_lower, ci_upper, mcse_lower, mcse_upper, wald_lower, wald_upper, and level. The attribute "n_success" gives the number of replicates that converged. Additional attributes include "R", "n_attempted", "ci_type", and optionally "boot_draws".

Methods (by generic)

• print(brs_bootstrap): Print method for bootstrap results

See Also

confint.brs for Wald intervals; brs_sim for simulation; brs for fitting.

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
boot <- brs_bootstrap(fit, R = 50, level = 0.95)
print(boot)

Graphical and tabular censoring summary

Description

Produces a visual summary of the censoring structure in a fitted "brs" model or a response matrix produced by brs_check. The summary includes:

1. Bar chart of censoring type counts

2. Histogram of midpoint responses colored by censoring type

3. Interval plot showing [l_i, u_i] segments

4. Proportion table of censoring types

Usage

brs_cens(
  object,
  n_sample = 100L,
  which = 1:4,
  caption = NULL,
  gg = FALSE,
  title = "Censoring diagnostic overview",
  sub.caption = NULL,
  theme = NULL,
  palette = NULL,
  inform = FALSE,
  ...
)

Arguments

Value

Invisibly returns a data frame with censoring counts and proportions, percentages, and interpretation flags.

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

y <- c(0, 3, 5, 7, 10)
Y <- brs_check(y, ncuts = 10)
brs_cens(Y)

prep <- brs_prep(data.frame(y = y), ncuts = 10)
brs_cens(prep)

Transform and validate a scale-derived response variable

Description

Takes a discrete (or continuous) response on the scale 0, 1, \ldots, K (where K = ncuts) and converts it to a pair of interval endpoints on the open unit interval (0, 1). Each observation is classified into one of four censoring types following the complete likelihood used in this package:

\delta = 0

Uncensored (exact): the observation is a continuous value already in (0, 1). The likelihood contribution is the density f(y_i | \theta). Endpoints: l_i = u_i = y_i (or y_i / K when on the scale).

\delta = 1

Left-censored: the latent value is below some upper bound u_i. The contribution is F(u_i | \theta). When the observation is at the scale minimum (y = 0), the upper bound is u_i = \mathrm{lim} / K. When the user forces \delta = 1 on a non-boundary observation (y \neq 0), the upper bound is u_i = (y + \mathrm{lim}) / K, preserving observation- specific variation. In both cases l_i = \epsilon.

\delta = 2

Right-censored: the latent value is above some lower bound l_i. The contribution is 1 - F(l_i | \theta). When the observation is at the scale maximum (y = K), the lower bound is l_i = (K - \mathrm{lim}) / K. When the user forces \delta = 2 on a non-boundary observation (y \neq K), the lower bound is l_i = (y - \mathrm{lim}) / K, preserving observation- specific variation. In both cases u_i = 1 - \epsilon.

\delta = 3

Interval-censored: the standard case for scale data. The contribution is F(u_i | \theta) - F(l_i | \theta) with midpoint interval endpoints [(y - \mathrm{lim})/K,\; (y + \mathrm{lim})/K].

Usage

brs_check(y, ncuts = 100L, lim = 0.5, delta = NULL)

Arguments

Details

Automatic classification (delta = NULL):

If the entire input vector is already in (0, 1) (i.e., all values satisfy 0 < y < 1), all observations are treated as uncensored (\delta = 0).

Otherwise, for scale (integer) data:

• y = 0: left-censored (\delta = 1).

• y = K: right-censored (\delta = 2).

• 0 < y < K: interval-censored (\delta = 3).

User-supplied delta (delta vector):

When the delta argument is provided, the user-supplied censoring indicators override the automatic boundary-based rules on a per-observation basis. This is the mechanism used by brs_sim when the analyst forces a specific censoring type in Monte Carlo studies.

The endpoint formulas for each delta value are:

All endpoints are clamped to [\epsilon, 1 - \epsilon] with \epsilon = 10^{-5} to avoid boundary issues in the beta likelihood.

The midpoint approximation yt is computed as:

• y_t = y when y \in (0, 1) (continuous data).

• y_t = y / K when y is on the integer scale.

This value is used exclusively as an initialization aid for starting-value computation and does not enter the likelihood.

Interaction with the fitting pipeline:

This function is called internally by .extract_response() when the data does not carry the "is_prepared" attribute. If data has already been processed by brs_prep or by simulation with forced delta (brs_sim with delta != NULL), the pre-computed columns are used directly and brs_check() is skipped.

Value

A numeric matrix with n rows and 5 columns:

left

Lower endpoint l_i on (0, 1), clamped to [\epsilon, 1 - \epsilon].

right

Upper endpoint u_i on (0, 1), clamped to [\epsilon, 1 - \epsilon].

yt

Midpoint approximation y_t for starting-value computation (does not enter the likelihood).

y

Original response value (preserved unchanged).

delta

Censoring indicator: 0 = exact (density), 1 = left-censored F(u), 2 = right-censored 1 - F(l), 3 = interval-censored F(u) - F(l).

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

See Also

brs_prep for the analyst-facing pre-processing function; brs_sim for simulation with forced delta.

Examples

# Scale data with boundary observations
y <- c(0, 3, 5, 7, 9, 10)
brs_check(y, ncuts = 10)

# Force all observations to be exact (delta = 0)
brs_check(y, ncuts = 10, delta = rep(0L, length(y)))

# Force delta = 1 on non-boundary observations:
# endpoints use actual y values, preserving variation
y2 <- c(30, 60)
brs_check(y2, ncuts = 100, delta = c(1L, 1L))
#  left = (eps, eps), right = (30.5/100, 60.5/100)

Internal coefficient table (deprecated, use brs_est() or summary())

Description

Deprecated convenience wrapper. Use brs_est for coefficient estimates or summary.brs for a full model summary.

Usage

brs_coef(fit, alpha = 0.05)

Arguments

Value

A list with components est (from brs_est) and gof (from brs_gof).

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

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

See Also

brs_est, brs_gof, summary.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
brs_coef(fit)

K-fold cross-validation for brs models

Description

Performs repeated k-fold cross-validation for brs models.

Usage

brs_cv(formula, data, k = 5L, repeats = 1L, ...)

Arguments

Details

The log_score is the mean log predictive contribution under the complete likelihood contribution implied by each observation's censoring type (delta).

Value

A data frame with one row per fold and columns: repeat, fold, n_train, n_test, log_score, rmse_yt, mae_yt, converged, and error. The object has class "brs_cv".

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
cv <- brs_cv(y ~ x1, data = prep, k = 3, repeats = 1)
cv

Coefficient estimates with inference

Description

Coefficient estimates with inference

Usage

brs_est(object, alpha = 0.05)

Arguments

Value

Data frame of estimates, standard errors, z-values, and p-values.

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

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

See Also

brs, brs_gof, brs_hessian, summary.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
brs_est(fit)

Fit a fixed-dispersion beta interval regression model

Description

Estimates the parameters of a beta regression model with a single (scalar) dispersion parameter using maximum likelihood. The log-likelihood and its gradient are evaluated by the compiled C++ backend supporting the complete likelihood with mixed censoring types.

Usage

brs_fit_fixed(
  formula,
  data,
  link = "logit",
  link_phi = "logit",
  ncuts = 100L,
  lim = 0.5,
  hessian_method = c("numDeriv", "optim"),
  repar = 2L,
  method = c("BFGS", "L-BFGS-B")
)

Arguments

Value

An object of class "brs".

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs_fit_fixed(y ~ x1 + x2, data = prep)
print(fit)

Fit a variable-dispersion beta interval regression model

Description

Estimates the parameters of a beta regression model with observation-specific dispersion governed by a second linear predictor. Both submodels are estimated jointly via maximum likelihood, using the complete likelihood with mixed censoring.

Usage

brs_fit_var(
  formula,
  data,
  link = "logit",
  link_phi = "logit",
  hessian_method = c("numDeriv", "optim"),
  ncuts = 100L,
  lim = 0.5,
  repar = 2L,
  method = c("BFGS", "L-BFGS-B")
)

Arguments

Value

An object of class "brs".

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs_fit_var(y ~ x1 | x2, data = prep)
print(fit)

Goodness-of-fit measures

Description

Goodness-of-fit measures

Usage

brs_gof(object)

Arguments

Value

Data frame with logLik, AIC, BIC, and pseudo-R-squared.

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

See Also

brs, brs_est, brs_hessian

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
brs_gof(fit)

Extract the Hessian matrix

Description

Extract the Hessian matrix

Usage

brs_hessian(object)

Arguments

Value

Numeric Hessian matrix.

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

See Also

brs, vcov.brs, brs_est

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
brs_hessian(fit)

Marginal effects for brs models

Description

Computes average marginal effects (AME) for numeric covariates in the mean or precision submodel of a fitted "brs" object.

Usage

brs_marginaleffects(
  object,
  newdata = NULL,
  model = c("mean", "precision"),
  type = c("response", "link"),
  variables = NULL,
  h = 1e-05,
  interval = TRUE,
  level = 0.95,
  n_sim = 400L,
  keep_draws = FALSE
)

Arguments

Details

AMEs are computed by finite differences on predictions:

\mathrm{AME}_j = \frac{1}{n}\sum_{i=1}^{n} \frac{\hat{g}_i(x_{ij} + h) - \hat{g}_i(x_{ij})}{h},

where \hat{g}_i is the selected prediction scale.

For binary covariates coded as 0/1, the effect is computed as the average discrete difference \hat{g}(x_j=1)-\hat{g}(x_j=0).

If interval = TRUE, uncertainty is approximated by asymptotic parameter simulation from \mathcal{N}(\hat{\theta}, \hat{V}).

Value

A data frame with one row per variable and columns: variable, ame, std.error, ci.lower, ci.upper, model, type, and n. The returned object has class "brs_marginaleffects" and attributes with analysis metadata.

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
brs_marginaleffects(fit, model = "mean", type = "response")

Predict score probabilities from a fitted brs model

Description

Computes predicted probabilities for integer scores on the original scale \{0, 1, \ldots, K\} implied by the fitted beta interval model.

Usage

brs_predict_scoreprob(
  object,
  newdata = NULL,
  scores = NULL,
  format = c("matrix", "long"),
  id_col = "id"
)

Arguments

Details

For a score s and K = ncuts, probabilities are computed as:

• P(Y=s)=F(\mathrm{lim}/K) for s=0,

• P(Y=s)=1-F((K-\mathrm{lim})/K) for s=K,

• P(Y=s)=F((s+\mathrm{lim})/K)-F((s-\mathrm{lim})/K) for s \in \{1,\ldots,K-1\},

where F is the beta CDF under the fitted (\mu_i,\phi_i).

Value

If format = "matrix", a numeric matrix with one row per observation and one column per requested score.

If format = "long", a long data frame with columns id_col, score, and prob.

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
pmat <- brs_predict_scoreprob(fit)
head(pmat[, 1:5])
plong <- brs_predict_scoreprob(fit, scores = 0:10, format = "long")
head(plong)

Pre-process analyst data for beta interval regression

Description

Validates and transforms raw data into the format required by brs. The analyst can supply data in several ways:

1. Minimal (Mode 1): only the score y. Censoring is inferred automatically: y = 0 \to \delta = 1, y = K \to \delta = 2, 0 < y < K \to \delta = 3, y \in (0, 1) \to \delta = 0.

2. Classic (Mode 2): y + explicit delta. The analyst declares the censoring type; interval endpoints are computed using the actual y value.

3. Interval (Mode 3): left and/or right columns (on the original scale). Censoring is inferred from the NA pattern.

4. Full (Mode 4): y, left, and right together. The analyst's own endpoints are rescaled directly to (0, 1).

All covariate columns are preserved unchanged in the output.

Usage

brs_prep(
  data,
  y = "y",
  delta = "delta",
  left = "left",
  right = "right",
  ncuts = 100L,
  lim = 0.5
)

Arguments

Details

Priority rule: if delta is provided (non-NA), it takes precedence over all automatic classification rules. When delta is NA, the function infers the censoring type from the pattern of left, right, and y:

When y, left, and right are all present for the same observation, the analyst's left/right values are used directly (rescaled by K = ncuts) and delta is set to 3 (interval-censored) unless the analyst supplied delta explicitly.

Endpoint formulas for Mode 2 (y + explicit delta):

When the analyst supplies delta explicitly, the endpoint computation uses the actual y value to produce observation-specific bounds. This is the same logic used by brs_check with a user-supplied delta vector:

Consistency warnings: when the analyst supplies delta values that are unusual for the given y (e.g., \delta = 1 but y \neq 0), the function emits a warning but proceeds. This is by design for Monte Carlo workflows where forced delta on non-boundary observations is intentional.

All endpoints are clamped to [\epsilon, 1 - \epsilon] with \epsilon = 10^{-5}.

Value

A data.frame with the following columns appended or replaced:

left

Lower endpoint on (0, 1).

right

Upper endpoint on (0, 1).

yt

Midpoint approximation on (0, 1).

y

Original scale value (preserved for reference).

delta

Censoring indicator: 0 = exact, 1 = left, 2 = right, 3 = interval.

Covariate columns are preserved. The output carries attributes "is_prepared" (TRUE), "ncuts" and "lim" so that brs can detect prepared data and skip the internal brs_check call.

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

See Also

brs_check for the automatic classification of raw scale scores; brs for fitting the model.

Examples

# --- Mode 1: y only (automatic classification, like brs_check) ---
d1 <- data.frame(y = c(0, 3, 5, 7, 10), x1 = rnorm(5))
brs_prep(d1, ncuts = 10)

# --- Mode 2: y + explicit delta ---
d2 <- data.frame(
  y = d1$y,
  delta = c(0, 3, 3, 3, 0), # Force interval-censoring for 3,5,7
  x1 = d1$x1
)
brs_prep(d2, ncuts = 100)

# --- Mode 3: left/right with NA patterns ---
d3 <- data.frame(
  left = c(NA, 20, 30, NA),
  right = c(5, NA, 45, NA),
  y = c(NA, NA, NA, 50),
  x1 = d1$x1[1:4]
)
brs_prep(d3, ncuts = 100)

# --- Mode 4: y + left + right (analyst-supplied intervals) ---
d4 <- data.frame(
  y = c(50, 75),
  left = c(48, 73),
  right = c(52, 77),
  x1 = rnorm(2)
)
brs_prep(d4, ncuts = 100)

# --- Fitting after prep ---

dat5 <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep5 <- brs_prep(dat5, ncuts = 100)
fit5 <- brs(y ~ x1, data = prep5)
summary(fit5)

Reparameterize (mu, phi) into beta shape parameters

Description

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

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.

Value

A data.frame with columns shape1 and shape2.

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)

Simulate data from beta interval models

Description

Simulates interval-censored responses from fixed- or variable-dispersion beta regression models.

Usage

brs_sim(
  formula,
  data,
  beta,
  phi = 1/5,
  zeta = NULL,
  link = "logit",
  link_phi = "logit",
  ncuts = 100L,
  lim = 0.5,
  repar = 2L,
  delta = NULL
)

Arguments

Details

The model structure is controlled by formula in the same style as brs:

• one-part formula (~ x1 + x2 or y ~ x1 + x2): fixed dispersion using scalar phi.

• two-part formula (~ x1 + x2 | z1 or y ~ x1 + x2 | z1): variable dispersion using coefficient vector zeta.

The delta argument can force a single censoring type (0,1,2,3) for all observations; otherwise, censoring is classified automatically from simulated scale values via brs_check.

Value

A data frame with columns left, right, yt, y, delta, plus simulated predictor columns from the model matrices. When delta != NULL, the output carries attr(, "is_prepared") = TRUE.

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

dat <- data.frame(
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
# Fixed dispersion
sim_fixed <- brs_sim(
  formula = ~ x1 + x2, data = dat,
  beta = c(0.2, -0.5, 0.3), phi = 1 / 5
)
# Variable dispersion
sim_var <- brs_sim(
  formula = ~ x1 | x2, data = dat,
  beta = c(0.2, -0.5), zeta = c(0.5, -0.5)
)

Compare fitted brs models in a single table

Description

Builds a comparison table for one or more fitted "brs" objects, summarizing fit statistics and (optionally) censoring composition.

Usage

brs_table(
  ...,
  models = NULL,
  include_censoring = TRUE,
  sort_by = c("none", "AIC", "BIC", "logLik"),
  decreasing = FALSE,
  digits = 4L
)

Arguments

Value

A data frame with one row per model.

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

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  x2 = rep(c(0, 0, 1, 1), 5)
)
prep <- brs_prep(dat, ncuts = 100)
m1 <- brs(y ~ 1, data = prep)
m2 <- brs(y ~ x1, data = prep)
brs_table(null = m1, x1 = m2, sort_by = "AIC")

Fit a mixed-effects beta interval regression model

Description

Fits a beta interval-censored mixed model with Gaussian random intercepts/slopes using marginal maximum likelihood. The implementation supports random-effects formulas such as ~ 1 | group and ~ 1 + x | group, and offers three integration methods for the random effects: Laplace approximation, Adaptive Gauss-Hermite Quadrature (AGHQ), and Quasi-Monte Carlo (QMC).

Usage

brsmm(
  formula,
  random = ~1 | id,
  data,
  link = "logit",
  link_phi = "logit",
  repar = 2L,
  ncuts = 100L,
  lim = 0.5,
  int_method = c("laplace", "aghq", "qmc"),
  n_points = 11L,
  qmc_points = 1024L,
  start = NULL,
  method = c("BFGS", "L-BFGS-B"),
  hessian_method = c("numDeriv", "optim"),
  control = list(maxit = 2000L)
)

Arguments

Details

The conditional contribution for each observation follows the same mixed censoring likelihood used by brs:

1. \delta=0: exact contribution via beta density,

2. \delta=1: left-censored contribution via beta CDF,

3. \delta=2: right-censored contribution via survival CDF,

4. \delta=3: interval contribution via CDF difference.

For group i, the random-effects vector \mathbf{b}_i \sim N(\mathbf{0}, D) is integrated out numerically.

• "laplace": Uses a second-order Laplace approximation at the conditional mode. Fast and generally accurate for n_i large.

• "aghq": Adaptive Gauss-Hermite Quadrature. Uses n_points quadrature nodes centered and scaled by the conditional mode and curvature. More accurate than Laplace, especially for small n_i.

• "qmc": Quasi-Monte Carlo integration using a Halton sequence. Uses qmc_points evaluation points. Suitable for high-dimensional integration (future proofing) or checking robustness.

Value

An object of class "brsmm".

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit_mm <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
fit_mm

Group modes for mixed model (Eigen backend)

Description

Group modes for mixed model (Eigen backend)

Usage

brsmm_group_modes_eigen(
  param,
  X,
  Z,
  Xr,
  y_left,
  y_right,
  yt,
  delta,
  group,
  link_mu,
  link_phi,
  repar
)

Mixed Model Log-Likelihood (Eigen)

Description

Computes marginal log-likelihood using Laplace, AGHQ, or QMC.

Usage

brsmm_loglik_eigen(
  param,
  X,
  Z,
  Xr,
  y_left,
  y_right,
  yt,
  delta,
  group,
  link_mu,
  link_phi,
  repar,
  method,
  n_points
)

Arguments

Random-effects study for brsmm models

Description

Provides a compact numeric study of random effects, including: estimated covariance matrix, correlation matrix, per-term standard deviations, empirical mean/SD of posterior modes, shrinkage ratio, and a normality check by Shapiro-Wilk (when applicable).

Usage

brsmm_re_study(object, ...)

Arguments

Value

A list with class "brsmm_re_study".

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.

Ferrari, S. L. P., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

See Also

brsmm, ranef.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
rs <- brsmm_re_study(fit)
print(rs)
rs$summary

Extract model coefficients

Description

Extract model coefficients

Usage

## S3 method for class 'brs'
coef(object, model = c("full", "mean", "precision"), ...)

Arguments

Value

Named numeric vector of estimated parameters.

See Also

brs, brs_est, vcov.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
coef(fit)
coef(fit, model = "mean")
coef(fit, model = "precision")

Extract coefficients from a brsmm fit

Description

Extract coefficients from a brsmm fit

Usage

## S3 method for class 'brsmm'
coef(object, model = c("full", "mean", "precision", "random"), ...)

Arguments

Value

Named numeric vector.

See Also

brsmm, vcov.brsmm, confint.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
coef(fit)
coef(fit, model = "mean")
coef(fit, model = "random")

Compute starting values for optimization

Description

Obtains rough starting values for the beta regression parameters by fitting a quasi-binomial GLM on the midpoint response. This provides a reasonable initialization for the interval likelihood optimizer.

Usage

compute_start(
  formula,
  data,
  link = "logit",
  link_phi = "logit",
  ncuts = 100L,
  lim = 0.5
)

Arguments

Value

Named numeric vector of starting values.

Wald confidence intervals

Description

Computes Wald confidence intervals for model parameters using the normal approximation.

Usage

## S3 method for class 'brs'
confint(
  object,
  parm,
  level = 0.95,
  model = c("full", "mean", "precision"),
  ...
)

Arguments

Value

Matrix with columns for lower and upper confidence bounds.

See Also

brs, coef.brs, vcov.brs, brs_est

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
confint(fit)
confint(fit, model = "mean")

Wald confidence intervals for brsmm models

Description

Wald confidence intervals for brsmm models

Usage

## S3 method for class 'brsmm'
confint(
  object,
  parm,
  level = 0.95,
  model = c("full", "mean", "precision", "random"),
  ...
)

Arguments

Value

Matrix with columns for lower and upper confidence bounds.

See Also

brsmm, coef.brsmm, vcov.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
confint(fit, model = "mean")

Extract fitted values

Description

Extract fitted values

Usage

## S3 method for class 'brs'
fitted(object, type = c("mu", "phi"), ...)

Arguments

Value

Numeric vector of fitted values.

See Also

brs, residuals.brs, predict.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
head(fitted(fit))
head(fitted(fit, type = "phi"))

Fitted values from a brsmm model

Description

Fitted values from a brsmm model

Usage

## S3 method for class 'brsmm'
fitted(object, type = c("mu", "phi"), ...)

Arguments

Value

Numeric vector.

See Also

brsmm, residuals.brsmm, predict.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
head(fitted(fit))
head(fitted(fit, type = "phi"))

Extract model formula

Description

Extract model formula

Usage

## S3 method for class 'brs'
formula(x, ...)

Arguments

Value

The formula used to fit the model.

See Also

brs, model.matrix.brs, coef.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
formula(fit)

Extract model formula

Description

Extract model formula

Usage

## S3 method for class 'brsmm'
formula(x, ...)

Arguments

Value

The formula used to fit the model.

See Also

brsmm, model.matrix.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
formula(fit)

Map link-function name to integer code for the C++ backend

Description

Map link-function name to integer code for the C++ backend

Usage

link_to_code(link)

Arguments

Value

Integer code consumed by the compiled likelihood.

Extract log-likelihood

Description

Extract log-likelihood

Usage

## S3 method for class 'brs'
logLik(object, ...)

Arguments

Value

An object of class "logLik" with attributes df (number of estimated parameters) and nobs (number of observations).

See Also

brs, AIC.brs, BIC.brs, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
logLik(fit)

Log-likelihood for brsmm models

Description

Log-likelihood for brsmm models

Usage

## S3 method for class 'brsmm'
logLik(object, ...)

Arguments

Value

Object of class "logLik".

See Also

brsmm, AIC.brsmm, BIC.brsmm, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
logLik(fit)

Extract design matrix

Description

Extract design matrix

Usage

## S3 method for class 'brs'
model.matrix(object, model = c("mean", "precision"), ...)

Arguments

Value

The design matrix for the specified submodel.

See Also

brs, formula.brs, coef.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
head(model.matrix(fit))
head(model.matrix(fit, model = "precision"))

Extract design matrix

Description

Extract design matrix

Usage

## S3 method for class 'brsmm'
model.matrix(object, model = c("mean", "precision", "random"), ...)

Arguments

Value

The design matrix for the specified submodel.

See Also

brsmm, formula.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
head(model.matrix(fit))
head(model.matrix(fit, model = "random"))

Number of observations

Description

Number of observations

Usage

## S3 method for class 'brs'
nobs(object, ...)

Arguments

Value

Integer: number of observations.

See Also

brs, fitted.brs, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
nobs(fit)

Number of observations in a brsmm fit

Description

Number of observations in a brsmm fit

Usage

## S3 method for class 'brsmm'
nobs(object, ...)

Arguments

Value

Integer.

See Also

brsmm, fitted.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
nobs(fit)

Diagnostic plots for beta interval regression

Description

Produces up to six diagnostic plots for a fitted "brs" model: residuals vs indices, Cook's distance, residuals vs linear predictor, residuals vs fitted values, a half-normal plot with simulated envelope, and predicted vs observed.

Usage

## S3 method for class 'brs'
plot(
  x,
  which = 1:4,
  type = "rqr",
  nsim = 100L,
  level = 0.9,
  caption = c("Residuals vs indices", "Cook's distance", "Residuals vs linear predictor",
    "Residuals vs fitted values", "Half-normal plot", "Predicted vs observed"),
  sub.caption = NULL,
  ask = prod(par("mfcol")) < length(which) && dev.interactive(),
  gg = FALSE,
  title = NULL,
  theme = NULL,
  ...
)

Arguments

Value

Invisibly returns x.

See Also

brs, residuals.brs, autoplot.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
plot(fit, which = 1:4)

Diagnostic plots for mixed beta interval regression

Description

Produces diagnostic plots for fitted "brsmm" models: residuals vs indices, Cook's distance, residuals vs linear predictor, residuals vs fitted values, half-normal envelope, and predicted vs observed.

Usage

## S3 method for class 'brsmm'
plot(
  x,
  which = 1:4,
  type = c("response", "pearson"),
  nsim = 100L,
  level = 0.9,
  caption = c("Residuals vs indices", "Cook's distance", "Residuals vs linear predictor",
    "Residuals vs fitted values", "Half-normal plot", "Predicted vs observed"),
  sub.caption = NULL,
  ask = prod(par("mfcol")) < length(which) && dev.interactive(),
  gg = FALSE,
  title = NULL,
  theme = NULL,
  ...
)

Arguments

Value

Invisibly returns x.

See Also

brsmm, residuals.brsmm, autoplot.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
plot(fit, which = 1:4)

Predict from a fitted model

Description

Predict from a fitted model

Usage

## S3 method for class 'brs'
predict(
  object,
  newdata = NULL,
  type = c("response", "link", "precision", "variance", "quantile"),
  at = 0.5,
  ...
)

Arguments

Value

Numeric vector or matrix.

See Also

brs, fitted.brs, brs_predict_scoreprob

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
head(predict(fit))
head(predict(fit, type = "precision"))
newdat <- data.frame(x1 = c(1, 2))
predict(fit, newdata = newdat)

Predict from a brsmm model

Description

Predict from a brsmm model

Usage

## S3 method for class 'brsmm'
predict(
  object,
  newdata = NULL,
  type = c("response", "link", "precision", "variance", "quantile"),
  at = 0.5,
  ...
)

Arguments

Value

Numeric vector.

See Also

brsmm, fitted.brsmm, brs_predict_scoreprob

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
head(predict(fit))
head(predict(fit, type = "precision"))

Print a fitted model (brief betareg style)

Description

Print a fitted model (brief betareg style)

Usage

## S3 method for class 'brs'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Invisibly returns the input object x. The function is called for its side effect of printing a formatted summary of the fitted model to the console, including the model call, mean coefficients (with link function), and precision coefficients (with link function).

See Also

summary.brs, print.summary.brs, brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
print(fit)

Print a fitted brsmm model

Description

Print a fitted brsmm model

Usage

## S3 method for class 'brsmm'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Invisibly returns x.

See Also

summary.brsmm, print.summary.brsmm, brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
print(fit)

Print a random-effects study

Description

Prints a compact summary of the random-effects study returned by brsmm_re_study, including per-term standard deviations, shrinkage ratios, Shapiro-Wilk p-values, and the estimated covariance and correlation matrices.

Usage

## S3 method for class 'brsmm_re_study'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Invisibly returns x. Called for its side-effect of printing the study to the console.

See Also

brsmm_re_study, brsmm, ranef.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
rs <- brsmm_re_study(fit)
print(rs)

Print a model summary (betareg style)

Description

Print a model summary (betareg style)

Usage

## S3 method for class 'summary.brs'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Invisibly returns the input object x. The function is called for its side effect of printing a comprehensive summary to the console, including the model call, quantile residuals, coefficient tables for mean and precision submodels with significance stars, goodness-of-fit statistics (log-likelihood, pseudo R-squared), optimization details, and censoring information.

See Also

summary.brs, brs, print.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
print(summary(fit))

Print summary for brsmm models

Description

Print summary for brsmm models

Usage

## S3 method for class 'summary.brsmm'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Invisibly returns x.

See Also

summary.brsmm, brsmm, print.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
print(summary(fit))

Extract random effects

Description

Generic function for extracting random effects.

Usage

ranef(object, ...)

Arguments

Value

Method-specific; for "brsmm" objects, a matrix or named numeric vector of group-specific random-effect modes.

See Also

ranef.brsmm, brsmm_re_study

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
ranef(fit)

Extract random effects from a brsmm model

Description

Extract random effects from a brsmm model

Usage

## S3 method for class 'brsmm'
ranef(object, ...)

Arguments

Value

A matrix or named numeric vector of group-specific random-effect posterior modes.

See Also

brsmm, brsmm_re_study, ranef

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
ranef(fit)

Extract residuals

Description

Extract residuals

Usage

## S3 method for class 'brs'
residuals(
  object,
  type = c("response", "pearson", "deviance", "rqr", "weighted", "sweighted"),
  ...
)

Arguments

Details

For Pearson residuals the variance formula depends on the reparameterization stored in object$repar:

repar = 1 (precision)

V = mu(1 - mu) / (1 + phi)

repar = 2 (mean-variance)

V = mu(1 - mu) * phi

The weighted and sweighted residuals use the digamma/trigamma formulation from the precision parameterization (repar = 1), so internal conversion is applied when repar != 1.

Value

Numeric vector of residuals.

See Also

brs, fitted.brs, plot.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
head(residuals(fit))
head(residuals(fit, type = "pearson"))

Residuals from a brsmm model

Description

Residuals from a brsmm model

Usage

## S3 method for class 'brsmm'
residuals(
  object,
  type = c("response", "pearson", "deviance", "rqr", "weighted", "sweighted"),
  ...
)

Arguments

Value

Numeric vector.

See Also

brsmm, fitted.brsmm, plot.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
head(residuals(fit))
head(residuals(fit, type = "pearson"))

Summarize a fitted model (betareg style)

Description

Summarize a fitted model (betareg style)

Usage

## S3 method for class 'brs'
summary(object, ...)

Arguments

Value

A list of class "summary.betaregscale".

See Also

brs, print.summary.brs, brs_est, brs_gof

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
s <- summary(fit)
s$coefficients$mean

Summarize a fitted brsmm model

Description

Summarize a fitted brsmm model

Usage

## S3 method for class 'brsmm'
summary(object, ...)

Arguments

Value

Object of class "summary.brsmm".

See Also

brsmm, print.summary.brsmm, brs_gof, brsmm_re_study

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
s <- summary(fit)
s$coefficients$mean

Variance-covariance matrix of estimated coefficients

Description

Variance-covariance matrix of estimated coefficients

Usage

## S3 method for class 'brs'
vcov(object, model = c("full", "mean", "precision"), ...)

Arguments

Value

A square numeric matrix.

See Also

brs, coef.brs, confint.brs

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10)
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brs(y ~ x1, data = prep)
vcov(fit)
vcov(fit, model = "mean")

Variance-covariance matrix for brsmm coefficients

Description

Variance-covariance matrix for brsmm coefficients

Usage

## S3 method for class 'brsmm'
vcov(object, model = c("full", "mean", "precision", "random"), ...)

Arguments

Value

Numeric matrix.

See Also

brsmm, coef.brsmm, confint.brsmm

Examples

dat <- data.frame(
  y = c(
    0, 5, 20, 50, 75, 90, 100, 30, 60, 45,
    10, 40, 55, 70, 85, 25, 35, 65, 80, 15
  ),
  x1 = rep(c(1, 2), 10),
  id = factor(rep(1:4, each = 5))
)
prep <- brs_prep(dat, ncuts = 100)
fit <- brsmm(y ~ x1, random = ~ 1 | id, data = prep)
vcov(fit, model = "mean")