Package 'betaregscale'

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)

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)

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)

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)

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", "all"),
  bins = 10L,
  scores = NULL,
  newdata = NULL,
  n_grid = 200L,
  max_curves = 6L,
  residual_type = "rqr",
  title = NULL,
  xlab = NULL,
  ylab = NULL,
  ncol = 2L,
  theme = ggplot2::theme_minimal(),
  ...
)

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 = "calibration",
  title = "My calibration", ylab = "Observed"
)
ggplot2::autoplot(fit, type = "all")

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")

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")

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", "shrinkage", "all"),
  bins = 10L,
  scores = NULL,
  residual_type = c("response", "pearson"),
  max_groups = 25L,
  title = NULL,
  xlab = NULL,
  ylab = NULL,
  ncol = 2L,
  theme = ggplot2::theme_minimal(),
  ...
)

Arguments

Value

A ggplot2 object, or (when type = "all") invisibly returns the list of all panels after rendering the grid.

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 = "ranef_caterpillar",
  title = "My title", ylab = "Mode"
)
ggplot2::autoplot(fit_mm, type = "all")

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)

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)

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)

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)

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)

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)

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)
suppressWarnings(brs_coef(fit))  # deprecated; use brs_est()

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

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)

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)

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)

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")

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)

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)

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)

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)
)

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")

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

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

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")

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")

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")

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")