Fit a fixed-dispersion beta interval regression model

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 = NULL,
  link_phi = NULL,
  ncuts = NULL,
  lim = NULL,
  hessian_method = c("cpp", "numDeriv", "optim"),
  repar = 2L,
  method = c("BFGS", "L-BFGS-B"),
  interval = NULL,
  start = NULL,
  control = list()
)

Arguments

formula: Two-sided formula y ~ x1 + x2 + ....
data: Data frame.
link: Link for the first parameter (the mean under repar = 1, 2; the shape \(p\) under repar = 0). NULL (default) selects the link implied by repar: "logit" for repar = 1, 2, "log" for repar = 0. See the 'Reparameterizations and links' section of brs for the admissible values.
link_phi: Link for the second parameter. NULL (default) selects "logit" for repar = 2 (dispersion on \((0, 1)\)) and "log" for repar = 0, 1 (positive shape/precision).
ncuts: Integer \(K\), the maximum score: the scale is \(0, 1, \ldots, K\) (\(K + 1\) categories). NULL (default) uses the value stored by brs_prep in attr(data, "ncuts"), or 100 when data was not prepared. A value that differs from the stored one is ignored with a warning (the endpoints were built with the stored value).
lim: Half-width of the score cell in \((0, 0.5]\) (interval = "mid" only). NULL (default) uses attr(data, "lim") from brs_prep, or 0.5; same rule as ncuts. Values below 0.5 warn (partial coarsening).
hessian_method: Character: "cpp" (default), "numDeriv" or "optim". "cpp" uses the compiled chain-rule Hessian (per-observation second derivatives in the linear predictors); "numDeriv" differentiates the log-likelihood with hessian; "optim" keeps the optimizer's own approximation.
repar: Reparameterization scheme (default 2); see brs_repar.
method: Optimization method: "BFGS" (default) or "L-BFGS-B".
interval: Direction of the uncertainty interval, "mid", "right" or "left" (see brs_check). NULL (default) uses attr(data, "interval") from brs_prep, or "mid"; same rule as ncuts.
start: Optional numeric vector of starting values (mean coefficients, then dispersion coefficients). NULL (default) uses compute_start(). Refits (bootstrap, jackknife) pass the parent estimate here.
control: Control list for optim; its entries are merged into the default list(maxit = 5000L).

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

# \donttest{
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)
#> brs_prep: n = 20 | exact = 0, left = 1, right = 1, interval = 18
fit <- brs_fit_fixed(y ~ x1 + x2, data = prep)
print(fit)
#> 
#> Call:
#> brs_fit_fixed(formula = y ~ x1 + x2, data = prep)
#> 
#> Coefficients (mean model with logit link):
#> (Intercept)          x1          x2 
#>      0.0664     -0.2268      0.3884 
#> 
#> Phi coefficients (precision model with logit link):
#>   (phi) 
#> -0.4091 
#> 
# }