Title: Censored Linear Regression Models under Heavy‑tailed Distributions
Version: 0.0.1
Maintainer: Yessenia Alvarez Gil <yessenia.alvarez@ufpe.br>
Description: Functions for fitting univariate linear regression models under Scale Mixtures of Skew-Normal (SMSN) distributions, considering left, right or interval censoring and missing responses. Estimation is performed via an EM-type algorithm. Includes selection criteria, sample generation and envelope. For details, see Gil, Y.A., Garay, A.M., and Lachos, V.H. (2025) <doi:10.1007/s10260-025-00797-x>.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: R (≥ 3.5.0)
Imports: mvtnorm, mnormt, cubature, ggplot2
NeedsCompilation: no
Packaged: 2025-11-15 02:01:56 UTC; Usuario
Author: Yessenia Alvarez Gil [aut, cre], Aldo M. Garay [aut], Victor H. Lachos [aut]
Repository: CRAN
Date/Publication: 2025-11-19 19:40:12 UTC

Fit Censored Linear Regression Model under Scale Mixtures of Skew-Normal Distributions

Description

Fits a univariate linear regression model with censoring and/or missing values in the response variable, assuming it follows a distribution from the Scale Mixtures of Skew-Normal (SMSN) family. Computes standard errors using the empirical information matrix and provides model selection criteria (AIC, BIC, CAIC, HQ). Optionally generates envelope plots based on martingale residuals.

Usage

CensRegSMSN(
  cc,
  x,
  y,
  beta = NULL,
  sigma2 = NULL,
  lambda = NULL,
  nu = NULL,
  cens = "Int",
  UL = NULL,
  get.init = TRUE,
  show.envelope = FALSE,
  error = 1e-04,
  iter.max = 300,
  family = "ST",
  verbose = TRUE
)

Arguments

cc

Indicator vector for incomplete observations of length n. Each element should be 0 if the observation is fully observed, or 1 if it is incomplete (either censored or missing).

x

Design matrix (of dimension n x p) corresponding to the covariates in the linear predictor.

y

Response vector of length n. For fully observed data, it contains the observed values. In the case of right or left censoring, it represents the censoring limit. For interval censoring, it corresponds to the lower bound of the censoring interval. Missing values (NA) are allowed.

beta

Optional initial values for the regression coefficients. Default is NULL.

sigma2

Optional initial value for the scale parameter. Default is NULL.

lambda

Optional initial value for the shape parameter (for skewed distributions). Default is NULL.

nu

Optional initial value for the distribution-specific parameter. Required for T, ST, CN, and SCN families. Must be a two-dimensional vector for CN and SCN. Should not be provided for N or SN. Default is NULL.

cens

Character indicating the type of censoring. Should be one of "Left", "Right" or "Int". Default is "Int".

UL

Vector of upper limits of length n for interval-censored observations. Must be provided when cens = "Int".

get.init

Logical; if TRUE, initial values are automatically computed. If FALSE, initial values must be provided. Default is TRUE.

show.envelope

Logical; if TRUE, an envelope plot based on transformed martingale residuals is produced. Default is FALSE.

error

Convergence threshold for the algorithm. Default is 0.0001.

iter.max

Maximum number of iterations allowed in the algorithm. Default is 300.

family

Character string indicating the distribution family. Possible values include: "SN" (Skew-Normal), "ST" (Skew-t), "SCN" (Skew Contaminated Normal), "N" (Normal), "T" (Student-t), "CN" (Contaminated Normal). Default is "ST".

verbose

Logical indicating whether results should be printed to the console. Default is TRUE.

Details

The model assumes that the response variable follows a distribution from the Scale Mixtures of Skew-Normal (SMSN) family, which allows for heavy tails and/or asymmetry.

Interval censoring is a general framework that includes left and right censoring and missing responses, providing a unified treatment for all cases.

For the Skew Contaminated Normal ("SCN") and the Contaminated Normal ("CN") distributions, the nu parameter must be a two-dimensional vector with values in the interval (0, 1).

Value

A list with the following components:

beta

Estimated regression coefficients.

sigma2

Estimated scale parameter.

lambda

Estimated shape parameter. For symmetric distributions ("N", "T", "CN"), this is zero.

nu

Estimated parameters of the scale mixture distribution. NULL for "SN" and "N" families. A scalar for "ST" and "T", and a vector for "SCN" and "CN".

SE

Standard errors of the estimated parameters.

iter

Number of iterations until convergence.

logver

Value of the log-likelihood function at convergence, computed under the fitted model.

AIC, BIC, CAIC, HQ

Information criteria for model selection.

residual

Transformed martingale residuals used for envelope plots. Returned only if show.envelope = TRUE; otherwise NULL.

References

Gil, Y. A., Garay, A. M. & Lachos, V. H. Likelihood-based inference for interval censored regression models under heavy-tailed distributions. Stat Methods Appl 34, 519–544 (2025). doi:10.1007/s10260-025-00797-x.

Examples

# See examples in ?gen_SMSNCens_sample  for a complete workflow
# illustrating data generation and model fitting.

Generate simulated censored data under heavy‑tailed Distributions

Description

Simulates a univariate linear regression dataset with censoring and/or missing values in the response variable, considering that the error follows a SMSN distribution.

Usage

gen_SMSNCens_sample(
  n,
  x,
  beta,
  sigma2,
  lambda,
  nu,
  cens = "Int",
  pcens = 0,
  pna = 0,
  family = "ST"
)

Arguments

n

Integer. Sample size to be generated.

x

Numeric matrix of covariates (dimension n x p). Not contain missing values.

beta

Numeric vector of regression coefficients of length p.

sigma2

Positive numeric scalar. Scale parameter of SMSN class.

lambda

Numeric scalar. Shape parameter that controls the skewness in the SMSN class. Ignored when family = "N", "T" or "CN".

nu

Distribution-specific parameter: for "ST" or "T", nu is a scalar > 2 (degrees of freedom); for "SCN" or "CN", a vector (nu1, nu2) with values in (0,1). Ignored for "SN" and "N".

cens

Character string indicating the type of censoring: "Left", "Right" or "Int". Default is "Int".

pcens

Proportion of censored observations. Must be between 0 and 1. Default is 0.

pna

Proportion of missing values (treated as extreme interval censoring). Must be between 0 and 1. Only allowed when cens = "Int". Default is 0.

family

Character string indicating the error distribution family. Possible values: "SN" (Skew-Normal), "ST" (Skew-t), "SCN" (Skew Contaminated Normal), "N" (Normal), "T" (Student-t) and "CN" (Contaminated Normal). Default is "ST".

Details

The following procedures are applied to the generated response variable with incomplete observation:

Value

A list with the following components:

y

Fully observed response values (uncensored).

yc

Incomplete response values.

cc

Censoring indicator. 0 for observed data and 1 for censored or missing case.

UL

Vector of upper limits of the censoring interval. Equal to NULL for left or right censoring. For missing data, equal to Inf.

Examples

set.seed(1997)

# Generate covariates and true parameter values
n      <- 500
x      <- cbind(1, rnorm(n))
beta   <- c(2, -1)
sigma2 <- 1
lambda <- 3
nu     <- 3

# Generate a simulated dataset under SMSN-ICR model, with interval censoring and/or missing values
sample <- gen_SMSNCens_sample(n = n, x = x, beta = beta, sigma2 = sigma2,
                         lambda = lambda, nu = nu, cens = "Int",
                         pcens = 0.1, pna = 0.05, family = "ST")

# Fit the SMSN-ICR model using the generated data
fit <- CensRegSMSN(sample$cc, x, sample$yc, cens = "Int", UL = sample$UL, get.init = TRUE,
                   show.envelope = TRUE, family = "ST")