Title: Finite Mixture of Censored Regression Models with Skewed Distributions
Version: 0.1.1
Author: Jiwon Park [aut, cre], Victor Hugo Lachos Davila [aut], Dipak Dey [aut]
Maintainer: Jiwon Park <pcjylove87@gmail.com>
Description: Provides an implementation of finite mixture regression models for censored data under four distributional families: Normal (FM-NCR), Student t (FM-TCR), skew-Normal (FM-SNCR), and skew-t (FM-STCR). The package enables flexible modeling of skewness and heavy tails often observed in real-world data, while explicitly accounting for censoring. Functions are included for parameter estimation via the Expectation-Maximization (EM) algorithm, computation of standard errors, and model comparison criteria such as the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Efficient Determination Criterion (EDC). The underlying methodology is described in Park et al. (2024) <doi:10.1007/s00180-024-01459-4>.
License: MIT + file LICENSE
URL: https://github.com/JiwonPark41/FMCensSkewReg
BugReports: https://github.com/JiwonPark41/FMCensSkewReg/issues
Depends: R (≥ 3.6.0)
Encoding: UTF-8
RoxygenNote: 7.3.3
Imports: stats, mvtnorm, MomTrunc, mnormt, sn, truncdist, mixsmsn
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2025-12-17 14:21:11 UTC; jiwonpark
Repository: CRAN
Date/Publication: 2025-12-22 18:10:09 UTC

FMCensSkewReg: Finite Mixture of Censored Regression with Skewed Distributions

Description

Functions to fit finite-mixture censored regression models under Normal ("Normal"), Student-t ("T"), Skew-Normal ("SN"), and Skew-t ("ST"). Supports left-censoring, k-means initialization, Aitken acceleration, and optional information-matrix standard errors.

Main function

Author(s)

Maintainer: Jiwon Park pcjylove87@gmail.com

Authors:

See Also

Useful links:

EM Algorithm for Finite Mixture Censored Regression

Description

Fits finite mixture censored regression models under four families: Normal ("Normal"), Student-t ("T"), Skew-Normal ("SN"), and Skew-t ("ST").

Usage

EM.skewCens.mixR(
  cc,
  y,
  x,
  Abetas = NULL,
  sigma2 = NULL,
  shape = NULL,
  pii = NULL,
  nu = NULL,
  g = NULL,
  get.init = TRUE,
  criteria = TRUE,
  group = FALSE,
  family = "Normal",
  error = 1e-05,
  iter.max = 100,
  obs.prob = FALSE,
  kmeans.param = NULL,
  aitken = TRUE,
  IM = TRUE
)

Arguments

cc

Integer vector of length n; censoring indicator (1 = censored, 0 = observed).

y

Numeric response vector (univariate).

x

Numeric design matrix (n x p); include intercept column if needed.

Abetas

Optional initial regression coefficient matrix (p x g).

sigma2

Optional initial variance(s), length g.

shape

Optional initial skewness parameter(s), length g (used in SN/ST).

pii

Optional initial mixing proportions, length g, must sum to 1.

nu

Degrees of freedom for T/ST models (scalar).

g

Number of mixture components (g \ge 1). Required if get.init = TRUE.

get.init

Logical; if TRUE, k-means-based initialization is used.

criteria

Logical; if TRUE, returns AIC/BIC/EDC.

group

Logical; if TRUE, returns hard cluster labels.

family

One of "Normal", "T", "SN", "ST".

error

Convergence tolerance for EM.

iter.max

Maximum number of EM iterations.

obs.prob

Logical; if TRUE, returns posterior membership matrix.

kmeans.param

Optional list for kmeans init.

aitken

Logical; use Aitken acceleration for convergence monitoring.

IM

Logical; if TRUE, compute (robust) standard errors via information matrix.

Details

Left-censoring is indicated by cc[i] = 1 and replacing y[i] by the censoring point. The routine supports Normal, t, Skew-Normal, and Skew-t families with finite mixtures.

Value

A list with elements:

Abetas

Estimated regression coefficients (p x g).

sigma2

Estimated variances (length g).

shape

Estimated skewness parameters (length g; SN/ST).

pii

Estimated mixing proportions (length g).

sd

Standard errors (if IM=TRUE).

nu

Estimated/used degrees of freedom (T/ST).

loglik

Final log-likelihood.

loglikT

Log-likelihood trace over iterations.

aic, bic, edc

Information criteria (if criteria=TRUE).

iter

Number of EM iterations.

n

Sample size.

group

Hard labels (if group=TRUE).

Examples


set.seed(1)
n <- 150
X <- cbind(1, runif(n), rnorm(n))
pi <- c(0.6, 0.4); nu <- 4
b1 <- c(0.5, 1.0, -1.0); sigma1 <- 1; shape1 <- 2
b2 <- c(1.0,-0.5, 0.5);  sigma2 <- 2; shape2 <- 3
mu1 <- drop(X %*% b1); mu2 <- drop(X %*% b2)
draw1 <- function(i){
  a1 <- list(mu=mu1[i], sigma2=sigma1, shape=shape1, nu=nu)
  a2 <- list(mu=mu2[i], sigma2=sigma2, shape=shape2, nu=nu)
  mixsmsn::rmix(1, pi, "Skew.t", list(a1,a2), cluster=FALSE)
}
y0 <- vapply(seq_len(n), draw1, numeric(1))
cutoff <- unname(stats::quantile(y0, 0.20))
cc <- as.integer(y0 <= cutoff)
y  <- ifelse(cc == 1, cutoff, y0)
fit <- EM.skewCens.mixR(cc, y, X, g=2, family="Normal", iter.max=50)
fit$loglik