Package 'FMCensSkewReg'

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

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