weibullRMM_SEM: St-EM algorithm for Reliability Mixture Models (RMM) of Weibull with right Censoring

Description

Parametric Stochastic EM (St-EM) algorithm for univariate finite mixture of Weibull distributions with randomly right censored data.

Usage

weibullRMM_SEM(x, d = NULL, lambda = NULL, shape = NULL, scale = NULL,
        k = 2, maxit = 200, maxit.survreg = 200, epsilon = 1e-03,
        averaged = TRUE, verb = FALSE)

Value

weibullRMM_SEM returns a list of class "mixEM" with the following items:

x: The input data.
d: The input censoring indicator.
lambda: The estimates for the mixing proportions.
scale: The estimates for the Weibull component scales.
shape: The estimates for the Weibull component shapes.
loglik: The log-likelihood value at convergence of the algorithm.
posterior: An \(n\times k\) matrix of posterior probabilities for observation, after convergence of the algorithm.
all.loglik: The sequence of log-likelihoods over iterations.
all.lambda: The sequence of mixing proportions over iterations.
all.scale: The sequence of component scales over iterations.
all.shape: The sequence of component shapes over iterations.
ft: A character vector giving the name of the function called.

Arguments

x: A vector of \(n\) real positive lifetime (possibly censored) durations. If d is not NULL then a vector of random censoring times c occured, so that \(x= min(x,c)\) and \(d = I(x <= c)\).
d: The vector of censoring indication, where 1 means observed lifetime data, and 0 means censored lifetime data.
lambda: Initial value of mixing proportions. If NULL, then lambda is set to rep(1/k,k).
shape: Initial value of Weibull component shapes, all set to 1 if NULL.
scale: Initial value of Weibull component scales, all set to 1 if NULL.
k: Number of components of the mixture.
maxit: The number of iterations allowed, since for St-EM algorithms convergence is not based on stabilization, exactly maxit iterations are performed (see Bordes L. and Chauveau D. (2016) reference below).
maxit.survreg: The number of iterations allowed in the computations of the MLE for censored weibull data from the survival package (see Bordes L. and Chauveau D. (2016) reference below).
epsilon: Tolerance parameter used in the numerical computations of the MLE for censored weibull data by survreg from the survival package (see Bordes L. and Chauveau D. (2016) reference below).
averaged: The way of updating parameters at each iteration: if TRUE, current values of the parameters are obtained by averaging the sequence (see Bordes L. and Chauveau D. (2016) reference below).
verb: If TRUE, print updates for every iteration of the algorithm as it runs

Author

Didier Chauveau

Details

This St-EM algorithm calls functions from the survival package to compute parametric MLE for censored weibull data.

References

Bordes, L., and Chauveau, D. (2016), Stochastic EM algorithms for parametric and semiparametric mixture models for right-censored lifetime data, Computational Statistics, Volume 31, Issue 4, pages 1513-1538. https://link.springer.com/article/10.1007/s00180-016-0661-7

Examples

Run this code

n = 500 # sample size
m = 2 # nb components
lambda=c(0.4, 0.6)
shape <- c(0.5,5); scale <- c(1,20) # model parameters
set.seed(321)
x <- rweibullmix(n, lambda, shape, scale) # iid ~ weibull mixture
cs=runif(n,0,max(x)+10) # iid censoring times
t <- apply(cbind(x,cs),1,min) # censored observations
d <- 1*(x <= cs)              # censoring indicator

## set arbitrary or "reasonable" (e.g., data-driven) initial values
l0 <- rep(1/m,m); sh0 <- c(1, 2); sc0 <- c(2,10)
# Stochastic EM algorithm 
a <- weibullRMM_SEM(t, d, lambda = l0, shape = sh0, scale = sc0, maxit = 200)

summary(a) # Parameters estimates etc
plotweibullRMM(a) # plot of St-EM sequences
plot(a, which=2) # or equivalently, S3 method for "mixEM" object

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