weibullRMM_SEM {mixtools}

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) 

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

Details

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

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.

Author(s)

Didier Chauveau

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

See Also

Related functions: plotweibullRMM, summary.mixEM.

Other models and algorithms for censored lifetime data (name convention is model_algorithm): expRMM_EM, spRMM_SEM.

Examples

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