expRMM_EM: EM algorithm for Reliability Mixture Models (RMM) with right Censoring

Description

Parametric EM algorithm for univariate finite mixture of exponentials distributions with randomly right censored data.

Usage

expRMM_EM(x, d=NULL, lambda = NULL, rate = NULL, k = 2, 
		    complete = "tdz", epsilon = 1e-08, maxit = 1000, verb = FALSE)

Value

expRMM_EM 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.
rate: The estimates for the component rates.
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.rate: The sequence of component rates over iterations.
ft: A character vector giving the name of the function.

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 occurred, 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).
rate: Initial value of component exponential rates, all set to 1 if NULL.
k: Number of components of the mixture.
complete: Nature of complete data involved within the EM machinery, can be "tdz" for (t,d,z) (the default), or "xz" for (x,z) (see Bordes L. and Chauveau D. (2016) reference below).
epsilon: Tolerance limit for declaring algorithm convergence based on the change between two consecutive iterations.
maxit: The maximum number of iterations allowed, convergence may be declared before maxit iterations (see epsilon above).
verb: If TRUE, print updates for every iteration of the algorithm as it runs

Author

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

Examples

Run this code

n <- 300 # sample size
m <- 2   # number of mixture components
lambda <- c(1/3,1-1/3); rate <- c(1,1/10) # mixture parameters
set.seed(1234)
x <- rexpmix(n, lambda, rate) # iid ~ exponential mixture
cs <- runif(n,0,max(x)) # Censoring (uniform) and incomplete data
t <- apply(cbind(x,cs),1,min) # observed or censored data
d <- 1*(x <= cs)              # censoring indicator

###### EM for RMM, exponential lifetimes
l0 <- rep(1/m,m); r0 <- c(1, 0.5) # "arbitrary" initial values
a <- expRMM_EM(t, d, lambda = l0, rate = r0, k = m)
summary(a)                 # EM estimates etc
plotexpRMM(a, lwd=2) # default plot of EM sequences
plot(a, which=2) # or equivalently, S3 method for "mixEM" object

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