spRMM_SEM: Stochastic EM algorithm for semiparametric scaled mixture of...

In mixtools: Tools for Analyzing Finite Mixture Models

Stochastic EM algorithm for semiparametric scaled mixture of censored data

Description

Stochastic EM algorithm for semiparametric scaled mixture for randomly right censored data.

Usage

  spRMM_SEM(t, d = NULL, lambda = NULL, scaling = NULL, 
          centers = 2, kernelft = triang_wkde, 
          bw = rep(bw.nrd0(t),length(t)), averaged = TRUE,
          epsilon = 1e-08, maxit = 100, batchsize = 1, verb = FALSE) 

Arguments

t	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).
scaling	Initial value of scaling between components, set to 1 if NULL.
centers	initial centers for initial call to kmeans for initialization.
kernelft	.
bw	Bandwidth in the kernel hazard estimates.
averaged	averaged.
epsilon	Tolerance limit.
maxit	The number of iterations allowed.
batchsize	The batchsize (see reference below).
verb	If TRUE, print updates for every iteration of the algorithm as it runs

Value

spRMM_SEM returns a list of class "spRMM" with the following items:

t	The input data.
d	The input censoring indicator.
lambda	The estimates for the mixing proportions.
scaling	The estimates for the components scaling.
posterior	An n\times k matrix of posterior probabilities for observation, after convergence of the algorithm.
loglik	The (pseudo) log-likelihood value at convergence of the algorithm.
all.loglik	The sequence of log-likelihood values over iterations.
all.lambda	The sequence of mixing proportions over iterations.
all.scaling	The sequence of scaling parameter over iterations.
meanpost	Posterior probabilities averaged over iterations.
survival	Kaplan-Meier last iteration estimate (a stepfun object).
hazard	Hazard rate last iteration estimate evaluated at final.t.
final.t	Last iteration unscaled sample (see reference).
s.hat	Kaplan-Meier average estimate.
t.hat	Ordered unscaled sample, for testing purpose.
avg.od	For testing purpose only.
hazard.hat	Hazard rate average estimate on t.hat.
batch.t	Batch sample (not ordered), see reference.
batch.d	Associated event indicators just rep(d,batchsize), for testing purpose.
sumNaNs	Internal control of numerical stability.
ft	A character vector giving the name of the function.

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: plotspRMM, summary.spRMM.

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

Examples

## Not run: 
n=500 # sample size
m=2 # nb components
lambda=c(0.4, 0.6) # parameters
meanlog=3; sdlog=0.5; scale=0.1
set.seed(12)
# simulate a scaled mixture of lognormals
x <- rlnormscalemix(n, lambda, meanlog, sdlog, scale)
cs=runif(n,20,max(x)+400) # Censoring (uniform) and incomplete data
t <- apply(cbind(x,cs),1,min)
d <- 1*(x <= cs)
tauxc <- 100*round( 1-mean(d),3)
cat(tauxc, "percents of data censored.\n")

c0 <- c(25, 180) # data-driven initial centers (visible modes)
sc0 <- 25/180    # and scaling
s <- spRMM_SEM(t, d, scaling = sc0, centers = c0, bw = 15, maxit = 100)

plotspRMM(s) # default
summary(s)   # S3 method for class "spRMM"

## End(Not run)

mixtools documentation built on April 12, 2025, 2:31 a.m.