Description Usage Arguments Details Value Note Author(s) See Also Examples
This function fits a normal mixture model to progressive Type-II censored mixture data by dealing with the two aspects of missing data, latent mixture components and the censored data, using a maximum likelihood estimation through a constrained two-layer EM algorithm.
1 2 3 4 5 | pcensmixSim(Pdat, ...)
## S3 method for class 'pcgen'
pcensmixSim(Pdat, r, p, param, iteration = 1e+05,
INERiter = 20, ...)
|
Pdat |
an object of class |
... |
additinal arguments to pass by. |
r |
desired number of failures to observe. |
p |
a parameter controlling the amount of censoring. The action of
censoring individuals after each failure occurs with probabilty |
param |
a numeric vector; used as starting values for the EM and simulating a new data to replace in case of happening singularity in the likelihood. |
iteration |
the maximum number of required iteration for the EM algorithm until convergence– default value is 1e+05. |
INERiter |
the maximum number of required iteration for the second EM algorithm– default is 20. |
This function fits a two-component normal mixture model to simulated progressive Type-II censored data with density function
π (1/ σ_1) φ[ (z - μ_1) / σ_1] + (1 - π) (1/ σ_2) φ[ (z - μ_2) / σ_2]
where φ is the standard normal density.
It uses a constrained two-layer EM algorithm to deal with the two forms of missing data: the censored survival times and the mixture component labels. Given the EM algorithm is at a particular iteration: (i) first, in the E-step it obtains the mixture component indicator estimates given the current parameter estimates and the observed data. (ii) Next, for re-estimation of the unknown parameters, a new EM algorithm is nested in the M-step of the initial EM algorithm to deal with the estimation of the missing censored survival times and consequently building the maximum likelihood equations. These steps are repeated until the model converges.
pcensmixSim
gives an object of class data.frame
containing the following components:
muhat1,sigmahat1 |
component one parameter estimates (\hat{μ_1}, \hat{σ_1} ) |
muhat2,sigmahat2 |
component two parameter estimates (\hat{μ_2}, \hat{σ_2} ) |
pihat |
estimation of mixture proportion \hat{π} |
se.muhat1,se.sigmahat1 |
standard errors of \hat{μ_1} and \hat{σ_1} |
se.muhat2,se.sigmahat2 |
standard errors of \hat{μ_2} and \hat{σ_2} |
se.pihat |
standard error of \hat{π} |
no.fails.comp1,no.fails.comp2 |
number of failures from each mixture component |
no.cens.comp1,no.cens.comp2 |
number of censored observations from each mixture component |
ll |
log-likelihood value |
datachange_flag |
|
In fitting the model, to overcome the problem of
singularity and model non-identifiability that might happen in some cases
depending on the true means and standard deviations of the components, we
use the constraint proposed by Hathaway (1985). Based on this, the
ratios of the standard deviations are considered to be greater than a
pre-fixed constant. We consider the constraints σ_1/σ_2>0.1
and σ_2/σ_1>0.1 which lead to obtain a parameter space with
no singularities. In case this conditions doesn't hold, the data will be
replaced by a new simulated one and datachange_flag
will appear as
TRUE
in the output.
See pcgen
for the
definition of censored version of data.
Lida Fallah, John Hinde
Maintainer: Lida Fallah <l.fallah22@gmail.com>
1 2 3 4 5 6 7 |
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