This method applies the expectationmaximization (EM) algorithm to estimate the parameters of a univariate Weibull mixture model. See 'Details'.
mixmod_em(x, ...) # S3 method for wt_reliability_data mixmod_em( x, distribution = "weibull", conf_level = 0.95, k = 2, method = "EM", n_iter = 100L, conv_limit = 1e06, diff_loglik = 0.01, ... )
x  A tibble with class 

...  Further arguments passed to or from other methods. Currently not used. 
distribution 

conf_level  Confidence level for the intervals of the Weibull parameters
of every component 
k  Number of mixture components. 
method 

n_iter  Integer defining the maximum number of iterations. 
conv_limit  Numeric value defining the convergence limit. 
diff_loglik  Numeric value defining the maximum difference between loglikelihood values, which seems permissible. 
A list with classes wt_model
and wt_mixmod_em
. The length of the
list depends on the number of specified subgroups k
. The first k
lists
contain information provided by ml_estimation. The values of logL
, aic
and bic
are the results of a weighted loglikelihood, where the weights are
the posterior probabilities determined by the algorithm. The last list summarizes
further results of the EM algorithm and is therefore called em_results
. It
contains the following elements:
a_priori
: A vector with estimated prior probabilities.
a_posteriori
: A matrix with estimated posterior probabilities.
groups
: Numeric vector specifying the group membership of every observation.
logL
: The value of the complete loglikelihood.
aic
: Akaike Information Criterion.
bic
: Bayesian Information Criterion.
The EM algorithm is an iterative algorithm for which starting values must be defined. Starting values can be provided for the unknown parameter vector as well as for the posterior probabilities. This implementation employs initial values for the posterior probabilities. These are assigned randomly by using the Dirichlet distribution, the conjugate prior of a multinomial distribution (see Mr. Gelissen's blog post listed under references).
MStep : On the basis of the initial posterior probabilities, the parameter vector is estimated with NewtonRaphson.
EStep : The actual estimated parameter vector is used to perform an update of the posterior probabilities.
This procedure is repeated until the complete loglikelihood has converged.
Doganaksoy, N.; Hahn, G.; Meeker, W. Q., Reliability Analysis by Failure Mode, Quality Progress, 35(6), 4752, 2002
Blog post by Stefan Gelissen: R code for fitting a mixture distribution to censored data ; last accessed on 8th December 2020
# Reliability data preparation: ## Data for mixture model: data_mix < reliability_data( voltage, x = hours, status = status ) # Example 1  EM algorithm with k = 2: mix_mod_em < mixmod_em( x = data_mix, conf_level = 0.95, k = 2, n_iter = 150 ) # Example 2  Maximum likelihood is applied when k = 1: mix_mod_em_2 < mixmod_em( x = data_mix, conf_level = 0.95, k = 1, n_iter = 150 )