fmcfust: Fitting Finite Mixtures of Multivariate Canonical Fundamental...

In EMMIXcskew: Fitting Mixtures of CFUST Distributions

Description

Computes maximum likelihood estimators (MLE) for finite mixtures of canonical fundamental multivariate skew t (FM-CFUST) model via the EM algorithm.

Usage

fmcfust(g=1, dat, q, initial=NULL, known=NULL, clust=NULL, itmax=100, eps=1e-6, 
    nkmeans=20, verbose=T, method=c("moments","transformation","EMMIXskew","EMMIXuskew"), 
    convergence=c("Aitken","likelihood","parameters"))
## S3 method for class 'fmcfust'
summary(object, ...)
## S3 method for class 'fmcfust'
print(x, ...)                     

Arguments

object, x	an object class of class "fmcfust", i.e. a fitted model.
g	a scalar specifying the number of components in the mixture model
dat	the data matrix giving the coordinates of the point(s) where the density is evaluated. This is either a vector of length p or a matrix with p columns.
q	a scalar specifying how many number of columns the skewness matrix delta has.
initial	(optional) a list containing the initial parameters of the mixture model. See the 'Details' section. The default is NULL.
known	(optional) a list containing parameters of the mixture model that are known and not required to be estimated. See the 'Details' section. The default is NULL.
itmax	(optional) a positive integer specifying the maximum number of EM iterations to perform. The default is 100.
eps	(optional) a numeric value used to control the termination criteria for the EM loops. It is the maximum tolerance for the absolute difference between the log-likelihood value and the asymptotic log likelihood value. The default is 1e-6.
clust	(optional) a numeric value of length nrow(dat) containing the initial labels for each data point in dat. The default is NULL, indicating no initial clustering is known.
nkmeans	(optional) a numeric value indicating how many k-means trials to be used when searching for initial values. The default is 20.
verbose	(optional) a logical value. If TRUE, output for each iteration will be printed out. if FALSE, no output is printed. The default is TRUE. See the 'Details' section.
method	(optional) a string indicating which method to use to generate initial values. See init.cfust.
convergence	(optional) a string indicating which convergence criterion to use to terminate the iterations. The default "Aitken" uses Aitken accelation, whereas "likelihood" uses the relative difference in log likleihood value, and "parameters" checks the changes in parameter estimates.
...	not used.

Details

The arguments init and known, if specified, is a list structure containing at least one of mu, sigma, delta, dof, pro (See dfmcfust for the structure of each of these elements). If init=FALSE (default), the program uses an automatic approach based on moments estimate and k-means clustering to generate an initial value for the model parameters. Note that this may not provide the best results.

As the EM algorithm is sensitive to the starting value, it is highly recommended to apply a wide range different initializations. Some strategies are implemented in init.cfust.

Value

mu	a list of g numeric matrices containing the location parameter for each component.
sigma	a list of g numeric matrices containing the scale parameter for each component.
delta	a list of g numeric matrices containing the skewness parameter for each component.
dof	a numeric vector of length g representing the degrees of freedom for each component.
pro	a vector of length of g specifying the mixing proportions for each component.
tau	an g by n matrix of posterior probability of component membership.
clusters	a vector of length n of final partition.
loglik	the final log likelihood value.
lk	a vector of log likelihood values at each EM iteration.
iter	number of iterations performed.
eps	the final absolute difference between the log likelihood value and the asymptotic log likelihood value.
aic, bic	Akaike Information Criterion (AIC), Bayes Information Criterion (BIC)

References

Lee S.X. and McLachlan, G.J. (2016). Finite mixtures of canonical fundamental skew t-distributions: the unification of the restricted and unrestricted skew t-mixture models. Statistics and Computing 26, 573-589

Lee S.X. and McLachlan, G.J. (2017). EMMIXcskew: An R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions. Journal of Statistical Software 83(3), 1-32. URL 10.18637/jss.v083.i03.

See Also

init.cfust, rfmcfust, dfmcfust, fmcfust.contour.2d

Examples

   
                
#a short demo using geyser data
library(MASS)
Fit <- fmcfust(3, geyser)
summary(Fit)
print(Fit)   

EMMIXcskew documentation built on May 2, 2019, 6:59 a.m.