MSGHD: Mixture of multiple scaled generalized hyperbolic...

In MixGHD: Model Based Clustering, Classification and Discriminant Analysis Using the Mixture of Generalized Hyperbolic Distributions

Mixture of multiple scaled generalized hyperbolic distributions (MSGHD).

Description

Carries out model-based clustering using the mixture of multiple scaled generalized hyperbolic distributions.

Usage

MSGHD(data=NULL,gpar0=NULL,G=2,max.iter=100,label=NULL,eps=1e-2,
	method="km",scale=TRUE,nr=10, modelSel="AIC")

Arguments

data	A n x p matrix or data frame such that rows correspond to observations and columns correspond to variables.
gpar0	(optional) A list containing the initial parameters of the mixture model. See the 'Details' section.
G	The range of values for the number of clusters.
max.iter	(optional) A numerical parameter giving the maximum number of iterations each EM algorithm is allowed to use.
label	( optional) A n dimensional vector, if label[i]=k then observation i belongs to group k, If label[i]=0 then observation i has no known group, if NULL then the data has no known groups.
eps	(optional) A number specifying the epsilon value for the convergence criteria used in the EM algorithms. For each algorithm, the criterion is based on the difference between the log-likelihood at an iteration and an asymptotic estimate of the log-likelihood at that iteration. This asymptotic estimate is based on the Aitken acceleration.
method	( optional) A string indicating the initialization criterion, if not specified kmeans clustering is used. Alternative methods are: hierarchical "hierarchical", random "random", and model based "modelBased" clustering
scale	( optional) A logical value indicating whether or not the data should be scaled, true by default.
nr	( optional) A number indicating the number of starting value when random is used, 10 by default.
modelSel	( optional) A string indicating the model selection criterion, if not specified AIC is used. Alternative methods are: BIC,ICL, and AIC3

Details

The arguments gpar0, if specified, is a list structure containing at least one p dimensional vector mu, alpha and phi, a pxp matrix gamma, and a px2 matrix cpl containing the vector omega and the vector lambda.

Value

A S4 object of class MixGHD with slots:

index	Value of the index used for model selection (AIC or ICL or BIC or AIC3) for each G,the index used is specified by the user, if not specified AIC is used.
BIC	Bayesian information criterion.
ICL	Integrated completed likelihood.
AIC	Akaike information criterion.
AIC3	Akaike information criterion 3.
gpar	A list of the model parameters
loglik	The log-likelihood values.
map	A vector of integers indicating the maximum a posteriori classifications for the best model.
z	A matrix giving the raw values upon which map is based.

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <[e-mail]>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification 36(1) 26-57.\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

See Also

MGHD

Examples

##loading banknote data
data(banknote)


##model estimation
model=MSGHD(banknote[,2:7],G=2,max.iter=30)

#result
table(banknote[,1],model@map)
summary(model)
plot(model)

MixGHD documentation built on May 11, 2022, 5:12 p.m.