EmSkewfit: Fit the Multivariate Skew Mixture Models
In EMMIXskew: The EM Algorithm and Skew Mixture Distribution

Description Usage Arguments Details Value References See Also Examples

The engines to fit the data into mixture models using initial partition or initial values. set.

1 2	EmSkewfit1(dat, g, clust, distr, ncov, itmax, epsilon,initloop=20) EmSkewfit2(dat, g, init, distr, ncov, itmax, epsilon)

`dat`	The dataset, an n by p numeric matrix, where n is number of observations and p the dimension of data.
`g`	The number of components of the mixture model
`distr`	A three letter string indicating the type of distribution to be fit. See Details.
`ncov`	A small integer indicating the type of covariance structure. See Details.
`clust`	A vector of integers specifying the initial partitions of the data
`init`	A list containing the initial parameters for the mixture model. See details.
`itmax`	A big integer specifying the maximum number of iterations to apply
`epsilon`	A small number used to stop the EM algorithm loop when the relative difference between log-likelihood at each iteration become sufficient small.
`initloop`	A integer specifying the number of initial loops

The distribution type, determined by the distr parameter, which may take any one of the following values: "mvn" for a multivariate normal, "mvt" for a multivariate t-distribution, "msn" for a multivariate skew normal distribution and "mst" for a multivariate skew t-distribution.

The covariance matrix type, represented by the ncov parameter, may be any one of the following: ncov=1 for a common variance, ncov=2 for a common diagonal variance, ncov=3 for a general variance, ncov =4 for a diagonal variance, ncov=5 for sigma(h)*I(p)(diagonal covariance with same identical diagonal element values).

The parameter init is a list with elements: pro, a numeric vector of the mixing proportion of each component; mu, a p by g matrix with each column as its corresponding mean; sigma, a three dimensional p by p by g array with its jth component matrix (p,p,j) as the covariance matrix for jth component of mixture models; dof, a vector of degrees of freedom for each component; delta, a p by g matrix with its columns corresponding to skew parameter vectors.

`error`	Error code, 0 = normal exit; 1 = did not converge within `itmax` iterations; 2 = failed to get the initial values; 3 = singularity
`aic`	Akaike Information Criterion (AIC)
`bic`	Bayes Information Criterion (BIC)
`pro`	A vector of mixing proportions, see Details.
`mu`	A numeric matrix with each column corresponding to the mean, see Details.
`sigma`	An array of dimension (p,p,g) with first two dimension corresponding covariance matrix of each component, see Details.
`dof`	A vector of degrees of freedom for each component, see Details.
`delta`	A p by g matrix with each column corresponding to a skew parameter vector, see Details.
`clust`	A vector of final partition
`loglik`	The loglikelihood at convergence
`lk`	A vector of loglikelihood at each EM iteration
`tau`	An n by g matrix of posterior probability for each data point

McLachlan G.J. and Krishnan T. (2008). The EM Algorithm and Extensions (2nd). New Jersay: Wiley.

McLachlan G.J. and Peel D. (2000). Finite Mixture Models. New York: Wiley.

init.mix,initEmmix,EmSkew, rdemmix,rdemmix2,rdmvn,rdmvt,rdmsn, rdmst.

n1=300;n2=300;n3=400;
nn <-c(n1,n2,n3)
n=1000
p=2
ng=3


sigma<-array(0,c(2,2,3))
for(h in 2:3) sigma[,,h]<-diag(2)
sigma[,,1]<-cbind( c(1,0),c(0,1))
mu  <- cbind(c(4,-4),c(3.5,4),c( 0, 0))

# for other distributions, 
#delta <- cbind(c(3,3),c(1,5),c(-3,1))
#dof    <- c(3,5,5)


pro   <- c(0.3,0.3,0.4)



distr="mvn"
ncov=3

#first we generate a data set
set.seed(111) #random seed is set 
dat <- rdemmix(nn,p,ng,distr,mu,sigma,dof=NULL,delta=NULL)

#start from initial partition
clust<- rep(1:ng,nn)
obj1 <- EmSkewfit1(dat, ng, clust, distr, ncov, itmax=1000, epsilon=1e-4)


#start from initial values
#alternatively, if we define initial values like 

init<-list()

init$pro<-pro
init$mu<-mu
init$sigma<-sigma


# for other distributions, 
#delta <- cbind(c(3,3),c(1,5),c(-3,1))
#dof    <- c(3,5,5)
#init$dof<-dof
#init$delta<-delta

obj2 <-EmSkewfit2(dat, ng, init, distr, ncov,itmax=1000, epsilon=1e-4)