The engines to fit the data into mixture models using initial partition or initial values. set.
EmSkewfit1(dat, g, clust, distr, ncov, itmax, epsilon,initloop=20)
EmSkewfit2(dat, g, init, distr, ncov, itmax, epsilon)The dataset, an n by p numeric matrix, where n is number of observations and p the dimension of data.
The number of components of the mixture model
A three letter string indicating the type of distribution to be fit. See Details.
A small integer indicating the type of covariance structure. See Details.
A vector of integers specifying the initial partitions of the data
A list containing the initial parameters for the mixture model. See details.
A big integer specifying the maximum number of iterations to apply
A small number used to stop the EM algorithm loop when the relative difference between log-likelihood at each iteration become sufficient small.
A integer specifying the number of initial loops
Error code, 0 = normal exit; 1 = did not converge within itmax iterations; 2 = failed to get the initial values; 3 = singularity
Akaike Information Criterion (AIC)
Bayes Information Criterion (BIC)
A vector of mixing proportions, see Details.
A numeric matrix with each column corresponding to the mean, see Details.
An array of dimension (p,p,g) with first two dimension corresponding covariance matrix of each component, see Details.
A vector of degrees of freedom for each component, see Details.
A p by g matrix with each column corresponding to a skew parameter vector, see Details.
A vector of final partition
The loglikelihood at convergence
A vector of loglikelihood at each EM iteration
An n by g matrix of posterior probability for each data point
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.
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.
# NOT RUN {
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)
# }
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