smsn.mmix {mixsmsn}

Fit multivariate FM-SMSN distributions.

Description

Return EM algorithm output for multivariate FM-SMSN distributions.

Usage

smsn.mmix(y, nu=1,
          mu = NULL, Sigma = NULL, shape = NULL, pii = NULL,
          g = NULL, get.init = TRUE, criteria = TRUE,
          group = FALSE, family = "Skew.normal", 
          error = 0.0001, iter.max = 100, uni.Gama = FALSE,
          calc.im=FALSE, obs.prob = FALSE, kmeans.param = NULL)

Arguments

y

the response matrix (dimension nxp)

nu

the parameter of the scale variable (vector or scalar) of the SMSN family (kurtosis parameter). It is necessary to all distributions. For the "Skew.cn" must be a vector of length 2 and values in (0,1)

mu

a list of g arguments of vectors of initial values (dimension p) for the location parameters

Sigma

a list of g arguments of matrices of initial values (dimension pxp) for the scale parameters

shape

a list of g arguments of vectors of initial values (dimension p)for the skewness parameters

pii

the vector of initial values (dimension g) for the weights for each cluster. Must sum one!

g

the number of cluster to be considered in fitting

get.init

if TRUE, the initial values are generated via k-means

criteria

if TRUE, log-likelihood (logLik), AIC, DIC, EDC and ICL will be calculated

group

if TRUE, the vector with the classification of the response is returned

family

distribution famility to be used in fitting ("Skew.t", "t", "Skew.cn", "Skew.slash", "slash", "Skew.normal", "Normal")

error

the covergence maximum error

iter.max

the maximum number of iterations of the EM algorithm. Default = 100

uni.Gama

if TRUE, the Gamma parameters are restricted to be the same for all clusters

calc.im

if TRUE, the information matrix is calculated and the starndard erros are reported

obs.prob

if TRUE, the posterior probability of each observation belonging to one of the g groups is reported

kmeans.param

a list with alternative parameters for the kmeans function when generating initial values, list(iter.max = 10, n.start = 1, algorithm = "Hartigan-Wong")

Value

Estimated values of the location, scale, skewness and kurtosis parameter. Note: The scale parameters estimated are relative to the entries of the squae root matrix of Sigma.

Author(s)

Marcos Prates [e-mail], Victor Lachos [e-mail] and Celso Cabral [e-mail]

References

Cabral, C. R. B., Lachos, V. H. and Prates, M. O. (2012). "Multivariate Mixture Modeling Using Skew-Normal Independent Distributions". Computational Statistics & Data Analysis, 56, 126-142, doi:10.1016/j.csda.2011.06.026.

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

See Also

mix.contour, rmmix and smsn.search

Examples

mu1 <- c(0,0)
Sigma1 <- matrix(c(3,1,1,3), 2,2)
shape1 <-c(4,4)
nu1 <- 4

mu2 <- c(5,5)
Sigma2 <- matrix(c(2,1,1,2), 2,2)
shape2 <-c(2,2)
nu2 <- 4

pii<-c(0.6,0.4)

arg1 = list(mu=mu1, Sigma=Sigma1, shape=shape1, nu=nu1)
arg2 = list(mu=mu2, Sigma=Sigma2, shape=shape2, nu=nu2)
y <- rmmix(n= 500, p = pii, "Skew.t", list(arg1,arg2))

## Not run: 

## Normal fit giving intial values
mu <- list(mu1,mu2)
Sigma <- list(Sigma1,Sigma2)
shape <- list(shape1,shape2)
pii <- c(0.6,0.4)

Norm.analysis <- smsn.mmix(y, nu=3, mu=mu, Sigma=Sigma, shape=shape, pii = pii,
                           criteria = TRUE, g=2, get.init = FALSE, group = TRUE,
                           family = "Normal")
mix.contour(y,Norm.analysis)

## Normal fit 
Norm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal")
mix.contour(y,Norm.analysis)

## Normal fit with a unique Gamma
Norm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal", uni.Gama = TRUE)
mix.contour(y,Norm.analysis)


## Skew Normal fit
Snorm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                            group = TRUE, family = "Skew.normal")
mix.contour(y,Snorm.analysis)

## t fit
t.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, family = "t")
mix.contour(y,t.analysis)

## Skew t fit
St.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, family = "Skew.t")
mix.contour(y,St.analysis)

## Skew Contaminated Normal fit
Scn.analysis <- smsn.mmix(y, nu=c(0.1,0.1), g=2, get.init = TRUE, criteria = TRUE, 
                          group = TRUE, family = "Skew.cn",error=0.01)
mix.contour(y,Scn.analysis)

## Skew Contaminated Normal fit
Sslash.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                             group = TRUE, family = "Skew.slash", error=0.1)
mix.contour(y,Sslash.analysis)


## End(Not run)