Mixt.fit {SenTinMixt}

Fitting for parsimonious mixtures of MSEN or MTIN distributions

Description

Fits, by using EM-based algorithms, parsimonious mixtures of MSEN or MTIN distributions to the given data. Parallel computing is implemented and highly recommended for a faster model fitting. The Bayesian information criterion (BIC) and the integrated completed likelihood (ICL) are used to select the best fitting models according to each information criterion.

Usage

Mixt.fit(
  X,
  k = 1:3,
  init.par = NULL,
  cov.model = "all",
  theta.model = "all",
  density,
  ncores = 1,
  verbose = FALSE,
  ret.all = FALSE
)

Arguments

X

A data matrix with n rows and d columns, being n the number of data points and d the data the dimensionality.

k

An integer or a vector indicating the number of groups of the models to be estimated.

init.par

The initial values for starting the algorithms, as produced by the Mixt.fit.init() function.

cov.model

A character vector indicating the parsimonious structure of the scale matrices. Possible values are: "EII", "VII", "EEI", "VEI", "EVI", "VVI", "EEE", "VEE", "EVE", "EEV", "VVE", "VEV", "EVV", "VVV" or "all". When "all" is used, all of the 14 parsimonious structures are considered.

theta.model

A character vector indicating the parsimonious structure of the tailedness parameters. Possible values are: "E", "V" or "all". When "all" is used, both parsimonious structures are considered.

density

A character indicating the density of the mixture components. Possible values are: "MSEN" or "MTIN".

ncores

A positive integer indicating the number of cores used for running in parallel.

verbose

A logical indicating whether the running output should be displayed.

ret.all

A logical indicating whether to report the results of all the models or only those of the best models according to BIC and ICL.

Value

A list with the following elements:

all.models

The results related to the all the fitted models (only when ret.all=TRUE).

BicWin

The best fitting model according to the BIC.

IclWin

The best fitting model according to the ICL.

Summary

A quick table showing summary results for the best fitting models according to BIC and ICL.

Examples

set.seed(1234)
n <- 50
k <- 2
Pi <- c(0.5, 0.5)
mu <- matrix(c(0, 0, 4, 5), 2, 2)
cov.model <- "EEE"
lambda <- c(0.5, 0.5)
delta <- c(0.7, 0.7)
gamma <- c(2.62, 2.62)
theta <- c(0.1, 0.1)
density <- "MSEN"
data <- rMixt(n, k, Pi, mu, cov.model, lambda, delta, gamma, theta, density)

X <- data$X
nstartR <- 1
init.par <- Mixt.fit.init(X, k, density, nstartR)

theta.model <- "E"
res <- Mixt.fit(X, k, init.par, cov.model, theta.model, density)