loglk_miss {gmmsslm}

Log likelihood function formed on the basis of the missing-label indicator

Description

Log likelihood for partially classified data based on the missing mechanism with the Shanon entropy

Usage

loglk_miss(dat, zm, pi, mu, sigma, xi)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Details

The log-likelihood function formed on the basis of the missing-label indicator can be expressed by

\log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi})=\sum_{j=1}^n\big[ (1-m_j)\log\left\lbrace 1-q(y_j;\theta,\boldsymbol{\xi})\right\rbrace +m_j\log q(y_j;\theta,\boldsymbol{\xi})\big],

where q(y_j;\theta,\boldsymbol{\xi}) is a logistic function of the Shannon entropy e_j(y_j;\theta), and m_j is a missing label indicator.

Value

lk

loglikelihood value