Log likelihood for partially classified data based on the missing mechanism with the Shanon entropy
loglk_miss(dat, zm, pi, mu, sigma, xi)loglikelihood value
An \(n\times p\) matrix where each row represents an individual observation
An n-dimensional vector containing the class labels including the missing-label denoted as NA.
A g-dimensional vector for the initial values of the mixing proportions.
A \(p \times g\) matrix for the initial values of the location parameters.
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.
A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.
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.