Log likelihood for partially classified data with ingoring the missing mechanism
loglk_ig(dat, zm, pi, mu, sigma)Log-likelihood 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.
The log-likelihood function for partially classified data with ingoring the missing mechanism can be expressed as $$ \log L_{PC}^{({ig})}(\theta)=\sum_{j=1}^n \left[ (1-m_j)\sum_{i=1}^g z_{ij}\left\lbrace \log\pi_i+\log f_i(y_j;\omega_i)\right\rbrace +m_j\log \left\lbrace \sum_{i=1}^g\pi_i f_i(y_j;\omega_i)\right\rbrace \right], $$ where \(m_j\) is a missing label indicator, \(z_{ij}\) is a zero-one indicator variable defining the known group of origin of each, and \(f_i(y_j;\omega_i)\) is a probability density function with parameters \(\omega_i\).