loglk_miss function

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

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

loglk_miss(dat, zm, pi, mu, sigma, ncov = 2, 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 if ncov=1, or a list of g covariance matrices with dimension $p\times p \times g$ if ncov=2.
• ncov: Options of structure of sigma matrix; the default value is 2; ncov = 1 for a common covariance matrix; ncov = 2 for the unequal covariance/scale matrices.
• xi: A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Returns

• lk: loglikelihood value

Details

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

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.