loglk_ig function

Log likelihood for partially classified data with ingoring the missing mechanism

loglk_ig(dat, zm, pi, mu, sigma, ncov = 2)

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.

Returns

• lk: Log-likelihood value.

Details

The log-likelihood function for partially classified data with ingoring the missing mechanism can be expressed as

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 $\omega_i$.