loglk_ig {gmmsslm}

Log likelihood for partially classified data with ingoring the missing mechanism

Description

Log likelihood for partially classified data with ingoring the missing mechanism

Usage

loglk_ig(dat, zm, pi, mu, sigma)

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.

Details

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.

Value

lk

Log-likelihood value.