loglk_ig {gmmsslm}R Documentation

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×pn\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×gp \times g matrix for the initial values of the location parameters.

sigma

A p×pp\times p covariance matrix,or a list of g covariance matrices with dimension p×p×gp\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p×pp\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

logLPC(ig)(θ)=j=1n[(1mj)i=1gzij{logπi+logfi(yj;ωi)}+mjlog{i=1gπifi(yj;ωi)}], \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 mjm_j is a missing label indicator, zijz_{ij} is a zero-one indicator variable defining the known group of origin of each, and fi(yj;ωi)f_i(y_j;\omega_i) is a probability density function with parameters ωi\omega_i.

Value

lk

Log-likelihood value.


[Package gmmsslm version 1.1.5 Index]