loglk_full {gmmsslm}

Full log-likelihood function

Description

Full log-likelihood function with both terms of ignoring and missing

Usage

loglk_full(dat, zm, pi, mu, sigma, 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,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.

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Details

The full log-likelihood function can be expressed as

\log L_{PC}^{({full})}(\boldsymbol{\Psi})=\log L_{PC}^{({ig})}(\theta)+\log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi}),

where\log L_{PC}^{({ig})}(\theta)is the log likelihood function formed ignoring the missing in the label of the unclassified features, and \log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi}) is the log likelihood function formed on the basis of the missing-label indicator.

Value

lk

Log-likelihood value