loglk_ig: Log likelihood for partially classified data with ingoring...

In EMMIXSSL: Semi-Supervised Gaussian Mixture Model with a Missing-Data Mechanism

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, 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.

Details

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

\log L_{PC}^{({ig})}(θ)=∑_{j=1}^n ≤ft[ (1-m_j)∑_{i=1}^g z_{ij}≤ft\lbrace \logπ_i+\log f_i(y_j;ω_i)\right\rbrace +m_j\log ≤ft\lbrace ∑_{i=1}^gπ_i f_i(y_j;ω_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;ω_i) is a probability density function with parameters ω_i.

Value

lk	Log-likelihood value.

EMMIXSSL documentation built on Oct. 18, 2022, 5:08 p.m.