loglk_miss: Log likelihood function formed on the basis of the...

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

Log likelihood function formed on the basis of the missing-label indicator

Description

Log likelihood for partially classified data based on the missing mechanism with the Shanon entropy

Usage

loglk_miss(dat, zm, pi, mu, sigma, ncov = 2, 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 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.
xi	A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Details

The log-likelihood function formed on the basis of the missing-label indicator can be expressed by

\log L_{PC}^{({miss})}(θ,\boldsymbol{ξ})=∑_{j=1}^n\big[ (1-m_j)\log≤ft\lbrace 1-q(y_j;θ,\boldsymbol{ξ})\right\rbrace +m_j\log q(y_j;θ,\boldsymbol{ξ})\big],

where q(y_j;θ,\boldsymbol{ξ}) is a logistic function of the Shannon entropy e_j(y_j;θ), and m_j is a missing label indicator.

Value

lk	loglikelihood value

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