Mixture Classification Quasi-Likelihood Approach Sample Clauses

Mixture Classification Quasi-Likelihood Approach. In the absence of a likelihood function, we consider replacing the feature-, class- and subject-specific log-likelihood function, logfjg(yij; θg), with an artificial-likelihood based objective function for assessing the model fit of the class-specific ▇▇▇ ▇▇ (yi; θ). In particular, we draw from Pan’s(2001)[60] quasi-likelihood under the independence model criteria (QIC) and consider replacing logfjg(yij; θg) with a feature-, class-, and subject-specific quasi-likelihood under the independence model. The feature- and class-specific quasi-likelihood under the working independence assumption is defined as Qjg (βˆjg (R) , ϕjg) = ∑ ∑ mij Qjg (βˆjg (R) , ϕjg; (Yik, Xik)) , where ϕjg denotes the dispersion parameter, R denotes the working correlation of interest, and the quasi-likelihood contribution of the kth observation on the ith subject evaluated at the regression parameters β is defined as Qjg (βˆjg (R) , ϕjg; (Yik, Xik)) = Qgijk/ϕjg. Under the independence model, Qgijk takes a closed-form for many standard distri- butions. In particular, note that for Normal: Qgijk = − 2 τig(yi; ψ) (yijk − µijk) Poisson: Qgijk = τig(yi; ψ) (yijklog (µijk) − µijk) Binary: Qgijk = τig(yi; ψ) [yijklog(pijk + (1 − yijk) log (1 − pijk)]. In the above equations, µijk refers to the mean or predicted value of yijk and pijk refers to the probability that a binary feature variable yijk attains the value 1. When Pan[60] developed QIC, he initially assumed that the dispersion parameter ϕ was known; however, in practice ϕ is typically unknown and estimated using the ▇▇▇▇▇▇▇ ▇▇▇-square residuals. In such situations, one may consider using information criteria based on the extended quasi-likelihood [82]. In the current context, we propose using the following objective function based on the extended quasi-likelihood function [59] as a measure of model fit: = Q + + (βˆjg (R) , ϕjg) = ∑ ∑ mij Qjg (βˆjg (R) , ϕjg; (Yik, Xik)) − (ϕˆjg ) , where ∑n ∑mij (y − µ )2 ϕˆ = n − p where p denotes the number of parameters in the model. Note that, by using an objective function based on the extended quasi-likelihood function, models are given an increased penalty for larger dispersion parameters. Here, we propose using the mixture classification extended quasi-likelihood to distinguish between multiple roots. More specifically, for a given number of latent classes, the root that maximizes the mixture classification extended quasi-likelihood is favored. Once the best root is selected for a given number of latent cl...
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