Bayesian estimation and influence diagnostics of generalized partially linear mixed-effects models for longitudinal data |
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Authors: | Xing-De Duan |
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Affiliation: | 1. Department of Statistics, Yunnan University, Kunming 650091, People's Republic of China;2. Institute of Applied Statistics, Chuxiong Normal School, Chuxiong 675000, People's Republic of China |
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Abstract: | This paper develops a Bayesian approach to obtain the joint estimates of unknown parameters, nonparametric functions and random effects in generalized partially linear mixed models (GPLMMs), and presents three case deletion influence measures to identify influential observations based on the φ-divergence, Cook's posterior mean distance and Cook's posterior mode distance of parameters. Fisher's iterative scoring algorithm is developed to evaluate the posterior modes of parameters in GPLMMs. The first-order approximation to Cook's posterior mode distance is presented. The computationally feasible formulae for the φ-divergence diagnostic and Cook's posterior mean distance are given. Several simulation studies and an example are presented to illustrate our proposed methodologies. |
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Keywords: | Bayesian case deletion influence Cook's posterior mean distance Fisher's iterative scoring algorithm generalized partial linear mixed models φ-divergence |
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