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Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model Shi, Xiaoping; Wang, Xiang-Sheng; Wong, Augustine

Abstract

In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms of an intractable integral, estimating the parameters and obtaining inference for the parameters are challenging problems. Some approximation procedures have been proposed in the literature; however, they are computationally intensive. Moreover, the existing studies of approximate parameter inference using the Gaussian variational approximation method are usually restricted to models with only one predictor. In this paper, we consider the Poisson lognormal mixed model with more than one predictor. By extending the Gaussian variational approximation method, we derive explicit forms for the estimators of the parameters and examine their properties, including the asymptotic distributions of the estimators of the parameters. Accurate inference for the parameters is also obtained. A real-life example demonstrates the applicability of the proposed method, and simulation studies illustrate the accuracy of the proposed method.

Item Metadata

Title
Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model
Creator
Shi, Xiaoping; Wang, Xiang-Sheng; Wong, Augustine
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2022-12-01
Description
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms of an intractable integral, estimating the parameters and obtaining inference for the parameters are challenging problems. Some approximation procedures have been proposed in the literature; however, they are computationally intensive. Moreover, the existing studies of approximate parameter inference using the Gaussian variational approximation method are usually restricted to models with only one predictor. In this paper, we consider the Poisson lognormal mixed model with more than one predictor. By extending the Gaussian variational approximation method, we derive explicit forms for the estimators of the parameters and examine their properties, including the asymptotic distributions of the estimators of the parameters. Accurate inference for the parameters is also obtained. A real-life example demonstrates the applicability of the proposed method, and simulation studies illustrate the accuracy of the proposed method.
Subject
Gaussian variational approximation; Poisson lognormal mixed model; exponential family model; maximum likelihood estimation; asymptotic distribution; Kullback–Leibler divergence
Genre
Article
Type
Text
Language
eng
Date Available
2023-11-16
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0437675
URI
http://hdl.handle.net/2429/86532
Affiliation
Science, Irving K. Barber Faculty of (Okanagan); Non UBC; Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Citation
Mathematics 10 (23): 4542 (2022)
Publisher DOI
10.3390/math10234542
Peer Review Status
Reviewed
Scholarly Level
Faculty
Rights URI
https://creativecommons.org/licenses/by/4.0/
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DSpace

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CC BY 4.0