Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model
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 inte...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4542 |
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| author | Xiaoping Shi Xiang-Sheng Wang Augustine Wong |
| author_facet | Xiaoping Shi Xiang-Sheng Wang Augustine Wong |
| author_sort | Xiaoping Shi |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-09T17:40:31Z |
| format | Article |
| id | doaj.art-399bca9f0f964f119f9e681cc7f48942 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:31Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-399bca9f0f964f119f9e681cc7f489422023-11-24T11:35:17ZengMDPI AGMathematics2227-73902022-12-011023454210.3390/math10234542Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed ModelXiaoping Shi0Xiang-Sheng Wang1Augustine Wong2Department of Computer Science, Mathematics, Physics and Statistics, University of British Columbia, Kelowna, BC V1V 1V7, CanadaDepartment of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70503, USADepartment of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, CanadaIn 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.https://www.mdpi.com/2227-7390/10/23/4542Gaussian variational approximationPoisson lognormal mixed modelexponential family modelmaximum likelihood estimationasymptotic distributionKullback–Leibler divergence |
| spellingShingle | Xiaoping Shi Xiang-Sheng Wang Augustine Wong Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model Mathematics Gaussian variational approximation Poisson lognormal mixed model exponential family model maximum likelihood estimation asymptotic distribution Kullback–Leibler divergence |
| title | Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model |
| title_full | Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model |
| title_fullStr | Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model |
| title_full_unstemmed | Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model |
| title_short | Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model |
| title_sort | explicit gaussian variational approximation for the poisson lognormal mixed model |
| topic | Gaussian variational approximation Poisson lognormal mixed model exponential family model maximum likelihood estimation asymptotic distribution Kullback–Leibler divergence |
| url | https://www.mdpi.com/2227-7390/10/23/4542 |
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