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On Adaptive Gauss-Hermite Quadrature for Estimation in GLMM’s

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Statistics and Data Science (RSSDS 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1150))

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Abstract

Adaptive Gauss-Hermite quadrature is used for the computation of the log-likelihood function for generalized linear mixed models. The basic first step in this method is to multiply and divide the integrand of interest by a carefully chosen probability density function. The same first step is used for the computation of this log-likelihood function using simulations that employ importance sampling. We compare these two methods by considering in detail a single cluster from a well-known teratology data set that is modelled using a logistic regression with random intercept. We show that while importance sampling fails for this computation, adaptive Gauss-Hermite quadrature does not. We derive a new upper bound on the error of approximation of adaptive Gauss-Hermite quadrature. Using this new upper bound, we show that the feature of this problem that makes importance sampling fail is useful in disclosing why adaptive Gauss-Hermite quadrature succeeds.

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Acknowledgements

This work was supported by an Australian Government Research Training Program Scholarship.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia

    Paul Kabaila & Nishika Ranathunga

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  1. Paul Kabaila
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  2. Nishika Ranathunga
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Correspondence to Paul Kabaila .

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Editors and Affiliations

  1. La Trobe University, Bundoora, VIC, Australia

    Hien Nguyen

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Kabaila, P., Ranathunga, N. (2019). On Adaptive Gauss-Hermite Quadrature for Estimation in GLMM’s. In: Nguyen, H. (eds) Statistics and Data Science. RSSDS 2019. Communications in Computer and Information Science, vol 1150. Springer, Singapore. https://doi.org/10.1007/978-981-15-1960-4_9

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  • DOI: https://doi.org/10.1007/978-981-15-1960-4_9

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-1959-8

  • Online ISBN: 978-981-15-1960-4

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