A Bayesian bivariate response mixedeffects model for zero-inflated count data containing large outliers

Oppen, Yulan van (2020) A Bayesian bivariate response mixedeffects model for zero-inflated count data containing large outliers. Master's Thesis / Essay, Mathematics.

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Abstract

This thesis proposes a bivariate response mixed-effects approach with a Bayesian specification for modeling zero-inflated, two-dimensional count data containing large outliers. A zero-inflated bivariate geometric distribution is derived and reparameterized in terms of its marginal medians, which can subsequently be modeled directly using both fixed and random effects. This configuration allows increasing robustness with respect to large observations as the zero-inflation fraction grows to 0.5. The model’s development is motivated by an observational study on green hawker populations in the northern Netherlands. The covariates include the host plant’s presence and abiotic factors relating to the water condition. Two competing ways of measuring population sizes are compared in a bivariate response setting to simultaneously compare the covariates’ effects on the marginal sizes as well as their correlation. Doing so provides a new perspective on their (dis)similarity given external factors. The relatively small sample size, the inclusion of repeated measurements, and the presence of large outliers incite the need for a Bayesian mixed-effects model that is comparatively insensitive to excessively high counts. An extension of JAGS with a custom distribution module to estimate the posterior parameter distribution using a Metropolis-Hastings MCMC algorithm is implemented and tested. With it, the model’s validity and practical use are demonstrated in a simulation study.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Grzegorczyk, M.A. and Krijnen, W.P.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	06 Nov 2020 10:57
Last Modified:	06 Nov 2020 10:57
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/23575

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