Bayesian Multilevel Models for Count Data
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Date
2021-08-29
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Publisher
Nigerian Society of Physical Sciences
Abstract
The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, a Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicates that all the observations are good. Also, all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further
analysis. Seven multi-level models were fitted and the Geometric model outperformed other models.
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Keywords
Count Data, Insurance, Dispersion, Multilevel Models