Modeling of count data with an informative time component in the presence of overdispersion
Date
2022
Authors
Owiti, Levi Alfred Orero
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
In real-world count data, several methods have been applied to handle the common problem of overdispersion. However, these methods have not comprehensively considered unique features that may exist in the data. This study sought to address robust statistical modelling of count response data that contains temporal features. The study proposed a Bayesian Negative Binomial model that will handle over dispersion while taking into account the temporal features of the data. Two count data models were compared and extended to incorporate an informative time component. To test the various models, this study conducted simulation studies under specified parameters to examine how the models behave under certain conditions. The data generation mechanism ensured the simulated data had seasonality as is with the real-world data on fire frequency, temperature, and rainfall. Further, the study examined the effect of the additional components on prediction intervals of the simulation studies for the different count models. The introduction of Bayesian techniques into the modeling was intended to create more accurate prediction intervals that take account of the prior distribution of the data. The Bayesian Negative Binomial model was better than the Negative Binomial model in terms of model bias. When validated on real data to confirm its effectiveness, the Bayesian model had better MASE and the prediction intervals enveloped the actual data in the testing dataset of fires in Kenya between the year 2000 and 2018.
Description
Submitted in partial fulfillment of the requirements for the degree of Master of Science in Statistical Science at Strathmore University