Classical vs Bayesian Approaches to Modeling Overdispersed Count Data: Case Study of Tomato Leaf Curl
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Authors
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Briefully Kharnongrum
North Eastern Hill University, Shillong
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Kimthianngak
North Eastern Hill University, Shillong
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Nidahamteinsar Papang
North Eastern Hill University, Shillong
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Priti Pradhan
North Eastern Hill University, Shillong
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Biwash Gurung
G.D. Goenka University, Gurugram
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Ramnunpuia
North Eastern Hill University, Shillong
Keywords:
Count data models; Poisson model; Negative Binomial model; Classical estimation; Bayesian estimation; Markov Chain Monte Carlo (MCMC); Over dispersion; Tomato Leaf Curl (TLC); Leave-One-Out Cross-Validation (LOO-CV).Abstract
Count data consisting of non-negative integer values arising from counting events require specific statistical methods for analysis. This study compares
Classical and Bayesian approaches for estimating count regression models using Tomato Leaf Curl (TLC) data consisting of 809 observations.
It is found that the simple Poisson regression model performs poorly due to over dispersion, where the variance greatly exceeds the mean. The
Negative Binomial model, which handles over dispersion, provides a good fit to the data under both approaches. Both frameworks produced nearly
the same parameter estimates confirming the consistency of the results. However, the Bayesian framework provided a full posterior distributions
enables posterior predictive checks supports Leave-One-Out Cross-Validation (LOO-CV) model comparison, providing a richer inferential tool for
uncertainty. Zero-inflated Poisson model is also used for count data modelling but it is not applicable here due to the absence of zero counts in the
data. Overall, the Bayesian framework provides a broader view of uncertainty around the estimates.
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