Which model is better when handling overdispersion in Poisson regressions?

In the context of handling overdispersion in Poisson regressions, hierarchical regression models are particularly well-suited. Overdispersion occurs when the observed variance in the data is greater than what the Poisson model expects, which can lead to biased estimations and misinterpretations of results. Hierarchical models, also known as multilevel models, provide flexibility to account for sources of variability by allowing for random effects.

These models can include both fixed effects, which capture average effects across the dataset, and random effects, which account for variability at different levels of data aggregation. This ability to model data structures with more complexity helps to more accurately reflect the underlying data distribution, accommodating the overdispersion seen in the count data typical of Poisson regression.

In contrast, models not designed to handle the varying levels of exposure or random effects—such as standard regression without varying exposures or standard multiple regression methods—might not address the additional variance effectively. As a result, hierarchical regression models are generally more effective and robust in scenarios where overdispersion is present.