In two Poisson regressions with differing exposure considerations, which statements are true?

In the context of Poisson regression, overdispersion occurs when the observed variance in the data exceeds the mean, which can compromise the validity of the model. The statement that one model can better handle overdispersion is accurate because there are alternatives to the standard Poisson regression that are specifically designed to address this issue. For instance, negative binomial regression is often used as a modified approach; it includes an extra parameter to account for overdispersion.

When comparing two Poisson regression models with different considerations for exposure, the way each model is specified can influence how well they fit the data. One model might incorporate adjustments or assumptions that allow it to reliably account for overdispersion phenomena, leading to more robust coefficient estimates and error structures.

On the other hand, the statements regarding coefficient estimates being the same, predictor changes affecting estimated means identically, and both models yielding identical results regardless of the method are not inherently true. Different exposure considerations imply different ways that data is modeled, leading to variations in coefficient estimates and their implications. Each model's ability to represent the underlying data generating process can also diverge significantly depending on how exposure is treated, especially when overdispersion is present. Thus, it is crucial to consider these aspects when interpreting the