What does the term 'overdispersion' in a count model imply?

Overdispersion in a count model refers specifically to the phenomenon where the variance of the count data exceeds its mean. This is particularly relevant when dealing with models such as Poisson regression, which typically assumes that the mean and variance are equal. When the variance is significantly larger than the mean, it indicates that the model's assumptions about the distribution of the data may not hold true.

In practical terms, overdispersion suggests that there may be unaccounted factors or variability in the data that are not captured by the model. It's important to recognize overdispersion because if it is present, using a standard model like Poisson regression could lead to underestimated standard errors, resulting in less reliable statistical inferences.

Thus, recognizing that the variance exceeds the mean is crucial for properly addressing and modeling the underlying data structure, potentially leading to the use of alternative models such as the Negative Binomial regression, which can accommodate this extra variability.