Which of the following models is best for overdispersed count data?

The best model for overdispersed count data is the negative binomial model. Overdispersion occurs when the variance of the count data is greater than the mean, which violates one of the key assumptions of the Poisson regression model. The negative binomial model is specifically designed to handle this situation by introducing an additional parameter that captures the overdispersion, allowing it to model the data more accurately.

In contrast, Poisson regression typically assumes that the mean and variance of the counts are equal, thus it becomes less effective when the variance exceeds the mean, leading to underestimated standard errors and potentially misleading inferences.

Linear regression is not suitable for count data as it assumes a continuous response variable and does not inherently handle non-negative integers effectively, which are typical for count data.

Logistic regression is meant for binary outcomes, not count data. It models the probability of a binary event rather than the count of occurrences.

Thus, the negative binomial model provides a robust framework for analyzing overdispersed count data, making it the appropriate choice in this scenario.