I am working with a panel data set of purchases over week.
Therefore, a poission distrubition is suitable.
When there is overdispersion, a negative binomal regression is adviced.
I am combing these distrubition with a random intecept model with multiple predictors (glmer). When i test for overdispersion, there is no need to use negative binomal
However, when i look at the assumptions of poission it assumes indepence of datapoints, which is not the case in panel data.
Is this assumption also implemented within negative binomnal? Or can I just use poission and ignore the indepence assumption as i have panel data?
The choice between Poisson and Negative Binomial models depends on the distribution of the data. Generally, the Negative Binomial model is preferred over Poisson when there are a lot of zeros in the distribution. The Poisson distribution does not account for this and underestimates them due to a violation of the assumptions. As such, the Poisson model will also deflate the standard errors and lead to incorrect z-tests and p-values.
When mean and variance are equal then poisson regression can be used. In case of overdeflation in data, use of negative binomial regression is preffered in case of count data.
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