Dear Sir/Madam,
Can you help me in the selection of a count data model? I have one dependent and 10 independent variables. Among 10 independent variables, 6 variables have variance greater than mean, which is a case of overdispersion. But remaining 4 independent variables have mean greater than variance, which is a case of underdispersion. In this case, can we use the Negative Binomial model? Or should I try the Poisson model? Please give your suggestion.
Thanking you.
The distribution of the independent variables is irrelevant.
A simple wayto check the (over-)dispersion is to fit a quasi-Poisson model that estimates a dispersion parameter. If this is considerably larger than 1, your data are overdispersed. Given the data are from a pure Poisson-process (no overdispersion), the product of the dispersion and v, the residual degrees of freedom of the model, is approximately chi²-distributed with v degrees of freedom.
I agree with Jochen Wilhelm here. This decision should not be based on the IV's but the distribution of the DV. Generally, the negative binomial is preferred over Poisson when you have a lot of zeros in the distribution. The Poisson distribution/method 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.
I agree with Jochen Wilhelm and Richard J Stringer and may get some mere information in this link as well
https://gamlj.github.io/glmmixed_example2.html
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