Negative binomial multilevel model

[Verena85]

Hi

We are using a two-level negative binomial model in MLwiN, because our dependent variable consists of count data, is right skewed and overdispersed (frequency of antisocial behavior of students nested in classes). There are two things about this model, we don't understand:

First: Why is the level 1 variance not displayed? If we use the program R, there is a level 1 variance.

Second: We could add an additional parameter for overdispersion: "Distributional assumptions, extra -ve binomial". When and why is it necessary to take this parameter into account? Does the negative binomial model not already control for overdispersion?

Thanks for your help
Verena

[ChrisCharlton]

The parameter being missing from the equations window was an oversight and will be displayed in future versions of MLwiN. In the mean time you can obtain the estimate for this by either using the "store model results" functionality or by looking at "level 1" section under Model->Estimate tables.

Professor Kelvyn Jones, who spoke about negative binomial models at a recent workshop, has provided the attached slides to explain the different parameters associated with these models.

[Verena85]

Thank you very much, i'll try it this way.

Verena

[ChrisCharlton]

Professor Harvey Goldstein has provided the following additional information in relation to your questions:

1) The level 1 variance is pi + pi^2/v.

2) Strictly speaking the extra negative binomial model is, like the extra Poisson just a way of allowing for a variance that is more complex than that given by the variance associated with negative binomial. i.e. we have (compared to the Poisson) both an additive extra variance (that associated with the negative binomial distribution) and an additional additive term that allows even more flexibility for describing the variance. In practice most people would usually stay with either an extra Poisson or the negative binomial.