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Hello,
Is mcmc now capable of estimating multilevel extra-Poisson variation and/or Negative Binomial models in mlwin's version 3? All the relevant references I have seen seem to suggest that it is not. As late as february 17 of this year, I see references suggesting that the only way to estimate dependent variables with multilevel extra-poisson variation or negative binomial models in mlwin is to use the (r)IGLS protocols. Is that correct or has that changed in the last month or so since mlwin 3 came out. Thank you.

Kelvyn and I have spent some time checking these models against published examples and we find broad agreement with regard to the parameter estimates, and their standard errors both of the fixed and random parts. However we are less certain about the DIC because it is taking account of estimating the dispersion parameter via MCMC in calculating pD (effective degrees of freedom). Other implementations appear to treat the dispersion parameter as a single parameter. We will try to find out more.

You can fit extra-Poisson variation by adding an additional level above level-1 using the the level-1 identifier and then adding a random effect for it. An example of this for Binomial models can be seen in W. J. Browne, S. V. Subramanian, K. Jones and H. Goldstein (2005) Variance partitioning in multilevel logistic models that exhibit overdispersion, JRSS, A Vol. 168(3),599-613 (https://www.jstor.org/stable/3559841), however the same approach can be applied to Poisson models.

Hello Chris,
Thank you very much for the prompt reply. I located the Browne et al. article and have been able to develop a model in mcmc for an overdispersion poisson regression. Thanks a great deal.