rglmmtmbglmm

GLMM with quasi-Poisson distribution


I'm interested in fitting a model using a GLMM with quasi-Poisson distribution (my data is event occurrence and there was an overdispersion). I'm looking at the different options available, but I feel confused as to which one to choose.

So far, what I encountered are the following:

  1. glmmPQL: family = quasipoisson. Used when a) the data is not normally distributed, b) the Poisson of mean >= 5, and c) overdispersion Bolker et al., 2009.

  2. glmmTMB: family = nbinom1 @D A Wells, 20017

  3. glmer with quasi_table: family = poisson, then use quasi_table function provided by @Ben Bolker, 2021.

What are the differences in these three methods, when to use one and when not to, or are there any other ways to go about it?

Thank you so much in advance.


Solution

  • All three of these methods use a GLMM estimation algorithm to estimate a model with the mean-variance relationship mean = phi*var, phi>0, but they do three different things:

    I would expect all three of these methods to give fairly similar, but not identical results: if they gave qualitatively different answers I would worry about the sensitivity of my model (except in the case where effective sample size per group was very low, where I would steer away from PQL). I might default to the glmmTMB/nbinom1 approach just because you'd be on slightly firmer theoretical ground (i.e. this is a proper MLE, not a quasi-likelihood estimate).


    Breslow, N. E. 2004. “Whither PQL?” In Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data, edited by Danyu Y. Lin and P. J. Heagerty, 1–22. Springer. http://www.bepress.com/uwbiostat/paper192/.

    Hardin, James William, and Joseph Hilbe. 2007. Generalized Linear Models and Extensions. Stata Press.