Ben, sorry but I am bit confused by your answer. If I understand correctly, the approach you would recommend is to calculate the dispersion parameter on the binomial model and if there is overdispersion compare models with different ways to deal with it (e.g observation-level random effects and beta-binomial) to the binomial one to find out which ones fits the data better. Is that correct? And so there would be no point in calculating the dispersion parameter for the OLRE and beta-binomial model and see how much it goes down? Cheers,
Correct. Overdispersion/underdispersion is only relevant for distributions in which the variance is determined by the mean. Like the Poisson: mean(Y) = var(Y)? and the binomial: E(Y) = N * pi and var(Y) = Pi * N * (1 - Pi). No need to check for overdispersion for the normal, Gamma, inverse Gaussian, beta-binomial, and beta distributions. These distributions have an extra parameter (like the variance in the normal distribution) in the variance term. Having said that...I am still confused why the Negative binomial GLM can be overdispersed. I guess that is because the NB GLM is not a real GLM and iterates between two algorithms (when doing frequentist analysis). I guess (again) it is more about whether the functional form of the NB variance is correct...or not. Instead of using a dispersion statistic based on Pearson residuals (coming from models with fancy random effects) it is perhaps better to simulate data from your model and compare the variation in the simulated data with the variation in the observed data. Or do what Ben Bolker suggested a few days/weeks ago...simulate data and compare the corresponding residuals with the original residuals. Alain
Dr. Alain F. Zuur Highland Statistics Ltd. 9 St Clair Wynd AB41 6DZ Newburgh, UK Email: highstat at highstat.com URL: www.highstat.com And: NIOZ Royal Netherlands Institute for Sea Research, Department of Coastal Systems, and Utrecht University, P.O. Box 59, 1790 AB Den Burg, Texel, The Netherlands Author of: 1. Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA. (2017). 2. Beginner's Guide to Zero-Inflated Models with R (2016). 3. Beginner's Guide to Data Exploration and Visualisation with R (2015). 4. Beginner's Guide to GAMM with R (2014). 5. Beginner's Guide to GLM and GLMM with R (2013). 6. Beginner's Guide to GAM with R (2012). 7. Zero Inflated Models and GLMM with R (2012). 8. A Beginner's Guide to R (2009). 9. Mixed effects models and extensions in ecology with R (2009). 10. Analysing Ecological Data (2007).