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R2 for Negative Binomial calculated with GLMMADMB

Dear Jens

Our proposed R2 is not 'the' R2 but is also an R2 for mixed models that has several of the useful properties of traditional R2 - actually first proposed by Snijders & Bosker (1994).

Let?s say NB(lambda, theta) with the log link ? the mean = lambda, and the variance = lambda+ lambda^2/theta

The level 1 variance (on the link scale) should be ln(1+1/lambda+1/theta): see the Appendix of our paper, Nakagawa & Schielzeth (2013)

For lambda, it is good to use mean(Y) (Y is the response; counts) and the package should give you the value of theta (also, one should use mean(Y) for Possion models). 

Here the level 1 variance, sigma^2_1= sigma^2_e (additive over-dispersion)+sigma^2_d (distribution specific) = sigma^2_epsilon (residual variance) as in our paper (2013).

But Holger and I are doing some simulation study to check this first before its use, and we think we can extend the proposed R2 to other distributions although we need to test a few things first (we should be ready in one month or so). 

Best wishes,

Shinichi

Shinichi Nakagawa, PhD
(Associate Professor of Behavioural Ecology)
Department of Zoology
University of Otago
340 Great King Street
P. O. Box 56
Dunedin, New Zealand
Tel:  +64-3-479-5046
Fax: +64-3-479-7584
http://sparrow.otago.ac.nz/