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What is the best tool-box for model selection when working with nested count data?

Is AICc appropriate for comparing Poisson and negative binomial mixed models? Is there anything special to the residual analysis?

For example, I want to compare

pfitc_c = glmer(data=cc, tubes ~ status + (1|site/plant/flower), 
    family = "poisson")

with

nb_c_disp = glmer(data=cc, tubes ~ status + (1|site/plant/flower), 
     family = negative.binomial(theta = 1.012206))
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    $\begingroup$ can you be a little more specific? Do you want to compare models with different fixed effects, different random effects, or both? glmm.wikidot.com/faq describes a variety of the issues with using information theoretic approaches with mixed models. $\endgroup$ – Ben Bolker Dec 14 '15 at 21:49
  • $\begingroup$ Thanks for the link @Ben Bolker. I am intrested in choosing between these two models: pfitc_c = glmer(data=cc, tubes ~ status + (1|site/plant/flower), family = "poisson") and nb_c_disp = glmer(data=cc, tubes ~ status + (1|site/plant/flower), family = negative.binomial(theta = 1.012206)) I am not sure of the best way to do so. $\endgroup$ – JKO Dec 14 '15 at 21:51

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