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Dispersion parameter in glmmadmb and model selection

3 messages · Zahwa Al Ayyash (Student), Paul Johnson

Original
Zahwa Al Ayyash (Student)
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Dear list,

1) I am fitting a negative binomial and zero-inflated negative binomial models using glmmadmb. I am getting a very high dispersion parameter:

Negative binomial dispersion parameter: 403.43 (std. err.: 0.39244)

I am aware that my data might be over-dispersed, but what does the very high value indicate? Could there be an error in estimation?
Also, surprisingly, I am using two different data sets to estimate the neg. bin. models, and I am getting the same value (403.43) but with different std. errors. Any clues?

2) My second question is rather general; What could be the best ways to compare glmmadmb models and select the best amongst Poisson, Neg. Bin, Zero-inflated Poisson, Zero-inflated Neg. Bin., Hurdle Poisson and Hurdle Neg. Bin?

PS: My models employ a random effect to capture correlation among individuals (IDs).

Many thanks to your help,
Zahwa Al-Ayyash
Paul Johnson
# 
Hi Zahwa, 

In answer to the first question, the dispersion parameter, alpha, is inversely proportional to the amount of additional variance due to overdispersion...

Y ~ Poisson(lambda)
Var(Y) = lambda

Y ~ NB(lambda, alpha)
Var(Y) = lambda + lambda^2 / alpha

...so your error distribution appears not to be very overdispersed. In fact, if probably isn?t overdispersed at all, as I think glmmadmb puts an upper limit on the alpha estimate of exp(6) = 403.43, presumably to prevent it wondering off towards infinity when there is no evidence of overdispersion. This would explain why you get the same estimate from different (non-overdispersed) data sets. Try simulating some Poisson data and fitting an NB model (see code below). 

I guess for low lambda, e.g. around 10, lambda^2 / 403 will be reasonable approximation of zero addition variance, but not for higher lambda, e.g. > 100. Not sure how glmmadmb copes with that, or if it?s possible to raise this ceiling.

Best wishes,
Paul
Call:
glmmadmb(formula = y ~ (1 | dummy.group), family = "nbinom2")

AIC: 422.6 

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)    1.520      0.047    32.3   <2e-16 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Number of observations: total=100, dummy.group=10 
Random effect variance(s):
Group=dummy.group
             Variance    StdDev
(Intercept) 2.696e-08 0.0001642

Negative binomial dispersion parameter: 403.43 (std. err.: 0.72454)

Log-likelihood: -208.295
[1] 403.43
[1] 6.000003
On 10 Mar 2015, at 01:39, Zahwa Al Ayyash (Student) <zsa11 at mail.aub.edu> wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Zahwa Al Ayyash (Student)
    

    

      
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Thanks a lot, things are much clearer now. My lambda is in fact around 2, so the 403 value of alpha seems to prove that my data is not over-dispersed.

Zahwa