[R-sig-ME] making inferences about overdispersion in nbinom glmmabmb

[Highland Statistics Ltd]

>>>
>>> On Wed, Jun 19, 2013 at 5:17 AM, Paul Johnson
>>> <paul.johnson at glasgow.ac.uk> wrote:
>>>> Hi,
>>>>
>>>> I'm fitting negative binomial GLMMs in glmmadmb using  glmmabmb(?, family = "nbinom"). I'm interested in making inferences about the amount of overdispersion in each model, and comparing overdispersion between models.

Paul

What about combining the data for these models...apply one model on all 
data (assuming you don't have too many data sets...i.e. creating too 
many interactions.....and then apply models with one alpha....and a 
model with multiple alphas, where alpha is the alpha in:

Y_i ~ NB(mu,alpha)
E(Y_i) ~ mu_i
var(Y_i) = mu_i + alpha * mu_i^2
log(mu_i) = covariate stuff + random stuff


In our 'Beginner's Guide to GLM and GLMM with R' we show how you can 
model alpha as a function of covariates in NB GLM (this is called 
heterogeneous negative binomial GLMs.....it is using the package 
msme...from Hilbe and Robinson, 2013). The beginner's Guide to GLM and 
GLMM  book also contains JAGS code..and it mentions somewhere how you 
can model the alpha parameter as a function of covariates in JAGS. It 
would actually be very simple to do this.

So...you fit:

Y_i ~ NB(mu,alpha)
E(Y_i) ~ mu_i
var(Y_i) = mu_i + alpha * mu_i^2
log(mu_i) = covariate stuff + random stuff

on one the combined data set...and also

Y_i ~ NB(mu, function(alphas))
E(Y_i) ~ mu_i
var(Y_i) = mu_i + alpha * mu_i^2
log(mu_i) = covariate stuff + random stuff

on the same combined data set. And you compare them. The easiest option 
is to use one alpha per data set....but it can also be something more 
complex (like things in that are done in varExp, varPower, varIdent). 
The only problem that may arise is that too many data sets means too 
many interactions in your covariate stuff.


However..as a word of warning....overdispersion quite often means that 
there is something else going wrong..e.g. zero inflation, non-linear 
patterns, outliers, wrong link function, missing interactions, missing 
covariates, dependency, etc, etc. See Beginner's Guide to GLM and GLMM 
with R for flowcharts and a long list of options to fix the problem. 
Only apply NB GLM(M) if you cannot pinpoint any reason for overdispersion.

Alain



   Joseph Hilbe and Andrew Robinson (2013). msme: Functions and Datasets 
for "Methods of
   Statistical Model Estimation".. R package version 0.4.2.
   http://CRAN.R-project.org/package=msme

A BibTeX entry for LaTeX users is

   @Manual{,
     title = {msme: Functions and Datasets for "Methods of Statistical Model
Estimation".},
     author = {Joseph Hilbe and Andrew Robinson},
     year = {2013},
     note = {R package version 0.4.2},
     url = {http://CRAN.R-project.org/package=msme},
   }








>>>>   The outcome is mosquito count and the different models are different designs of mosquito trap. Each model fit gives an estimate of alpha (the [inverse] overdispersion parameter) and sd_alpha, the standard error of alpha. It's tempting to use the standard error of alpha to construct CIs, test for differences, etc, but I have no idea if this is justified. It seems over-optimistic to assume that sampling error in alpha is approximately normally distributed. Are there conditions (e.g large sample size) where this assumption is justified?
>>>>
>>>> Thanks for your help,
>>>> Paul Johnson
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>>
>>> --
>>> Joshua Wiley
>>> Ph.D. Student, Health Psychology
>>> University of California, Los Angeles
>>> http://joshuawiley.com/
>>> Senior Analyst - Elkhart Group Ltd.
>>> http://elkhartgroup.com
>
>


-- 

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


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