


-------- Original Message --------
Subject: 	Re: Mixed model and negative binomial distribution
Date: 	Fri, 05 Oct 2012 12:37:28 +0200
From: 	Highland Statistics Ltd <highstat@highstat.com>
To: 	r-sig-mixed-models@r-project.org <r-sig-mixed-models@r-project.org>



------------------------------

Message: 2
Date: Fri, 5 Oct 2012 04:32:36 +0000 (UTC)
From: Ben Bolker <bbolker@gmail.com>
To: r-sig-mixed-models@r-project.org
Subject: Re: [R-sig-ME] Mixed model and negative binomial distribution
Message-ID: <loom.20121005T062854-986@post.gmane.org>
Content-Type: text/plain; charset=us-ascii

Seth W. Bigelow <seth@...> writes:

>
> Dear mixed-model brain trust:
>
> I am comparing snag (dead tree) densities 1 year and 5 years after
> silvicultural treatment in forest plots to densities prior to treatment. In
> nlme, my model is
>
> lme(snagnum~treatment, random=(~1|plot), correlation=corExp(form=~year)).
>
> {Treatment is a factor with values of Pre/1-year post/5-year post}. This
> gives reasonable output, but I'm having a niggling doubt that I should be
> using something akin to a negative binomial distribution, since about half
> of the values are zeros (i.e., many plots had no snags prior to treatment,
> and did not gain additional snags as a result of treatment). Can anyone
> suggest an appropriate package and associated syntax for doing this mixed
> model based on an alternative probability density function?

>  Negative binomial would be a reasonable distribution; the other
>answer gives you some methods for doing this.  *However*, incorporating
>both serial correlation and non-Gaussian errors in a model of this form
>is a bit of a nuisance.
>The model you want might be something like

>  snagnum ~ Poisson(lambda)
>  lambda ~ MVN(mean=treatment,Sigma=...)

>where the variance-covariance matrix gives you both some extra-Poisson
>variation (to handle overdispersion) and some correlation between
>observations.  I'm hoping Alain Zuur will pop up shortly to point you
>to a reference in his new book that will tell you how to do this in
>WinBUGS ...



-----------
Yesterday, Alain was on a nice beach in the Caribbean enjoying his wedding. Now he is close to the north pole.


Yes....this sounds MCMC. And code for NB GLMM with AR1 correlation and zero inflation is indeed in the 2012 book.
However...if the zeros are sequential in time then the correlation and zero inflation components may fight
for the same information. And the NB distribution may try to take its share of zeros as well. Better start with
the Poisson version of it....and if a Poisson + correlation + ZIP still shows problems, then consider the NB.
For irregular time series consider a CAR correlation.

As to the implementation..try WinBUGS, OpenBUGS, JAGS....code is nearly the same. I recently downloaded STAN...looks promising too.

You may also want to have a look at "Generalized Additive Mixed Model Analysis via gammSlice" by Pham and Wand.
GAMM is essentially a GLMM.... But I don;t think it can do zero inflation....but perhaps it does NB GLMM. Not sure.



Alain

-- 

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


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: highstat@highstat.com
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