[R-sig-ME] Mixed mutlinomial regression for count data with overdisperion & zero-inflation

[Stéphanie Périquet]

Dear list members,



First sorry for this very long first post …


I am looking for advises to fit a mixed multinomial regression on count
data that are overdispersed and zero-inflated. My question is to evaluate
the effect of season and moonlight on diet composition of bat-eared foxes.
My dataset is composed of 14 possible prey item, 20 individual foxes
observed, 4 seasons and a moon illumination index ranging from 0 to 1 by
0.1 implements (considered as a continuous variable even if takes only 11
values). For each unique combination of individual*season*moon, I thus has
14 lines, one for the count of each prey item.


>From what I gathered, it would be possible to use a standard glmm model of
the following form to answer my question (ie a multinomial regression):

glmer(count~item+item:season+item:moon+offset(logduration)+(1+indiv)+(1|obs)+
(1|id), family=poisson)

where count is the number of prey of a given type recorded eaten;

item is the prey type;

logduration is the log(total time observed for a given combination of
individual*season*moon);

obs is a unique id for each combination of individual*season*moon, so each
obs value regroups 14 lines (one for each prey item) with the same
individual*season*moon;

id is a unique id for each line to account for overdispersion (as
quasi-poisson or negative binomial distributions are not implemented in
lme4, Elston et al. 2001).



However, they are a lot of zeros in my data i.e. lot of prey items has
never been observed being eaten for mane combinations of
individual*season*moon.

Following Ben Bolker wiki (http://glmm.wikidot.com/faq) I summarize that I
should use of the following methods to answer my question


   - ·      glmmADMB, with family=nbinom
   - ·      MCMCglmm, with family=zipoisson
   - ·      "expectation-maximization (EM) algorithm" in lme4



Here come the questions:

1.               1. Is it correct to assume that I could use the same model
structure (count~item+item:season+item:moon+offset(logduration)+(1+indiv)+(1|obs))
in glmmADMB or MCMCglmm to answer my question ?

2.   I then wouldn't need the (1|id) to correct for overdispersion as both
methods would already account for it, correct?

3.   I am totally new to MCMCglmm, so would it be correct to define the
priors and model as follows (inspired from Ben Bolker et al. 2012 Owls
example: a zero-inflated, generalized linear mixed model for count data
2012)

# define the fixed effects

fixef2 <- count~trait-1+  at.level(trait,1):logduration  +
at.level(trait,1):(item*season) +  at.level(trait,1):(item*moon)

#Set up a variable that will pick out the offset (duration) parameter,
which will be in 3rd position

offvec <- c(1,1,2,rep(1,))

#define the priors with 2 random factors and log(duration) as offset

prior2 <- list(R=list(V=diag(c(1,1)),nu=0.002,fix=2),

G=list(G1=list(V=diag(c(1,1e-6)),nu=0.002,fix=2),
G2=list(V=diag(c(1,1e-6)),nu=0.002,fix=2)),

list(B=list(mu=c(0,1)[offvec],

V=diag(c(1e6,1e-6)[offvec]))))

# define the model

mfit1 <- MCMCglmm(fixef2, rcov=~idh(trait):units,
random=~idh(trait):indiv+idh(trait):obs, prior=prior2,data=diet,
family="zipoisson",verbose=FALSE))

4.     4.  If I were to use the EM algorithm method, how should the results
be interpreted?



Thanks in advance for your help!

Stephanie

-- 
*Stéphanie PERIQUET (PhD) * - Bat-eared Fox Research Project
*Dept of Zoology & Entomology*
*University of the Free State, Qwaqwa Campus*
*Cell: +27 79 570 2683*
ResearchGate profile
<https://www.researchgate.net/profile/Stephanie_Periquet>


Kalahari bat-eared foxes on Twitter <https://twitter.com/kal_batearedfox>

	[[alternative HTML version deleted]]